Load relevant packages

library(dplyr)
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## 
##     filter, lag
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## 
##     intersect, setdiff, setequal, union
library(tidyverse)
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library(lavaan)
## Warning: package 'lavaan' was built under R version 4.2.3
## This is lavaan 0.6-16
## lavaan is FREE software! Please report any bugs.
library(remotes)
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library(foreign)
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library(semPlot)
## Warning: package 'semPlot' was built under R version 4.2.3

Import data

#Data import#
imported_data <- read.csv("C:/Users/alfre/Documents/Master´s Thesis/Data/All Countries Complete corrected electricity data wide imputed.csv", header  = TRUE, sep = ";")

data <- imported_data

Wrangling/renaming

#Exclude participants from Austria, Italy & Turkey
data <- data %>%
  filter(Country <= 3)

data <- data %>%
  mutate(initial_survey_age = gsub(",", ".", initial_survey_age),
         initial_survey_age = as.numeric(initial_survey_age)) 
data <- data %>%
  mutate(inital_survey_age = round(initial_survey_age))

data <- data %>%
  mutate(initial_survey_socialstatus = gsub(",", ".", initial_survey_socialstatus),
         initial_survey_socialstatus = as.numeric(initial_survey_socialstatus)) 
data <- data %>%
  mutate(initial_survey_socialstatus = round(initial_survey_socialstatus))

data <- data %>%
  mutate(T1_attitude = gsub(",", ".", T1_attitude),
         T1_attitude = as.numeric(T1_attitude)) 
data <- data %>%
  mutate(T1_attitude = round(T1_attitude))

data <- data %>%
  mutate(T2_attitude = gsub(",", ".", T2_attitude),
         T2_attitude = as.numeric(T2_attitude)) 
data <- data %>%
  mutate(T2_attitude = round(T2_attitude))

data <- data %>%
  mutate(T3_attitude = gsub(",", ".", T3_attitude),
         T3_attitude = as.numeric(T3_attitude)) 
data <- data %>%
  mutate(T3_attitude = round(T3_attitude))

data <- data %>%
  mutate(T4_attitude = gsub(",", ".", T4_attitude),
         T4_attitude = as.numeric(T4_attitude)) 
data <- data %>%
  mutate(T4_attitude = round(T4_attitude))

data <- data %>%
  mutate(T5_attitude = gsub(",", ".", T5_attitude),
         T5_attitude = as.numeric(T5_attitude)) 
data <- data %>%
  mutate(T5_attitude = round(T5_attitude))

data <- data %>%
  mutate(T1_Inorms = gsub(",", ".", T1_Inorms),
         T1_Inorms = as.numeric(T1_Inorms)) 
data <- data %>%
  mutate(T1_Inorms = round(T1_Inorms))

data <- data %>%
  mutate(T2_Inorms = gsub(",", ".", T2_Inorms),
         T2_Inorms = as.numeric(T2_Inorms)) 
data <- data %>%
  mutate(T2_Inorms = round(T2_Inorms))

data <- data %>%
  mutate(T3_Inorms = gsub(",", ".", T3_Inorms),
         T3_Inorms = as.numeric(T3_Inorms)) 
data <- data %>%
  mutate(T3_Inorms = round(T3_Inorms))

data <- data %>%
  mutate(T4_Inorms = gsub(",", ".", T4_Inorms),
         T4_Inorms = as.numeric(T4_Inorms)) 
data <- data %>%
  mutate(T4_Inorms = round(T4_Inorms))

data <- data %>%
  mutate(T5_Inorms = gsub(",", ".", T5_Inorms),
         T5_Inorms = as.numeric(T5_Inorms)) 
data <- data %>%
  mutate(T5_Inorms = round(T5_Inorms))

data <- data %>%
  mutate(T1_dnorms = gsub(",", ".", T1_dnorms),
         T1_dnorms = as.numeric(T1_dnorms)) 
data <- data %>%
  mutate(T1_dnorms = round(T1_dnorms))

data <- data %>%
  mutate(T2_dnorms = gsub(",", ".", T2_dnorms),
         T2_dnorms = as.numeric(T2_dnorms)) 
data <- data %>%
  mutate(T2_dnorms = round(T2_dnorms))

data <- data %>%
  mutate(T3_dnorms = gsub(",", ".", T3_dnorms),
         T3_dnorms = as.numeric(T3_dnorms)) 
data <- data %>%
  mutate(T3_dnorms = round(T3_dnorms))

data <- data %>%
  mutate(T4_dnorms = gsub(",", ".", T4_dnorms),
         T4_dnorms = as.numeric(T4_dnorms)) 
data <- data %>%
  mutate(T4_dnorms = round(T4_dnorms))

data <- data %>%
  mutate(T5_dnorms = gsub(",", ".", T5_dnorms),
         T5_dnorms = as.numeric(T5_dnorms)) 
data <- data %>%
  mutate(T5_dnorms = round(T5_dnorms))

data <- data %>%
  mutate(T1_pbc1 = gsub(",", ".", T1_pbc1),
         T1_pbc1 = as.numeric(T1_pbc1)) 
data <- data %>%
  mutate(T1_pbc1 = round(T1_pbc1))

data <- data %>%
  mutate(T2_pbc1 = gsub(",", ".", T2_pbc1),
         T2_pbc1 = as.numeric(T2_pbc1)) 
data <- data %>%
  mutate(T2_pbc1 = round(T2_pbc1))

data <- data %>%
  mutate(T3_pbc1 = gsub(",", ".", T3_pbc1),
         T3_pbc1 = as.numeric(T3_pbc1)) 
data <- data %>%
  mutate(T3_pbc1 = round(T3_pbc1))

data <- data %>%
  mutate(T4_pbc1 = gsub(",", ".", T4_pbc1),
         T4_pbc1 = as.numeric(T4_pbc1)) 
data <- data %>%
  mutate(T4_pbc1 = round(T4_pbc1))

data <- data %>%
  mutate(T5_pbc1 = gsub(",", ".", T5_pbc1),
         T5_pbc1 = as.numeric(T5_pbc1)) 
data <- data %>%
  mutate(T5_pbc1 = round(T5_pbc1))

data <- data %>%
  mutate(T1_pbc2 = gsub(",", ".", T1_pbc2),
         T1_pbc2 = as.numeric(T1_pbc2)) 
data <- data %>%
  mutate(T1_pbc2 = round(T1_pbc2))

data <- data %>%
  mutate(T2_pbc2 = gsub(",", ".", T2_pbc2),
         T2_pbc2 = as.numeric(T2_pbc2)) 
data <- data %>%
  mutate(T2_pbc2 = round(T2_pbc2))

data <- data %>%
  mutate(T3_pbc2 = gsub(",", ".", T3_pbc2),
         T3_pbc2 = as.numeric(T3_pbc2)) 
data <- data %>%
  mutate(T3_pbc2 = round(T3_pbc2))

data <- data %>%
  mutate(T4_pbc2 = gsub(",", ".", T4_pbc2),
         T4_pbc2 = as.numeric(T4_pbc2)) 
data <- data %>%
  mutate(T4_pbc2 = round(T4_pbc2))

data <- data %>%
  mutate(T5_pbc2 = gsub(",", ".", T5_pbc2),
         T5_pbc2 = as.numeric(T5_pbc2)) 
data <- data %>%
  mutate(T5_pbc2 = round(T5_pbc2))

data <- data %>%
  mutate(T1_intention = gsub(",", ".", T1_intention),
         T1_intention = as.numeric(T1_intention)) 
data <- data %>%
  mutate(T1_intention = round(T1_intention))

data <- data %>%
  mutate(T2_intention = gsub(",", ".", T2_intention),
         T2_intention = as.numeric(T2_intention)) 
data <- data %>%
  mutate(T2_intention = round(T2_intention))

data <- data %>%
  mutate(T3_intention = gsub(",", ".", T3_intention),
         T3_intention = as.numeric(T3_intention)) 
data <- data %>%
  mutate(T3_intention = round(T3_intention))

data <- data %>%
  mutate(T4_intention = gsub(",", ".", T4_intention),
         T4_intention = as.numeric(T4_intention)) 
data <- data %>%
  mutate(T4_intention = round(T4_intention))

data <- data %>%
  mutate(T5_intention = gsub(",", ".", T5_intention),
         T5_intention = as.numeric(T5_intention)) 
data <- data %>%
  mutate(T5_intention = round(T5_intention))

data <- data %>%
  mutate(W1_comsumption_pp_7days = gsub(",", ".", W1_comsumption_pp_7days),
         W1_comsumption_pp_7days = as.numeric(W1_comsumption_pp_7days)) 

data <- data %>%
  mutate(W2_comsumption_pp_7days = gsub(",", ".", W2_comsumption_pp_7days),
         W2_comsumption_pp_7days = as.numeric(W2_comsumption_pp_7days)) 

data <- data %>%
  mutate(W3_comsumption_pp_7days = gsub(",", ".", W3_comsumption_pp_7days),
         W3_comsumption_pp_7days = as.numeric(W3_comsumption_pp_7days)) 

data <- data %>%
  mutate(W4_comsumption_pp_7days = gsub(",", ".", W4_comsumption_pp_7days),
         W4_comsumption_pp_7days = as.numeric(W4_comsumption_pp_7days))

data <- data %>%
  mutate(W5_comsumption_pp_7days = gsub(",", ".", W5_comsumption_pp_7days),
         W5_comsumption_pp_7days = as.numeric(W5_comsumption_pp_7days)) 

# Renaming variables
data <- data %>%
  rename(v11 = T1_attitude,
         v12 = T2_attitude,
         v13 = T3_attitude,
         v14 = T4_attitude,
         v15 = T5_attitude)
data <- data %>%
  rename(v21 = T1_Inorms,
         v22 = T2_Inorms,
         v23 = T3_Inorms,
         v24 = T4_Inorms,
         v25 = T5_Inorms)
data <- data %>%
  rename(v31 = T1_dnorms,
         v32 = T2_dnorms,
         v33 = T3_dnorms,
         v34 = T4_dnorms,
         v35 = T5_dnorms)
data <- data %>%
  rename(v41 = T1_pbc1,
         v42 = T2_pbc1,
         v43 = T3_pbc1,
         v44 = T4_pbc1,
         v45 = T5_pbc1)
data <- data %>%
  rename(v51 = T1_pbc2,
         v52 = T2_pbc2,
         v53 = T3_pbc2,
         v54 = T4_pbc2,
         v55 = T5_pbc2)
data <- data %>%
  rename(v61 = T1_intention,
         v62 = T2_intention,
         v63 = T3_intention,
         v64 = T4_intention,
         v65 = T5_intention)
data <- data %>%
  rename(v71 = W1_comsumption_pp_7days,
         v72 = W2_comsumption_pp_7days,
         v73 = W3_comsumption_pp_7days,
         v74 = W4_comsumption_pp_7days,
         v75 = W5_comsumption_pp_7days)

Removing negative imputed values from v7

variances_v7 <- apply(data[, c("v71", "v72", "v73", "v74", "v75")], 2, var)
variances_v7
##       v71       v72       v73       v74       v75 
## 10475.916  9251.266  9267.434  8115.179  7543.790
variances_v6 <- apply(data[, c("v61", "v62", "v63", "v64", "v65")], 2, var)
variances_v6
##       v61       v62       v63       v64       v65 
## 0.8348481 0.7412842 0.7085184 0.7355892 0.6885547
#Assessing the effect of imputation on v71-v75#####
num_negative_v71 <- sum(data$v71 < 0)
num_negative_v72 <- sum(data$v72 < 0)
num_negative_v73 <- sum(data$v73 < 0)
num_negative_v74 <- sum(data$v74 < 0)
num_negative_v75 <- sum(data$v75 < 0)

#Removing negative values from v71-v75#
data_no_negative_v7 <- data

# For v71
no_negative_v71 <- data_no_negative_v7$v71 >= 0
data_no_negative_v7 <- data_no_negative_v7[no_negative_v71, ]
# For v72
no_negative_v72 <- data_no_negative_v7$v72 >= 0
data_no_negative_v7 <- data_no_negative_v7[no_negative_v72, ]
# For v73
no_negative_v73 <- data_no_negative_v7$v73 >= 0
data_no_negative_v7 <- data_no_negative_v7[no_negative_v73, ]
# For v71
no_negative_v74 <- data_no_negative_v7$v74 >= 0
data_no_negative_v7 <- data_no_negative_v7[no_negative_v74, ]
# For v71
no_negative_v75 <- data_no_negative_v7$v75 >= 0
data_no_negative_v7 <- data_no_negative_v7[no_negative_v75, ]

Standardizing no negative v7 data (NONEG)

#Standardising no negative v7-dataset#
variables_to_standardize <- c("v11", "v21", "v31", "v41", "v51", "v21", "v22", "v23", "v24", "v25", "v31", "v32", "v33", "v34", "v35", "v41", "v42", "v43", "v44", "v45", "v51", "v52", "v53", "v54", "v55", "v61", "v62", "v63", "v64", "v65", "v71", "v72", "v73", "v74", "v75")

noneg_data_standardized <- data_no_negative_v7

noneg_data_standardized <- noneg_data_standardized %>%
  mutate(across(all_of(variables_to_standardize), scale))

Demographics

#Demographics
noneg_data_standardized <- noneg_data_standardized %>%
  mutate(initial_survey_hhsize = as.numeric(initial_survey_hhsize))

noneg_data_standardized <- noneg_data_standardized %>%
  mutate(initial_survey_energypoverty = gsub(",", ".", initial_survey_energypoverty),
         initial_survey_energypoverty = as.numeric(initial_survey_energypoverty)) 
noneg_data_standardized <- noneg_data_standardized %>%
  mutate(initial_survey_energypoverty = round(initial_survey_energypoverty))

noneg_data_standardized <- noneg_data_standardized %>%
  mutate(initial_survey_energypovpercent = gsub(",", ".", initial_survey_energypovpercent),
         initial_survey_energypovpercent = as.numeric(initial_survey_energypovpercent))
noneg_data_standardized <- noneg_data_standardized %>%
  mutate(initial_survey_energypovpercent = round(initial_survey_energypovpercent))

noneg_data_standardized <- noneg_data_standardized %>%
  group_by(id) %>%
  mutate(energypoverty_MEAN = mean(c(initial_survey_energypoverty, initial_survey_energypovpercent)))

Shapiro-Wilks test

selected_columns <- noneg_data_standardized[, c("v11", "v21", "v31", "v41", "v51", "v21", "v22", "v23", "v24", "v25", "v31", "v32", "v33", "v34", "v35", "v41", "v42", "v43", "v44", "v45", "v51", "v52", "v53", "v54", "v55", "v61", "v62", "v63", "v64", "v65", "v71", "v72", "v73", "v74", "v75")]

normality_tests <- lapply(selected_columns, shapiro.test)

names(normality_tests) <- c("v11", "v21", "v31", "v41", "v51", "v21", "v22", "v23", "v24", "v25", "v31", "v32", "v33", "v34", "v35", "v41", "v42", "v43", "v44", "v45", "v51", "v52", "v53", "v54", "v55", "v61", "v62", "v63", "v64", "v65", "v71", "v72", "v73", "v74", "v75")

normality_tests
## $v11
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.86286, p-value < 2.2e-16
## 
## 
## $v21
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.87353, p-value < 2.2e-16
## 
## 
## $v31
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.84644, p-value < 2.2e-16
## 
## 
## $v41
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.87011, p-value < 2.2e-16
## 
## 
## $v51
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.89559, p-value < 2.2e-16
## 
## 
## $v21
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.87353, p-value < 2.2e-16
## 
## 
## $v22
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.84992, p-value < 2.2e-16
## 
## 
## $v23
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.86538, p-value < 2.2e-16
## 
## 
## $v24
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.8472, p-value < 2.2e-16
## 
## 
## $v25
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.84331, p-value < 2.2e-16
## 
## 
## $v31
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.84644, p-value < 2.2e-16
## 
## 
## $v32
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.83406, p-value < 2.2e-16
## 
## 
## $v33
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.83349, p-value < 2.2e-16
## 
## 
## $v34
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.83378, p-value < 2.2e-16
## 
## 
## $v35
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.82355, p-value < 2.2e-16
## 
## 
## $v41
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.87011, p-value < 2.2e-16
## 
## 
## $v42
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.85783, p-value < 2.2e-16
## 
## 
## $v43
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.85917, p-value < 2.2e-16
## 
## 
## $v44
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.8573, p-value < 2.2e-16
## 
## 
## $v45
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.86033, p-value < 2.2e-16
## 
## 
## $v51
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.89559, p-value < 2.2e-16
## 
## 
## $v52
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.86917, p-value < 2.2e-16
## 
## 
## $v53
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.87857, p-value < 2.2e-16
## 
## 
## $v54
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.88186, p-value < 2.2e-16
## 
## 
## $v55
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.88024, p-value < 2.2e-16
## 
## 
## $v61
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.87105, p-value < 2.2e-16
## 
## 
## $v62
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.85346, p-value < 2.2e-16
## 
## 
## $v63
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.85035, p-value < 2.2e-16
## 
## 
## $v64
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.86823, p-value < 2.2e-16
## 
## 
## $v65
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.86115, p-value < 2.2e-16
## 
## 
## $v71
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.84098, p-value < 2.2e-16
## 
## 
## $v72
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.83168, p-value < 2.2e-16
## 
## 
## $v73
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.81724, p-value < 2.2e-16
## 
## 
## $v74
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.83624, p-value < 2.2e-16
## 
## 
## $v75
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.84444, p-value < 2.2e-16

Initial SEM

sem <- 'Att =~ v11 + v12 + v13 + v14 + v15
        Sub =~ v21 + v22 + v23 + v24 + v25
            + v31 + v32 + v33 + v34 + v35
        PBC =~ v41 + v42 + v43 + v44 + v45
            + v51 + v52 + v53 + v54 + v55
        Int =~ v61 + v62 + v63 + v64 + v65
        kWh =~ v71 + v72 + v73 + v74 + v75

        Int ~ Att + Sub + PBC
        kWh ~ Int + PBC + energypoverty_MEAN + initial_survey_age + initial_survey_hhsize + initial_survey_gender

        Att ~~ Sub
        Sub ~~ PBC
        PBC ~~ Att'

fit <- sem(sem, data=noneg_data_standardized)

summary(fit, fit.measures=TRUE, standardized=TRUE, rsquare=TRUE, modindices=TRUE)
## lavaan 0.6.16 ended normally after 84 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        82
## 
##                                                   Used       Total
##   Number of observations                          2352        2363
## 
## Model Test User Model:
##                                                        
##   Test statistic                              12483.550
##   Degrees of freedom                                688
##   P-value (Chi-square)                            0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             66738.515
##   Degrees of freedom                               735
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.821
##   Tucker-Lewis Index (TLI)                       0.809
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -88095.288
##   Loglikelihood unrestricted model (H1)     -81853.513
##                                                       
##   Akaike (AIC)                              176354.576
##   Bayesian (BIC)                            176827.144
##   Sample-size adjusted Bayesian (SABIC)     176566.613
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.085
##   90 Percent confidence interval - lower         0.084
##   90 Percent confidence interval - upper         0.087
##   P-value H_0: RMSEA <= 0.050                    0.000
##   P-value H_0: RMSEA >= 0.080                    1.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.082
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Att =~                                                                
##     v11               1.000                               0.656    0.655
##     v12               0.972    0.030   32.180    0.000    0.637    0.776
##     v13               1.042    0.032   33.011    0.000    0.683    0.802
##     v14               1.089    0.032   33.879    0.000    0.714    0.830
##     v15               1.058    0.031   33.699    0.000    0.693    0.824
##   Sub =~                                                                
##     v21               1.000                               0.648    0.647
##     v22               1.128    0.037   30.583    0.000    0.731    0.730
##     v23               1.148    0.037   31.030    0.000    0.743    0.743
##     v24               1.177    0.037   31.672    0.000    0.762    0.763
##     v25               1.124    0.037   30.505    0.000    0.728    0.728
##     v31               0.826    0.035   23.460    0.000    0.535    0.535
##     v32               0.994    0.036   27.533    0.000    0.644    0.643
##     v33               1.084    0.037   29.639    0.000    0.702    0.703
##     v34               1.085    0.037   29.631    0.000    0.703    0.702
##     v35               1.075    0.037   29.414    0.000    0.696    0.696
##   PBC =~                                                                
##     v41               1.000                               0.516    0.516
##     v42               1.292    0.056   22.916    0.000    0.667    0.667
##     v43               1.292    0.056   22.916    0.000    0.667    0.667
##     v44               1.345    0.057   23.412    0.000    0.694    0.693
##     v45               1.293    0.056   22.936    0.000    0.667    0.668
##     v51               1.162    0.054   21.554    0.000    0.600    0.600
##     v52               1.303    0.057   23.008    0.000    0.672    0.672
##     v53               1.388    0.058   23.808    0.000    0.716    0.716
##     v54               1.378    0.058   23.722    0.000    0.711    0.711
##     v55               1.365    0.058   23.598    0.000    0.704    0.704
##   Int =~                                                                
##     v61               1.000                               0.513    0.512
##     v62               1.295    0.058   22.229    0.000    0.664    0.664
##     v63               1.452    0.062   23.553    0.000    0.744    0.744
##     v64               1.521    0.063   24.057    0.000    0.780    0.779
##     v65               1.440    0.061   23.471    0.000    0.738    0.738
##   kWh =~                                                                
##     v71               1.000                               0.960    0.961
##     v72               1.009    0.008  126.300    0.000    0.969    0.971
##     v73               1.009    0.008  125.252    0.000    0.968    0.970
##     v74               1.003    0.008  120.789    0.000    0.963    0.964
##     v75               0.998    0.009  116.962    0.000    0.958    0.960
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Int ~                                                                 
##     Att               0.184    0.019    9.756    0.000    0.235    0.235
##     Sub               0.294    0.024   12.402    0.000    0.372    0.372
##     PBC               0.341    0.032   10.784    0.000    0.343    0.343
##   kWh ~                                                                 
##     Int              -0.341    0.072   -4.758    0.000   -0.182   -0.182
##     PBC               0.069    0.069    0.996    0.319    0.037    0.037
##     enrgypvrt_MEAN    0.083    0.021    3.864    0.000    0.086    0.079
##     initial_srvy_g   -0.009    0.002   -5.780    0.000   -0.009   -0.122
##     intl_srvy_hhsz   -0.095    0.016   -5.890    0.000   -0.099   -0.124
##     intl_srvy_gndr   -0.010    0.039   -0.249    0.803   -0.010   -0.005
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   Att ~~                                                                
##     Sub               0.235    0.014   17.342    0.000    0.554    0.554
##   Sub ~~                                                                
##     PBC               0.234    0.014   17.269    0.000    0.700    0.700
##   Att ~~                                                                
##     PBC               0.202    0.012   16.311    0.000    0.597    0.597
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .v11               0.571    0.018   31.425    0.000    0.571    0.570
##    .v12               0.268    0.009   28.462    0.000    0.268    0.398
##    .v13               0.259    0.009   27.340    0.000    0.259    0.357
##    .v14               0.231    0.009   25.730    0.000    0.231    0.312
##    .v15               0.228    0.009   26.113    0.000    0.228    0.321
##    .v21               0.583    0.018   32.015    0.000    0.583    0.582
##    .v22               0.467    0.015   30.668    0.000    0.467    0.467
##    .v23               0.447    0.015   30.370    0.000    0.447    0.447
##    .v24               0.418    0.014   29.873    0.000    0.418    0.418
##    .v25               0.470    0.015   30.717    0.000    0.470    0.470
##    .v31               0.713    0.022   33.023    0.000    0.713    0.713
##    .v32               0.586    0.018   32.056    0.000    0.586    0.586
##    .v33               0.505    0.016   31.200    0.000    0.505    0.506
##    .v34               0.507    0.016   31.204    0.000    0.507    0.507
##    .v35               0.515    0.016   31.311    0.000    0.515    0.515
##    .v41               0.734    0.022   32.980    0.000    0.734    0.734
##    .v42               0.556    0.018   31.391    0.000    0.556    0.556
##    .v43               0.556    0.018   31.391    0.000    0.556    0.556
##    .v44               0.520    0.017   30.929    0.000    0.520    0.519
##    .v45               0.553    0.018   31.374    0.000    0.553    0.554
##    .v51               0.640    0.020   32.257    0.000    0.640    0.640
##    .v52               0.550    0.018   31.312    0.000    0.550    0.549
##    .v53               0.488    0.016   30.471    0.000    0.488    0.487
##    .v54               0.495    0.016   30.579    0.000    0.495    0.494
##    .v55               0.505    0.016   30.725    0.000    0.505    0.504
##    .v61               0.738    0.023   32.538    0.000    0.738    0.737
##    .v62               0.560    0.018   30.379    0.000    0.560    0.560
##    .v63               0.447    0.016   28.078    0.000    0.447    0.447
##    .v64               0.393    0.015   26.497    0.000    0.393    0.393
##    .v65               0.455    0.016   28.282    0.000    0.455    0.455
##    .v71               0.076    0.003   28.133    0.000    0.076    0.076
##    .v72               0.058    0.002   25.967    0.000    0.058    0.058
##    .v73               0.060    0.002   26.292    0.000    0.060    0.060
##    .v74               0.070    0.003   27.506    0.000    0.070    0.070
##    .v75               0.079    0.003   28.364    0.000    0.079    0.079
##     Att               0.430    0.025   17.164    0.000    1.000    1.000
##     Sub               0.419    0.025   17.010    0.000    1.000    1.000
##     PBC               0.266    0.021   12.843    0.000    1.000    1.000
##    .Int               0.084    0.007   11.380    0.000    0.318    0.318
##    .kWh               0.860    0.027   31.522    0.000    0.933    0.933
## 
## R-Square:
##                    Estimate
##     v11               0.430
##     v12               0.602
##     v13               0.643
##     v14               0.688
##     v15               0.679
##     v21               0.418
##     v22               0.533
##     v23               0.553
##     v24               0.582
##     v25               0.530
##     v31               0.287
##     v32               0.414
##     v33               0.494
##     v34               0.493
##     v35               0.485
##     v41               0.266
##     v42               0.444
##     v43               0.444
##     v44               0.481
##     v45               0.446
##     v51               0.360
##     v52               0.451
##     v53               0.513
##     v54               0.506
##     v55               0.496
##     v61               0.263
##     v62               0.440
##     v63               0.553
##     v64               0.607
##     v65               0.545
##     v71               0.924
##     v72               0.942
##     v73               0.940
##     v74               0.930
##     v75               0.921
##     Int               0.682
##     kWh               0.067
## 
## Modification Indices:
## 
##                       lhs op                   rhs      mi    epc sepc.lv
## 1                     Att =~                   v21   0.071 -0.009  -0.006
## 2                     Att =~                   v22   8.414 -0.089  -0.058
## 3                     Att =~                   v23   0.502 -0.021  -0.014
## 4                     Att =~                   v24   3.600 -0.056  -0.037
## 5                     Att =~                   v25   1.204 -0.034  -0.022
## 6                     Att =~                   v31   0.990  0.036   0.024
## 7                     Att =~                   v32   0.550 -0.025  -0.016
## 8                     Att =~                   v33   7.531  0.086   0.057
## 9                     Att =~                   v34   0.005  0.002   0.001
## 10                    Att =~                   v35  22.434  0.150   0.098
## 11                    Att =~                   v41  91.373  0.369   0.242
## 12                    Att =~                   v42  54.683  0.256   0.168
## 13                    Att =~                   v43 124.800  0.387   0.254
## 14                    Att =~                   v44 135.789  0.394   0.258
## 15                    Att =~                   v45 138.063  0.406   0.266
## 16                    Att =~                   v51  34.244 -0.214  -0.140
## 17                    Att =~                   v52 132.302 -0.397  -0.260
## 18                    Att =~                   v53  83.741 -0.303  -0.199
## 19                    Att =~                   v54  72.240 -0.283  -0.185
## 20                    Att =~                   v55 128.499 -0.380  -0.249
## 21                    Att =~                   v61   5.324 -0.098  -0.064
## 22                    Att =~                   v62   9.483 -0.121  -0.079
## 23                    Att =~                   v63   3.286 -0.068  -0.045
## 24                    Att =~                   v64   0.053 -0.008  -0.006
## 25                    Att =~                   v65   8.544  0.110   0.072
## 26                    Att =~                   v71  10.201 -0.032  -0.021
## 27                    Att =~                   v72   0.002  0.000   0.000
## 28                    Att =~                   v73   2.216  0.014   0.009
## 29                    Att =~                   v74   0.422  0.006   0.004
## 30                    Att =~                   v75   7.663 -0.028  -0.019
## 31                    Sub =~                   v11   7.540 -0.092  -0.059
## 32                    Sub =~                   v12   0.149 -0.009  -0.006
## 33                    Sub =~                   v13   1.935  0.034   0.022
## 34                    Sub =~                   v14   0.700 -0.020  -0.013
## 35                    Sub =~                   v15   2.922  0.040   0.026
## 36                    Sub =~                   v41  52.449  0.327   0.212
## 37                    Sub =~                   v42  91.564  0.390   0.252
## 38                    Sub =~                   v43  82.802  0.370   0.240
## 39                    Sub =~                   v44  74.896  0.344   0.223
## 40                    Sub =~                   v45  44.737  0.272   0.176
## 41                    Sub =~                   v51  92.386 -0.412  -0.267
## 42                    Sub =~                   v52  63.713 -0.324  -0.210
## 43                    Sub =~                   v53  62.237 -0.307  -0.199
## 44                    Sub =~                   v54  58.157 -0.298  -0.193
## 45                    Sub =~                   v55  32.224 -0.224  -0.145
## 46                    Sub =~                   v61  14.911  0.200   0.129
## 47                    Sub =~                   v62   0.083  0.014   0.009
## 48                    Sub =~                   v63   4.078  0.094   0.061
## 49                    Sub =~                   v64   4.729 -0.100  -0.065
## 50                    Sub =~                   v65   2.458 -0.073  -0.047
## 51                    Sub =~                   v71  12.295 -0.036  -0.023
## 52                    Sub =~                   v72   0.001  0.000   0.000
## 53                    Sub =~                   v73   2.935  0.016   0.010
## 54                    Sub =~                   v74   0.444  0.007   0.004
## 55                    Sub =~                   v75   2.761  0.017   0.011
## 56                    PBC =~                   v11  12.238 -0.155  -0.080
## 57                    PBC =~                   v12   0.698 -0.027  -0.014
## 58                    PBC =~                   v13   1.452  0.039   0.020
## 59                    PBC =~                   v14   0.031  0.006   0.003
## 60                    PBC =~                   v15   3.141  0.056   0.029
## 61                    PBC =~                   v21   0.007 -0.004  -0.002
## 62                    PBC =~                   v22   1.482 -0.058  -0.030
## 63                    PBC =~                   v23   0.048 -0.010  -0.005
## 64                    PBC =~                   v24   0.197  0.020   0.011
## 65                    PBC =~                   v25   0.022  0.007   0.004
## 66                    PBC =~                   v31   5.349 -0.130  -0.067
## 67                    PBC =~                   v32   0.170 -0.021  -0.011
## 68                    PBC =~                   v33   4.255  0.101   0.052
## 69                    PBC =~                   v34   1.022 -0.050  -0.026
## 70                    PBC =~                   v35   3.321  0.090   0.046
## 71                    PBC =~                   v61   1.891  0.091   0.047
## 72                    PBC =~                   v62   0.136  0.023   0.012
## 73                    PBC =~                   v63   1.210 -0.065  -0.034
## 74                    PBC =~                   v64   0.785 -0.052  -0.027
## 75                    PBC =~                   v65   0.767  0.052   0.027
## 76                    PBC =~                   v71   7.841 -0.036  -0.019
## 77                    PBC =~                   v72   0.179 -0.005  -0.003
## 78                    PBC =~                   v73   2.569  0.019   0.010
## 79                    PBC =~                   v74   1.924  0.017   0.009
## 80                    PBC =~                   v75   0.005  0.001   0.000
## 81                    Int =~                   v11  17.835 -0.208  -0.106
## 82                    Int =~                   v12   0.000  0.000   0.000
## 83                    Int =~                   v13  14.577  0.139   0.071
## 84                    Int =~                   v14   1.405 -0.042  -0.022
## 85                    Int =~                   v15   0.180  0.015   0.008
## 86                    Int =~                   v21   0.330 -0.034  -0.017
## 87                    Int =~                   v22  25.836 -0.278  -0.142
## 88                    Int =~                   v23   3.632 -0.103  -0.053
## 89                    Int =~                   v24  14.504 -0.201  -0.103
## 90                    Int =~                   v25  28.677 -0.293  -0.150
## 91                    Int =~                   v31   1.046  0.066   0.034
## 92                    Int =~                   v32   0.092  0.018   0.009
## 93                    Int =~                   v33  44.311  0.374   0.192
## 94                    Int =~                   v34  20.365  0.254   0.130
## 95                    Int =~                   v35  37.566  0.347   0.178
## 96                    Int =~                   v41 119.110  0.722   0.370
## 97                    Int =~                   v42 247.757  0.940   0.482
## 98                    Int =~                   v43 267.996  0.977   0.501
## 99                    Int =~                   v44 286.552  0.988   0.507
## 100                   Int =~                   v45 251.085  0.945   0.484
## 101                   Int =~                   v51 164.789 -0.806  -0.413
## 102                   Int =~                   v52 168.348 -0.772  -0.396
## 103                   Int =~                   v53 178.257 -0.764  -0.392
## 104                   Int =~                   v54 266.942 -0.939  -0.481
## 105                   Int =~                   v55 227.503 -0.872  -0.447
## 106                   Int =~                   v71  15.453 -0.052  -0.027
## 107                   Int =~                   v72   0.350  0.007   0.004
## 108                   Int =~                   v73   3.906  0.024   0.012
## 109                   Int =~                   v74   2.915  0.022   0.011
## 110                   Int =~                   v75   0.470 -0.009  -0.005
## 111                   kWh =~                   v11  40.607 -0.109  -0.104
## 112                   kWh =~                   v12   9.890 -0.038  -0.037
## 113                   kWh =~                   v13  13.274 -0.045  -0.043
## 114                   kWh =~                   v14   2.074 -0.017  -0.016
## 115                   kWh =~                   v15  12.737 -0.042  -0.040
## 116                   kWh =~                   v21   0.929 -0.017  -0.016
## 117                   kWh =~                   v22   0.607  0.012   0.012
## 118                   kWh =~                   v23   0.003  0.001   0.001
## 119                   kWh =~                   v24  46.042  0.102   0.098
## 120                   kWh =~                   v25  11.547  0.053   0.051
## 121                   kWh =~                   v31   0.802  0.017   0.016
## 122                   kWh =~                   v32   0.057 -0.004  -0.004
## 123                   kWh =~                   v33  10.165 -0.052  -0.049
## 124                   kWh =~                   v34   0.402  0.010   0.010
## 125                   kWh =~                   v35   4.940 -0.036  -0.035
## 126                   kWh =~                   v41  41.990 -0.123  -0.119
## 127                   kWh =~                   v42  21.885 -0.080  -0.077
## 128                   kWh =~                   v43  59.295 -0.131  -0.126
## 129                   kWh =~                   v44  25.078 -0.083  -0.080
## 130                   kWh =~                   v45  66.740 -0.139  -0.133
## 131                   kWh =~                   v51   4.384  0.038   0.036
## 132                   kWh =~                   v52  73.410  0.145   0.140
## 133                   kWh =~                   v53  53.295  0.119   0.114
## 134                   kWh =~                   v54  73.838  0.140   0.135
## 135                   kWh =~                   v55  52.965  0.120   0.115
## 136                   kWh =~                   v61   9.564  0.060   0.058
## 137                   kWh =~                   v62  10.840  0.058   0.056
## 138                   kWh =~                   v63   1.921  0.023   0.022
## 139                   kWh =~                   v64   0.106  0.005   0.005
## 140                   kWh =~                   v65   6.762 -0.043  -0.041
## 141                   v11 ~~                   v12  10.247  0.031   0.031
## 142                   v11 ~~                   v13  21.859  0.045   0.045
## 143                   v11 ~~                   v14   6.835 -0.025  -0.025
## 144                   v11 ~~                   v15   3.493 -0.017  -0.017
## 145                   v11 ~~                   v21  22.567  0.061   0.061
## 146                   v11 ~~                   v22   1.237  0.013   0.013
## 147                   v11 ~~                   v23   0.021 -0.002  -0.002
## 148                   v11 ~~                   v24  18.266 -0.048  -0.048
## 149                   v11 ~~                   v25  15.580 -0.046  -0.046
## 150                   v11 ~~                   v31  57.698  0.106   0.106
## 151                   v11 ~~                   v32   3.435  0.024   0.024
## 152                   v11 ~~                   v33   0.927  0.012   0.012
## 153                   v11 ~~                   v34   3.131 -0.021  -0.021
## 154                   v11 ~~                   v35   3.283 -0.022  -0.022
## 155                   v11 ~~                   v41 115.255  0.152   0.152
## 156                   v11 ~~                   v42   0.852  0.012   0.012
## 157                   v11 ~~                   v43   1.284 -0.014  -0.014
## 158                   v11 ~~                   v44   4.995 -0.027  -0.027
## 159                   v11 ~~                   v45  11.455 -0.042  -0.042
## 160                   v11 ~~                   v51  34.714  0.078   0.078
## 161                   v11 ~~                   v52   0.220  0.006   0.006
## 162                   v11 ~~                   v53   2.018 -0.017  -0.017
## 163                   v11 ~~                   v54  23.496 -0.058  -0.058
## 164                   v11 ~~                   v55   2.580 -0.019  -0.019
## 165                   v11 ~~                   v61 136.140  0.166   0.166
## 166                   v11 ~~                   v62   1.507  0.016   0.016
## 167                   v11 ~~                   v63   6.246 -0.029  -0.029
## 168                   v11 ~~                   v64  28.648 -0.061  -0.061
## 169                   v11 ~~                   v65  15.745 -0.047  -0.047
## 170                   v11 ~~                   v71   0.278 -0.003  -0.003
## 171                   v11 ~~                   v72   1.548 -0.006  -0.006
## 172                   v11 ~~                   v73   0.100 -0.001  -0.001
## 173                   v11 ~~                   v74   0.290  0.003   0.003
## 174                   v11 ~~                   v75   0.199 -0.002  -0.002
## 175                   v12 ~~                   v13   1.935  0.010   0.010
## 176                   v12 ~~                   v14   6.651 -0.019  -0.019
## 177                   v12 ~~                   v15   0.558 -0.005  -0.005
## 178                   v12 ~~                   v21   0.624  0.007   0.007
## 179                   v12 ~~                   v22  13.217  0.030   0.030
## 180                   v12 ~~                   v23   1.706  0.011   0.011
## 181                   v12 ~~                   v24   1.510 -0.010  -0.010
## 182                   v12 ~~                   v25   2.083  0.012   0.012
## 183                   v12 ~~                   v31   1.034 -0.010  -0.010
## 184                   v12 ~~                   v32   1.732  0.012   0.012
## 185                   v12 ~~                   v33   2.179  0.013   0.013
## 186                   v12 ~~                   v34  13.553 -0.032  -0.032
## 187                   v12 ~~                   v35  22.498 -0.041  -0.041
## 188                   v12 ~~                   v41   0.338 -0.006  -0.006
## 189                   v12 ~~                   v42  80.707  0.081   0.081
## 190                   v12 ~~                   v43   0.890 -0.008  -0.008
## 191                   v12 ~~                   v44  17.480 -0.037  -0.037
## 192                   v12 ~~                   v45   1.542 -0.011  -0.011
## 193                   v12 ~~                   v51   0.234 -0.005  -0.005
## 194                   v12 ~~                   v52   3.252  0.016   0.016
## 195                   v12 ~~                   v53   0.079  0.002   0.002
## 196                   v12 ~~                   v54  13.468 -0.031  -0.031
## 197                   v12 ~~                   v55   0.704 -0.007  -0.007
## 198                   v12 ~~                   v61   0.095 -0.003  -0.003
## 199                   v12 ~~                   v62  80.779  0.082   0.082
## 200                   v12 ~~                   v63   0.296 -0.005  -0.005
## 201                   v12 ~~                   v64  19.387 -0.036  -0.036
## 202                   v12 ~~                   v65   2.275 -0.013  -0.013
## 203                   v12 ~~                   v71   5.207 -0.008  -0.008
## 204                   v12 ~~                   v72   0.207 -0.001  -0.001
## 205                   v12 ~~                   v73   0.651  0.003   0.003
## 206                   v12 ~~                   v74   0.071 -0.001  -0.001
## 207                   v12 ~~                   v75   1.619  0.005   0.005
## 208                   v13 ~~                   v14   2.094 -0.011  -0.011
## 209                   v13 ~~                   v15  28.121 -0.039  -0.039
## 210                   v13 ~~                   v21   0.547 -0.007  -0.007
## 211                   v13 ~~                   v22   0.496 -0.006  -0.006
## 212                   v13 ~~                   v23  18.930  0.036   0.036
## 213                   v13 ~~                   v24   0.177 -0.003  -0.003
## 214                   v13 ~~                   v25  19.837 -0.037  -0.037
## 215                   v13 ~~                   v31   2.224  0.015   0.015
## 216                   v13 ~~                   v32   2.452 -0.014  -0.014
## 217                   v13 ~~                   v33  16.996  0.035   0.035
## 218                   v13 ~~                   v34  10.350 -0.028  -0.028
## 219                   v13 ~~                   v35   0.117  0.003   0.003
## 220                   v13 ~~                   v41   1.770  0.013   0.013
## 221                   v13 ~~                   v42   0.346  0.005   0.005
## 222                   v13 ~~                   v43 175.360  0.119   0.119
## 223                   v13 ~~                   v44   1.635  0.011   0.011
## 224                   v13 ~~                   v45   4.167 -0.018  -0.018
## 225                   v13 ~~                   v51  21.967 -0.045  -0.045
## 226                   v13 ~~                   v52  24.479 -0.044  -0.044
## 227                   v13 ~~                   v53   0.143  0.003   0.003
## 228                   v13 ~~                   v54   0.782 -0.008  -0.008
## 229                   v13 ~~                   v55  27.901 -0.046  -0.046
## 230                   v13 ~~                   v61  14.833 -0.039  -0.039
## 231                   v13 ~~                   v62   1.951 -0.013  -0.013
## 232                   v13 ~~                   v63 177.240  0.113   0.113
## 233                   v13 ~~                   v64   4.680 -0.018  -0.018
## 234                   v13 ~~                   v65   8.404 -0.025  -0.025
## 235                   v13 ~~                   v71   0.293 -0.002  -0.002
## 236                   v13 ~~                   v72   5.016 -0.007  -0.007
## 237                   v13 ~~                   v73   0.113  0.001   0.001
## 238                   v13 ~~                   v74   2.137  0.005   0.005
## 239                   v13 ~~                   v75   0.037  0.001   0.001
## 240                   v14 ~~                   v15  40.066  0.047   0.047
## 241                   v14 ~~                   v21   0.587  0.007   0.007
## 242                   v14 ~~                   v22   2.159 -0.012  -0.012
## 243                   v14 ~~                   v23   1.961 -0.011  -0.011
## 244                   v14 ~~                   v24  14.846  0.030   0.030
## 245                   v14 ~~                   v25   3.003 -0.014  -0.014
## 246                   v14 ~~                   v31   2.921 -0.016  -0.016
## 247                   v14 ~~                   v32   1.313 -0.010  -0.010
## 248                   v14 ~~                   v33  24.132 -0.041  -0.041
## 249                   v14 ~~                   v34  28.989  0.045   0.045
## 250                   v14 ~~                   v35   0.430  0.005   0.005
## 251                   v14 ~~                   v41   1.514 -0.012  -0.012
## 252                   v14 ~~                   v42   3.209 -0.016  -0.016
## 253                   v14 ~~                   v43   4.850 -0.019  -0.019
## 254                   v14 ~~                   v44 109.596  0.089   0.089
## 255                   v14 ~~                   v45   0.384 -0.005  -0.005
## 256                   v14 ~~                   v51   0.000  0.000   0.000
## 257                   v14 ~~                   v52   0.254 -0.004  -0.004
## 258                   v14 ~~                   v53  12.496 -0.029  -0.029
## 259                   v14 ~~                   v54  23.428  0.040   0.040
## 260                   v14 ~~                   v55  18.776 -0.036  -0.036
## 261                   v14 ~~                   v61  22.497 -0.047  -0.047
## 262                   v14 ~~                   v62  25.944 -0.045  -0.045
## 263                   v14 ~~                   v63  30.452 -0.045  -0.045
## 264                   v14 ~~                   v64 146.220  0.095   0.095
## 265                   v14 ~~                   v65   7.255 -0.022  -0.022
## 266                   v14 ~~                   v71   1.893  0.005   0.005
## 267                   v14 ~~                   v72   1.634  0.004   0.004
## 268                   v14 ~~                   v73   0.018  0.000   0.000
## 269                   v14 ~~                   v74   0.216 -0.002  -0.002
## 270                   v14 ~~                   v75   6.819 -0.009  -0.009
## 271                   v15 ~~                   v21  15.475 -0.034  -0.034
## 272                   v15 ~~                   v22   9.030 -0.024  -0.024
## 273                   v15 ~~                   v23  14.784 -0.030  -0.030
## 274                   v15 ~~                   v24   0.349 -0.005  -0.005
## 275                   v15 ~~                   v25  59.046  0.061   0.061
## 276                   v15 ~~                   v31   6.177 -0.024  -0.024
## 277                   v15 ~~                   v32   0.255 -0.004  -0.004
## 278                   v15 ~~                   v33   0.130 -0.003  -0.003
## 279                   v15 ~~                   v34   0.691  0.007   0.007
## 280                   v15 ~~                   v35  50.170  0.059   0.059
## 281                   v15 ~~                   v41   0.535 -0.007  -0.007
## 282                   v15 ~~                   v42  28.441 -0.046  -0.046
## 283                   v15 ~~                   v43  10.125 -0.027  -0.027
## 284                   v15 ~~                   v44   0.835 -0.008  -0.008
## 285                   v15 ~~                   v45 149.546  0.105   0.105
## 286                   v15 ~~                   v51   0.042 -0.002  -0.002
## 287                   v15 ~~                   v52  13.153 -0.031  -0.031
## 288                   v15 ~~                   v53   0.299 -0.004  -0.004
## 289                   v15 ~~                   v54   0.465 -0.006  -0.006
## 290                   v15 ~~                   v55  23.765  0.040   0.040
## 291                   v15 ~~                   v61   2.091 -0.014  -0.014
## 292                   v15 ~~                   v62  25.244 -0.044  -0.044
## 293                   v15 ~~                   v63  40.306 -0.051  -0.051
## 294                   v15 ~~                   v64   8.013 -0.022  -0.022
## 295                   v15 ~~                   v65 140.554  0.096   0.096
## 296                   v15 ~~                   v71   0.323  0.002   0.002
## 297                   v15 ~~                   v72   3.101  0.005   0.005
## 298                   v15 ~~                   v73   0.201 -0.001  -0.001
## 299                   v15 ~~                   v74   2.432 -0.005  -0.005
## 300                   v15 ~~                   v75   3.595 -0.006  -0.006
## 301                   v21 ~~                   v22  42.831  0.078   0.078
## 302                   v21 ~~                   v23  47.413  0.081   0.081
## 303                   v21 ~~                   v24   9.603  0.036   0.036
## 304                   v21 ~~                   v25   2.864  0.020   0.020
## 305                   v21 ~~                   v31  33.391  0.081   0.081
## 306                   v21 ~~                   v32   5.376 -0.030  -0.030
## 307                   v21 ~~                   v33  50.184 -0.087  -0.087
## 308                   v21 ~~                   v34  35.645 -0.073  -0.073
## 309                   v21 ~~                   v35  71.943 -0.105  -0.105
## 310                   v21 ~~                   v41 100.905  0.142   0.142
## 311                   v21 ~~                   v42  10.245  0.040   0.040
## 312                   v21 ~~                   v43   0.859 -0.012  -0.012
## 313                   v21 ~~                   v44   5.338 -0.028  -0.028
## 314                   v21 ~~                   v45  11.312 -0.042  -0.042
## 315                   v21 ~~                   v51  37.673  0.082   0.082
## 316                   v21 ~~                   v52   0.024  0.002   0.002
## 317                   v21 ~~                   v53   2.267 -0.018  -0.018
## 318                   v21 ~~                   v54  20.347 -0.054  -0.054
## 319                   v21 ~~                   v55   2.084 -0.018  -0.018
## 320                   v21 ~~                   v61  46.282  0.097   0.097
## 321                   v21 ~~                   v62   1.410  0.015   0.015
## 322                   v21 ~~                   v63   0.332 -0.007  -0.007
## 323                   v21 ~~                   v64   0.060 -0.003  -0.003
## 324                   v21 ~~                   v65  25.776 -0.060  -0.060
## 325                   v21 ~~                   v71  10.381 -0.016  -0.016
## 326                   v21 ~~                   v72   0.079 -0.001  -0.001
## 327                   v21 ~~                   v73   0.010  0.000   0.000
## 328                   v21 ~~                   v74   5.856  0.012   0.012
## 329                   v21 ~~                   v75   0.234  0.002   0.002
## 330                   v22 ~~                   v23 123.195  0.120   0.120
## 331                   v22 ~~                   v24  84.573  0.098   0.098
## 332                   v22 ~~                   v25  30.112  0.061   0.061
## 333                   v22 ~~                   v31  31.398 -0.072  -0.072
## 334                   v22 ~~                   v32   0.201 -0.005  -0.005
## 335                   v22 ~~                   v33  81.345 -0.102  -0.102
## 336                   v22 ~~                   v34  63.034 -0.090  -0.090
## 337                   v22 ~~                   v35  82.561 -0.104  -0.104
## 338                   v22 ~~                   v41  14.255 -0.049  -0.049
## 339                   v22 ~~                   v42   1.642  0.015   0.015
## 340                   v22 ~~                   v43  34.019 -0.067  -0.067
## 341                   v22 ~~                   v44  15.250 -0.044  -0.044
## 342                   v22 ~~                   v45  15.717 -0.046  -0.046
## 343                   v22 ~~                   v51   0.180  0.005   0.005
## 344                   v22 ~~                   v52  55.926  0.086   0.086
## 345                   v22 ~~                   v53   8.811  0.032   0.032
## 346                   v22 ~~                   v54  14.876  0.042   0.042
## 347                   v22 ~~                   v55   2.893  0.019   0.019
## 348                   v22 ~~                   v61   0.813 -0.012  -0.012
## 349                   v22 ~~                   v62  13.412  0.043   0.043
## 350                   v22 ~~                   v63   1.459 -0.013  -0.013
## 351                   v22 ~~                   v64  17.678 -0.044  -0.044
## 352                   v22 ~~                   v65   6.456 -0.028  -0.028
## 353                   v22 ~~                   v71   0.002  0.000   0.000
## 354                   v22 ~~                   v72   1.828 -0.005  -0.005
## 355                   v22 ~~                   v73   0.043  0.001   0.001
## 356                   v22 ~~                   v74   0.705  0.004   0.004
## 357                   v22 ~~                   v75   0.428  0.003   0.003
## 358                   v23 ~~                   v24 165.033  0.134   0.134
## 359                   v23 ~~                   v25  67.212  0.089   0.089
## 360                   v23 ~~                   v31  60.422 -0.099  -0.099
## 361                   v23 ~~                   v32 123.986 -0.131  -0.131
## 362                   v23 ~~                   v33  29.775 -0.061  -0.061
## 363                   v23 ~~                   v34 117.919 -0.121  -0.121
## 364                   v23 ~~                   v35  80.019 -0.100  -0.100
## 365                   v23 ~~                   v41  25.681 -0.064  -0.064
## 366                   v23 ~~                   v42   2.019 -0.016  -0.016
## 367                   v23 ~~                   v43  24.730  0.056   0.056
## 368                   v23 ~~                   v44  16.980 -0.045  -0.045
## 369                   v23 ~~                   v45  54.463 -0.083  -0.083
## 370                   v23 ~~                   v51   2.116 -0.017  -0.017
## 371                   v23 ~~                   v52   0.016 -0.001  -0.001
## 372                   v23 ~~                   v53  98.640  0.107   0.107
## 373                   v23 ~~                   v54  10.953  0.036   0.036
## 374                   v23 ~~                   v55   0.455 -0.007  -0.007
## 375                   v23 ~~                   v61   1.683 -0.017  -0.017
## 376                   v23 ~~                   v62   2.993 -0.020  -0.020
## 377                   v23 ~~                   v63  29.482  0.058   0.058
## 378                   v23 ~~                   v64   4.126 -0.021  -0.021
## 379                   v23 ~~                   v65  12.625 -0.038  -0.038
## 380                   v23 ~~                   v71   0.055 -0.001  -0.001
## 381                   v23 ~~                   v72   0.039  0.001   0.001
## 382                   v23 ~~                   v73   0.198  0.002   0.002
## 383                   v23 ~~                   v74   0.424 -0.003  -0.003
## 384                   v23 ~~                   v75   0.176  0.002   0.002
## 385                   v24 ~~                   v25 132.249  0.122   0.122
## 386                   v24 ~~                   v31 116.042 -0.133  -0.133
## 387                   v24 ~~                   v32 108.967 -0.120  -0.120
## 388                   v24 ~~                   v33 120.953 -0.120  -0.120
## 389                   v24 ~~                   v34   1.794 -0.015  -0.015
## 390                   v24 ~~                   v35  61.467 -0.086  -0.086
## 391                   v24 ~~                   v41  31.540 -0.069  -0.069
## 392                   v24 ~~                   v42  29.925 -0.060  -0.060
## 393                   v24 ~~                   v43  26.981 -0.057  -0.057
## 394                   v24 ~~                   v44   5.787  0.026   0.026
## 395                   v24 ~~                   v45  10.466 -0.036  -0.036
## 396                   v24 ~~                   v51  10.088 -0.037  -0.037
## 397                   v24 ~~                   v52   2.958  0.019   0.019
## 398                   v24 ~~                   v53  21.462  0.048   0.048
## 399                   v24 ~~                   v54 106.082  0.108   0.108
## 400                   v24 ~~                   v55   8.100  0.030   0.030
## 401                   v24 ~~                   v61  19.857 -0.056  -0.056
## 402                   v24 ~~                   v62  11.751 -0.038  -0.038
## 403                   v24 ~~                   v63   0.622 -0.008  -0.008
## 404                   v24 ~~                   v64  10.394  0.032   0.032
## 405                   v24 ~~                   v65   2.623 -0.017  -0.017
## 406                   v24 ~~                   v71   1.732 -0.006  -0.006
## 407                   v24 ~~                   v72   1.098  0.004   0.004
## 408                   v24 ~~                   v73   0.346  0.002   0.002
## 409                   v24 ~~                   v74   1.443 -0.005  -0.005
## 410                   v24 ~~                   v75   8.453  0.013   0.013
## 411                   v25 ~~                   v31  41.517 -0.083  -0.083
## 412                   v25 ~~                   v32  32.611 -0.068  -0.068
## 413                   v25 ~~                   v33  91.526 -0.108  -0.108
## 414                   v25 ~~                   v34  13.911 -0.042  -0.042
## 415                   v25 ~~                   v35  12.675 -0.041  -0.041
## 416                   v25 ~~                   v41  24.105 -0.064  -0.064
## 417                   v25 ~~                   v42  14.030 -0.043  -0.043
## 418                   v25 ~~                   v43  29.005 -0.062  -0.062
## 419                   v25 ~~                   v44  44.278 -0.075  -0.075
## 420                   v25 ~~                   v45  10.102  0.037   0.037
## 421                   v25 ~~                   v51   0.392 -0.008  -0.008
## 422                   v25 ~~                   v52   0.006 -0.001  -0.001
## 423                   v25 ~~                   v53   1.296  0.012   0.012
## 424                   v25 ~~                   v54  27.600  0.058   0.058
## 425                   v25 ~~                   v55 162.443  0.142   0.142
## 426                   v25 ~~                   v61   0.096  0.004   0.004
## 427                   v25 ~~                   v62  14.960 -0.045  -0.045
## 428                   v25 ~~                   v63   2.614 -0.018  -0.018
## 429                   v25 ~~                   v64  35.859 -0.062  -0.062
## 430                   v25 ~~                   v65  12.423  0.038   0.038
## 431                   v25 ~~                   v71   7.474  0.012   0.012
## 432                   v25 ~~                   v72   2.581 -0.007  -0.007
## 433                   v25 ~~                   v73   0.108 -0.001  -0.001
## 434                   v25 ~~                   v74   2.495 -0.007  -0.007
## 435                   v25 ~~                   v75   4.306  0.009   0.009
## 436                   v31 ~~                   v32 121.275  0.155   0.155
## 437                   v31 ~~                   v33  92.675  0.128   0.128
## 438                   v31 ~~                   v34  17.261  0.055   0.055
## 439                   v31 ~~                   v35  38.307  0.083   0.083
## 440                   v31 ~~                   v41 115.029  0.166   0.166
## 441                   v31 ~~                   v42   1.984  0.019   0.019
## 442                   v31 ~~                   v43   1.634 -0.018  -0.018
## 443                   v31 ~~                   v44   0.338  0.008   0.008
## 444                   v31 ~~                   v45   0.457  0.009   0.009
## 445                   v31 ~~                   v51  14.080  0.055   0.055
## 446                   v31 ~~                   v52   1.266 -0.015  -0.015
## 447                   v31 ~~                   v53  35.488 -0.078  -0.078
## 448                   v31 ~~                   v54  21.547 -0.061  -0.061
## 449                   v31 ~~                   v55  15.622 -0.052  -0.052
## 450                   v31 ~~                   v61  87.096  0.145   0.145
## 451                   v31 ~~                   v62   7.231  0.038   0.038
## 452                   v31 ~~                   v63   2.129 -0.019  -0.019
## 453                   v31 ~~                   v64   1.042 -0.013  -0.013
## 454                   v31 ~~                   v65   4.453 -0.027  -0.027
## 455                   v31 ~~                   v71   0.194 -0.002  -0.002
## 456                   v31 ~~                   v72   0.304  0.003   0.003
## 457                   v31 ~~                   v73   0.266 -0.003  -0.003
## 458                   v31 ~~                   v74   1.711  0.007   0.007
## 459                   v31 ~~                   v75   0.318 -0.003  -0.003
## 460                   v32 ~~                   v33 138.181  0.145   0.145
## 461                   v32 ~~                   v34  46.460  0.084   0.084
## 462                   v32 ~~                   v35  54.471  0.092   0.092
## 463                   v32 ~~                   v41  11.014  0.047   0.047
## 464                   v32 ~~                   v42  46.780  0.086   0.086
## 465                   v32 ~~                   v43   0.063  0.003   0.003
## 466                   v32 ~~                   v44   0.087 -0.004  -0.004
## 467                   v32 ~~                   v45   0.870 -0.012  -0.012
## 468                   v32 ~~                   v51   0.000  0.000   0.000
## 469                   v32 ~~                   v52   3.104  0.022   0.022
## 470                   v32 ~~                   v53  26.772 -0.062  -0.062
## 471                   v32 ~~                   v54  18.160 -0.051  -0.051
## 472                   v32 ~~                   v55   0.002  0.001   0.001
## 473                   v32 ~~                   v61   4.142  0.029   0.029
## 474                   v32 ~~                   v62  40.195  0.081   0.081
## 475                   v32 ~~                   v63   0.091 -0.004  -0.004
## 476                   v32 ~~                   v64   3.256 -0.021  -0.021
## 477                   v32 ~~                   v65  10.012 -0.038  -0.038
## 478                   v32 ~~                   v71   0.871  0.005   0.005
## 479                   v32 ~~                   v72   0.220 -0.002  -0.002
## 480                   v32 ~~                   v73   0.261 -0.002  -0.002
## 481                   v32 ~~                   v74   5.043 -0.011  -0.011
## 482                   v32 ~~                   v75   4.866  0.011   0.011
## 483                   v33 ~~                   v34  90.331  0.111   0.111
## 484                   v33 ~~                   v35 168.759  0.152   0.152
## 485                   v33 ~~                   v41  21.053  0.061   0.061
## 486                   v33 ~~                   v42   7.979  0.034   0.034
## 487                   v33 ~~                   v43  66.447  0.097   0.097
## 488                   v33 ~~                   v44   4.087  0.023   0.023
## 489                   v33 ~~                   v45   9.413  0.036   0.036
## 490                   v33 ~~                   v51   0.001  0.000   0.000
## 491                   v33 ~~                   v52  14.540 -0.045  -0.045
## 492                   v33 ~~                   v53   0.295 -0.006  -0.006
## 493                   v33 ~~                   v54  57.281 -0.086  -0.086
## 494                   v33 ~~                   v55  52.376 -0.083  -0.083
## 495                   v33 ~~                   v61   1.119  0.014   0.014
## 496                   v33 ~~                   v62   4.595  0.026   0.026
## 497                   v33 ~~                   v63  21.961  0.052   0.052
## 498                   v33 ~~                   v64   0.986  0.011   0.011
## 499                   v33 ~~                   v65   0.323 -0.006  -0.006
## 500                   v33 ~~                   v71   1.799 -0.006  -0.006
## 501                   v33 ~~                   v72   1.479  0.005   0.005
## 502                   v33 ~~                   v73   0.005  0.000   0.000
## 503                   v33 ~~                   v74   0.938 -0.004  -0.004
## 504                   v33 ~~                   v75   0.000  0.000   0.000
## 505                   v34 ~~                   v35 114.536  0.126   0.126
## 506                   v34 ~~                   v41   4.699 -0.029  -0.029
## 507                   v34 ~~                   v42   0.660  0.010   0.010
## 508                   v34 ~~                   v43  16.355  0.048   0.048
## 509                   v34 ~~                   v44 105.615  0.119   0.119
## 510                   v34 ~~                   v45  24.603  0.059   0.059
## 511                   v34 ~~                   v51  23.800 -0.061  -0.061
## 512                   v34 ~~                   v52  23.108 -0.057  -0.057
## 513                   v34 ~~                   v53  38.190 -0.070  -0.070
## 514                   v34 ~~                   v54  17.371 -0.047  -0.047
## 515                   v34 ~~                   v55  10.837 -0.038  -0.038
## 516                   v34 ~~                   v61   9.725 -0.042  -0.042
## 517                   v34 ~~                   v62   1.911 -0.017  -0.017
## 518                   v34 ~~                   v63   1.244 -0.012  -0.012
## 519                   v34 ~~                   v64  56.370  0.080   0.080
## 520                   v34 ~~                   v65  16.888  0.046   0.046
## 521                   v34 ~~                   v71   2.317  0.007   0.007
## 522                   v34 ~~                   v72   1.396 -0.005  -0.005
## 523                   v34 ~~                   v73   1.599  0.005   0.005
## 524                   v34 ~~                   v74   0.547  0.003   0.003
## 525                   v34 ~~                   v75   4.000 -0.009  -0.009
## 526                   v35 ~~                   v41  15.942  0.054   0.054
## 527                   v35 ~~                   v42   3.093  0.021   0.021
## 528                   v35 ~~                   v43  21.229  0.055   0.055
## 529                   v35 ~~                   v44  18.539  0.050   0.050
## 530                   v35 ~~                   v45  53.914  0.088   0.088
## 531                   v35 ~~                   v51  15.631 -0.050  -0.050
## 532                   v35 ~~                   v52  27.795 -0.063  -0.063
## 533                   v35 ~~                   v53  56.882 -0.086  -0.086
## 534                   v35 ~~                   v54  15.020 -0.044  -0.044
## 535                   v35 ~~                   v55   2.992 -0.020  -0.020
## 536                   v35 ~~                   v61   0.586  0.010   0.010
## 537                   v35 ~~                   v62   5.540 -0.029  -0.029
## 538                   v35 ~~                   v63   0.382 -0.007  -0.007
## 539                   v35 ~~                   v64   0.847  0.010   0.010
## 540                   v35 ~~                   v65  51.159  0.081   0.081
## 541                   v35 ~~                   v71   0.484 -0.003  -0.003
## 542                   v35 ~~                   v72   3.085  0.007   0.007
## 543                   v35 ~~                   v73   1.348 -0.005  -0.005
## 544                   v35 ~~                   v74   0.437  0.003   0.003
## 545                   v35 ~~                   v75   1.885 -0.007  -0.007
## 546                   v41 ~~                   v42 149.079  0.172   0.172
## 547                   v41 ~~                   v43  39.681  0.089   0.089
## 548                   v41 ~~                   v44  27.187  0.072   0.072
## 549                   v41 ~~                   v45  32.061  0.080   0.080
## 550                   v41 ~~                   v51   5.580  0.035   0.035
## 551                   v41 ~~                   v52 110.853 -0.148  -0.148
## 552                   v41 ~~                   v53  89.874 -0.128  -0.128
## 553                   v41 ~~                   v54 116.665 -0.146  -0.146
## 554                   v41 ~~                   v55 141.985 -0.162  -0.162
## 555                   v41 ~~                   v61 262.235  0.256   0.256
## 556                   v41 ~~                   v62   0.208 -0.006  -0.006
## 557                   v41 ~~                   v63   0.814 -0.012  -0.012
## 558                   v41 ~~                   v64   0.006 -0.001  -0.001
## 559                   v41 ~~                   v65   0.911 -0.013  -0.013
## 560                   v41 ~~                   v71   0.996 -0.005  -0.005
## 561                   v41 ~~                   v72   0.642  0.004   0.004
## 562                   v41 ~~                   v73   1.642 -0.006  -0.006
## 563                   v41 ~~                   v74   0.259  0.003   0.003
## 564                   v41 ~~                   v75   0.306 -0.003  -0.003
## 565                   v42 ~~                   v43 132.087  0.146   0.146
## 566                   v42 ~~                   v44  57.245  0.094   0.094
## 567                   v42 ~~                   v45  76.763  0.111   0.111
## 568                   v42 ~~                   v51  80.746 -0.120  -0.120
## 569                   v42 ~~                   v52  13.279 -0.046  -0.046
## 570                   v42 ~~                   v53 156.641 -0.152  -0.152
## 571                   v42 ~~                   v54 214.120 -0.178  -0.178
## 572                   v42 ~~                   v55 156.423 -0.153  -0.153
## 573                   v42 ~~                   v61   0.599  0.011   0.011
## 574                   v42 ~~                   v62 226.165  0.190   0.190
## 575                   v42 ~~                   v63   0.611  0.009   0.009
## 576                   v42 ~~                   v64   0.785  0.010   0.010
## 577                   v42 ~~                   v65   0.020 -0.002  -0.002
## 578                   v42 ~~                   v71   1.584 -0.006  -0.006
## 579                   v42 ~~                   v72   0.773  0.004   0.004
## 580                   v42 ~~                   v73   7.367  0.012   0.012
## 581                   v42 ~~                   v74   9.021 -0.014  -0.014
## 582                   v42 ~~                   v75   0.200 -0.002  -0.002
## 583                   v43 ~~                   v44 178.813  0.166   0.166
## 584                   v43 ~~                   v45 122.938  0.140   0.140
## 585                   v43 ~~                   v51 124.269 -0.149  -0.149
## 586                   v43 ~~                   v52 190.684 -0.175  -0.175
## 587                   v43 ~~                   v53  23.356 -0.059  -0.059
## 588                   v43 ~~                   v54 191.425 -0.168  -0.168
## 589                   v43 ~~                   v55 236.875 -0.189  -0.189
## 590                   v43 ~~                   v61  18.711 -0.061  -0.061
## 591                   v43 ~~                   v62   2.798  0.021   0.021
## 592                   v43 ~~                   v63 172.489  0.153   0.153
## 593                   v43 ~~                   v64   2.588  0.018   0.018
## 594                   v43 ~~                   v65   0.253 -0.006  -0.006
## 595                   v43 ~~                   v71   0.037 -0.001  -0.001
## 596                   v43 ~~                   v72   2.007 -0.006  -0.006
## 597                   v43 ~~                   v73   3.873  0.009   0.009
## 598                   v43 ~~                   v74   3.375 -0.009  -0.009
## 599                   v43 ~~                   v75   0.107 -0.002  -0.002
## 600                   v44 ~~                   v45 239.612  0.191   0.191
## 601                   v44 ~~                   v51 184.864 -0.177  -0.177
## 602                   v44 ~~                   v52 179.361 -0.165  -0.165
## 603                   v44 ~~                   v53 184.467 -0.161  -0.161
## 604                   v44 ~~                   v54  22.153 -0.056  -0.056
## 605                   v44 ~~                   v55 181.304 -0.161  -0.161
## 606                   v44 ~~                   v61   9.113 -0.041  -0.041
## 607                   v44 ~~                   v62  23.753 -0.060  -0.060
## 608                   v44 ~~                   v63   0.836  0.010   0.010
## 609                   v44 ~~                   v64 247.323  0.171   0.171
## 610                   v44 ~~                   v65   5.732  0.027   0.027
## 611                   v44 ~~                   v71   3.784 -0.009  -0.009
## 612                   v44 ~~                   v72   0.050  0.001   0.001
## 613                   v44 ~~                   v73   0.678  0.004   0.004
## 614                   v44 ~~                   v74   0.856  0.004   0.004
## 615                   v44 ~~                   v75   1.265 -0.005  -0.005
## 616                   v45 ~~                   v51 136.480 -0.156  -0.156
## 617                   v45 ~~                   v52 224.373 -0.189  -0.189
## 618                   v45 ~~                   v53 198.340 -0.170  -0.170
## 619                   v45 ~~                   v54 163.247 -0.155  -0.155
## 620                   v45 ~~                   v55   9.884 -0.039  -0.039
## 621                   v45 ~~                   v61   2.969  0.024   0.024
## 622                   v45 ~~                   v62   7.369 -0.034  -0.034
## 623                   v45 ~~                   v63  10.693 -0.038  -0.038
## 624                   v45 ~~                   v64   1.244 -0.012  -0.012
## 625                   v45 ~~                   v65 388.455  0.231   0.231
## 626                   v45 ~~                   v71   0.020 -0.001  -0.001
## 627                   v45 ~~                   v72   0.000  0.000   0.000
## 628                   v45 ~~                   v73   3.582  0.008   0.008
## 629                   v45 ~~                   v74   1.220  0.005   0.005
## 630                   v45 ~~                   v75  27.011 -0.025  -0.025
## 631                   v51 ~~                   v52 257.292  0.214   0.214
## 632                   v51 ~~                   v53 235.618  0.196   0.196
## 633                   v51 ~~                   v54 179.076  0.172   0.172
## 634                   v51 ~~                   v55 130.186  0.147   0.147
## 635                   v51 ~~                   v61  17.801  0.063   0.063
## 636                   v51 ~~                   v62   2.903 -0.023  -0.023
## 637                   v51 ~~                   v63   5.094 -0.028  -0.028
## 638                   v51 ~~                   v64  20.677 -0.054  -0.054
## 639                   v51 ~~                   v65  23.719 -0.060  -0.060
## 640                   v51 ~~                   v71   0.074  0.001   0.001
## 641                   v51 ~~                   v72   0.005  0.000   0.000
## 642                   v51 ~~                   v73   0.030 -0.001  -0.001
## 643                   v51 ~~                   v74   0.034 -0.001  -0.001
## 644                   v51 ~~                   v75   0.028  0.001   0.001
## 645                   v52 ~~                   v53 299.460  0.209   0.209
## 646                   v52 ~~                   v54 261.641  0.196   0.196
## 647                   v52 ~~                   v55 334.487  0.224   0.224
## 648                   v52 ~~                   v61   2.834 -0.024  -0.024
## 649                   v52 ~~                   v62  14.179  0.047   0.047
## 650                   v52 ~~                   v63  16.369 -0.047  -0.047
## 651                   v52 ~~                   v64   5.858 -0.027  -0.027
## 652                   v52 ~~                   v65  14.510 -0.044  -0.044
## 653                   v52 ~~                   v71   2.705 -0.008  -0.008
## 654                   v52 ~~                   v72   2.136  0.006   0.006
## 655                   v52 ~~                   v73   0.002  0.000   0.000
## 656                   v52 ~~                   v74   1.056  0.005   0.005
## 657                   v52 ~~                   v75   0.966  0.005   0.005
## 658                   v53 ~~                   v54 333.250  0.213   0.213
## 659                   v53 ~~                   v55 275.746  0.195   0.195
## 660                   v53 ~~                   v61  16.720 -0.055  -0.055
## 661                   v53 ~~                   v62   0.268  0.006   0.006
## 662                   v53 ~~                   v63   8.483  0.032   0.032
## 663                   v53 ~~                   v64  21.354 -0.049  -0.049
## 664                   v53 ~~                   v65  41.609 -0.072  -0.072
## 665                   v53 ~~                   v71   0.084  0.001   0.001
## 666                   v53 ~~                   v72   0.404 -0.003  -0.003
## 667                   v53 ~~                   v73   0.044 -0.001  -0.001
## 668                   v53 ~~                   v74   0.196  0.002   0.002
## 669                   v53 ~~                   v75   2.857  0.008   0.008
## 670                   v54 ~~                   v55 464.568  0.254   0.254
## 671                   v54 ~~                   v61   3.061 -0.023  -0.023
## 672                   v54 ~~                   v62  38.376 -0.075  -0.075
## 673                   v54 ~~                   v63  22.528 -0.053  -0.053
## 674                   v54 ~~                   v64   0.299  0.006   0.006
## 675                   v54 ~~                   v65  26.812 -0.058  -0.058
## 676                   v54 ~~                   v71  10.778  0.015   0.015
## 677                   v54 ~~                   v72   5.291 -0.010  -0.010
## 678                   v54 ~~                   v73   5.926 -0.010  -0.010
## 679                   v54 ~~                   v74   0.778  0.004   0.004
## 680                   v54 ~~                   v75  10.024  0.015   0.015
## 681                   v55 ~~                   v61   0.207 -0.006  -0.006
## 682                   v55 ~~                   v62   8.635 -0.036  -0.036
## 683                   v55 ~~                   v63  21.695 -0.052  -0.052
## 684                   v55 ~~                   v64  46.703 -0.074  -0.074
## 685                   v55 ~~                   v65   1.435  0.014   0.014
## 686                   v55 ~~                   v71   6.910  0.012   0.012
## 687                   v55 ~~                   v72   0.137 -0.002  -0.002
## 688                   v55 ~~                   v73   9.675 -0.013  -0.013
## 689                   v55 ~~                   v74   1.064  0.005   0.005
## 690                   v55 ~~                   v75   2.759  0.008   0.008
## 691                   v61 ~~                   v62  11.620  0.050   0.050
## 692                   v61 ~~                   v63   0.724 -0.012  -0.012
## 693                   v61 ~~                   v64  10.964 -0.044  -0.044
## 694                   v61 ~~                   v65   0.003 -0.001  -0.001
## 695                   v61 ~~                   v71   1.303 -0.006  -0.006
## 696                   v61 ~~                   v72   0.090  0.001   0.001
## 697                   v61 ~~                   v73   0.971 -0.005  -0.005
## 698                   v61 ~~                   v74   2.386  0.008   0.008
## 699                   v61 ~~                   v75   1.458  0.007   0.007
## 700                   v62 ~~                   v63  15.427  0.050   0.050
## 701                   v62 ~~                   v64   4.987 -0.028  -0.028
## 702                   v62 ~~                   v65   3.935 -0.025  -0.025
## 703                   v62 ~~                   v71   0.019  0.001   0.001
## 704                   v62 ~~                   v72   0.079  0.001   0.001
## 705                   v62 ~~                   v73   5.089 -0.010  -0.010
## 706                   v62 ~~                   v74   1.408  0.006   0.006
## 707                   v62 ~~                   v75   2.782  0.008   0.008
## 708                   v63 ~~                   v64   4.166  0.025   0.025
## 709                   v63 ~~                   v65  18.331 -0.053  -0.053
## 710                   v63 ~~                   v71   0.041  0.001   0.001
## 711                   v63 ~~                   v72   0.054  0.001   0.001
## 712                   v63 ~~                   v73   6.045  0.010   0.010
## 713                   v63 ~~                   v74   9.174 -0.013  -0.013
## 714                   v63 ~~                   v75   0.664  0.004   0.004
## 715                   v64 ~~                   v65  18.681  0.053   0.053
## 716                   v64 ~~                   v71   3.580 -0.008  -0.008
## 717                   v64 ~~                   v72   0.990  0.004   0.004
## 718                   v64 ~~                   v73   0.068 -0.001  -0.001
## 719                   v64 ~~                   v74   6.293  0.011   0.011
## 720                   v64 ~~                   v75   1.327 -0.005  -0.005
## 721                   v65 ~~                   v71   0.005  0.000   0.000
## 722                   v65 ~~                   v72   0.214  0.002   0.002
## 723                   v65 ~~                   v73   2.173  0.006   0.006
## 724                   v65 ~~                   v74   0.589  0.003   0.003
## 725                   v65 ~~                   v75  13.823 -0.017  -0.017
## 726                   v71 ~~                   v72   6.988 -0.005  -0.005
## 727                   v71 ~~                   v73   5.919 -0.005  -0.005
## 728                   v71 ~~                   v74   0.930 -0.002  -0.002
## 729                   v71 ~~                   v75  39.307  0.013   0.013
## 730                   v72 ~~                   v73 373.140  0.036   0.036
## 731                   v72 ~~                   v74  52.441 -0.014  -0.014
## 732                   v72 ~~                   v75 103.277 -0.020  -0.020
## 733                   v73 ~~                   v74  43.591 -0.013  -0.013
## 734                   v73 ~~                   v75 125.333 -0.022  -0.022
## 735                   v74 ~~                   v75 253.533  0.033   0.033
## 736                   Att ~~                   kWh 285.949 -0.195  -0.321
## 737                   Sub ~~                   kWh  65.878  0.089   0.148
## 738                   PBC ~~                   kWh  34.677  0.076   0.158
## 739                   Int ~~                   kWh  45.266  0.084   0.314
## 740                   Int  ~                   kWh  19.983  0.061   0.114
## 741                   Int  ~    energypoverty_MEAN  38.281  0.053   0.103
## 742                   Int  ~    initial_survey_age  38.502  0.004   0.007
## 743                   Int  ~ initial_survey_hhsize  42.618  0.040   0.079
## 744                   Int  ~ initial_survey_gender  16.311  0.062   0.122
## 745                   kWh  ~                   Att 267.866 -0.739  -0.505
## 746                   kWh  ~                   Sub  16.921  0.230   0.155
## 747                   Att  ~                   kWh 303.329 -0.228  -0.334
## 748                   Att  ~    energypoverty_MEAN   3.351 -0.023  -0.036
## 749                   Att  ~    initial_survey_age  22.207  0.004   0.006
## 750                   Att  ~ initial_survey_hhsize   1.716  0.012   0.019
## 751                   Att  ~ initial_survey_gender   9.963 -0.073  -0.111
## 752                   Sub  ~                   kWh  52.539  0.090   0.133
## 753                   Sub  ~    energypoverty_MEAN   1.477  0.014   0.022
## 754                   Sub  ~    initial_survey_age   0.640 -0.001  -0.001
## 755                   Sub  ~ initial_survey_hhsize  37.150  0.051   0.079
## 756                   Sub  ~ initial_survey_gender   2.427  0.032   0.050
## 757                   PBC  ~                   kWh  60.448  0.109   0.203
## 758                   PBC  ~    energypoverty_MEAN   0.056  0.002   0.004
## 759                   PBC  ~    initial_survey_age   1.693 -0.001  -0.002
## 760                   PBC  ~ initial_survey_hhsize  95.867 -0.064  -0.125
## 761                   PBC  ~ initial_survey_gender  20.878  0.075   0.145
## 762    energypoverty_MEAN  ~                   Int   3.412  0.072   0.037
## 763    energypoverty_MEAN  ~                   kWh   5.286 -0.313  -0.300
## 764    energypoverty_MEAN  ~                   Att   1.601 -0.038  -0.025
## 765    energypoverty_MEAN  ~                   Sub   0.016 -0.004  -0.002
## 766    energypoverty_MEAN  ~                   PBC   0.159 -0.015  -0.008
## 767    initial_survey_age  ~                   Int  15.750  2.119   1.086
## 768    initial_survey_age  ~                   kWh  17.355 -7.781  -7.471
## 769    initial_survey_age  ~                   Att  22.147  1.936   1.269
## 770    initial_survey_age  ~                   Sub   0.251  0.207   0.134
## 771    initial_survey_age  ~                   PBC   5.244  1.194   0.616
## 772 initial_survey_hhsize  ~                   Int   0.385 -0.032  -0.016
## 773 initial_survey_hhsize  ~                   kWh   0.745 -0.156  -0.150
## 774 initial_survey_hhsize  ~                   Att   8.414 -0.116  -0.076
## 775 initial_survey_hhsize  ~                   Sub   0.002 -0.002  -0.001
## 776 initial_survey_hhsize  ~                   PBC  42.485 -0.329  -0.170
## 777 initial_survey_gender  ~                   Int  22.279  0.100   0.051
## 778 initial_survey_gender  ~                   kWh  20.411 -0.336  -0.322
## 779 initial_survey_gender  ~                   Att   0.276  0.009   0.006
## 780 initial_survey_gender  ~                   Sub  16.892  0.068   0.044
## 781 initial_survey_gender  ~                   PBC  20.237  0.093   0.048
##     sepc.all sepc.nox
## 1     -0.006   -0.006
## 2     -0.058   -0.058
## 3     -0.014   -0.014
## 4     -0.037   -0.037
## 5     -0.022   -0.022
## 6      0.024    0.024
## 7     -0.016   -0.016
## 8      0.057    0.057
## 9      0.001    0.001
## 10     0.098    0.098
## 11     0.241    0.241
## 12     0.168    0.168
## 13     0.254    0.254
## 14     0.258    0.258
## 15     0.267    0.267
## 16    -0.140   -0.140
## 17    -0.260   -0.260
## 18    -0.198   -0.198
## 19    -0.185   -0.185
## 20    -0.249   -0.249
## 21    -0.064   -0.064
## 22    -0.079   -0.079
## 23    -0.045   -0.045
## 24    -0.006   -0.006
## 25     0.072    0.072
## 26    -0.021   -0.021
## 27     0.000    0.000
## 28     0.009    0.009
## 29     0.004    0.004
## 30    -0.019   -0.019
## 31    -0.059   -0.059
## 32    -0.007   -0.007
## 33     0.026    0.026
## 34    -0.015   -0.015
## 35     0.031    0.031
## 36     0.212    0.212
## 37     0.252    0.252
## 38     0.240    0.240
## 39     0.223    0.223
## 40     0.176    0.176
## 41    -0.267   -0.267
## 42    -0.209   -0.209
## 43    -0.199   -0.199
## 44    -0.193   -0.193
## 45    -0.145   -0.145
## 46     0.129    0.129
## 47     0.009    0.009
## 48     0.061    0.061
## 49    -0.065   -0.065
## 50    -0.047   -0.047
## 51    -0.023   -0.023
## 52     0.000    0.000
## 53     0.010    0.010
## 54     0.004    0.004
## 55     0.011    0.011
## 56    -0.080   -0.080
## 57    -0.017   -0.017
## 58     0.024    0.024
## 59     0.003    0.003
## 60     0.034    0.034
## 61    -0.002   -0.002
## 62    -0.030   -0.030
## 63    -0.005   -0.005
## 64     0.011    0.011
## 65     0.004    0.004
## 66    -0.067   -0.067
## 67    -0.011   -0.011
## 68     0.052    0.052
## 69    -0.026   -0.026
## 70     0.046    0.046
## 71     0.047    0.047
## 72     0.012    0.012
## 73    -0.034   -0.034
## 74    -0.027   -0.027
## 75     0.027    0.027
## 76    -0.019   -0.019
## 77    -0.003   -0.003
## 78     0.010    0.010
## 79     0.009    0.009
## 80     0.000    0.000
## 81    -0.106   -0.106
## 82     0.000    0.000
## 83     0.083    0.083
## 84    -0.025   -0.025
## 85     0.009    0.009
## 86    -0.017   -0.017
## 87    -0.142   -0.142
## 88    -0.053   -0.053
## 89    -0.103   -0.103
## 90    -0.150   -0.150
## 91     0.034    0.034
## 92     0.009    0.009
## 93     0.192    0.192
## 94     0.130    0.130
## 95     0.178    0.178
## 96     0.370    0.370
## 97     0.482    0.482
## 98     0.501    0.501
## 99     0.506    0.506
## 100    0.485    0.485
## 101   -0.413   -0.413
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## 715    0.125    0.125
## 716   -0.048   -0.048
## 717    0.026    0.026
## 718   -0.007   -0.007
## 719    0.064    0.064
## 720   -0.029   -0.029
## 721   -0.002   -0.002
## 722    0.012    0.012
## 723    0.037    0.037
## 724    0.019    0.019
## 725   -0.091   -0.091
## 726   -0.078   -0.078
## 727   -0.071   -0.071
## 728   -0.027   -0.027
## 729    0.170    0.170
## 730    0.619    0.619
## 731   -0.220   -0.220
## 732   -0.298   -0.298
## 733   -0.198   -0.198
## 734   -0.324   -0.324
## 735    0.442    0.442
## 736   -0.321   -0.321
## 737    0.148    0.148
## 738    0.158    0.158
## 739    0.314    0.314
## 740    0.114    0.114
## 741    0.094    0.103
## 742    0.095    0.007
## 743    0.100    0.079
## 744    0.062    0.122
## 745   -0.505   -0.505
## 746    0.155    0.155
## 747   -0.334   -0.334
## 748   -0.033   -0.036
## 749    0.084    0.006
## 750    0.023    0.019
## 751   -0.056   -0.111
## 752    0.133    0.133
## 753    0.020    0.022
## 754   -0.013   -0.001
## 755    0.099    0.079
## 756    0.025    0.050
## 757    0.203    0.203
## 758    0.004    0.004
## 759   -0.021   -0.002
## 760   -0.157   -0.125
## 761    0.073    0.145
## 762    0.040    0.040
## 763   -0.327   -0.327
## 764   -0.027   -0.027
## 765   -0.003   -0.003
## 766   -0.008   -0.008
## 767    0.084    0.084
## 768   -0.575   -0.575
## 769    0.098    0.098
## 770    0.010    0.010
## 771    0.047    0.047
## 772   -0.013   -0.013
## 773   -0.119   -0.119
## 774   -0.060   -0.060
## 775   -0.001   -0.001
## 776   -0.135   -0.135
## 777    0.101    0.101
## 778   -0.636   -0.636
## 779    0.011    0.011
## 780    0.086    0.086
## 781    0.095    0.095
#Modification Indices
mod_ind <- modificationindices(fit)
#Spotting the top 10
head_mod <- head(mod_ind[order(mod_ind$mi, decreasing=TRUE), ], 10)
head_mod
##     lhs op rhs      mi    epc sepc.lv sepc.all sepc.nox
## 767 v54 ~~ v55 464.568  0.254   0.254    0.508    0.508
## 722 v45 ~~ v65 388.455  0.231   0.231    0.460    0.460
## 827 v72 ~~ v73 373.140  0.036   0.036    0.619    0.619
## 744 v52 ~~ v55 334.487  0.224   0.224    0.424    0.424
## 755 v53 ~~ v54 333.250  0.213   0.213    0.433    0.433
## 848 Att  ~ kWh 303.329 -0.228  -0.334   -0.334   -0.334
## 742 v52 ~~ v53 299.460  0.209   0.209    0.404    0.404
## 196 Int =~ v44 286.552  0.988   0.507    0.506    0.506
## 834 Att ~~ kWh 285.949 -0.195  -0.321   -0.321   -0.321
## 756 v53 ~~ v55 275.746  0.195   0.195    0.393    0.393
#Making a graph
png("initial_SEM_diagram.png", width = 800, height = 600)
semPlot::semPaths(fit, whatLabels = "std", layout = "tree", rotation = 2)
dev.off()
## png 
##   2

Initial Longitudinal MODEL

original_longitudinal_model <- '#Defining latent variables#
#Defining indicators for week 1
f1_w1 =~ v11
f2_w1 =~ v21 + v31
f3_w1 =~ v41 + v51
f4_w1 =~ v61
f5_w1 =~ v71

#Defining indicators for week 2
f1_w2 =~ v12
f2_w2 =~ v22 + v32
f3_w2 =~ v42 + v52
f4_w2 =~ v62
f5_w2 =~ v72

#Defining indicators for week 3
f1_w3 =~ v13
f2_w3 =~ v23 + v33
f3_w3 =~ v43 + v53
f4_w3 =~ v63
f5_w3 =~ v73

#Defining indicators for week 4
f1_w4 =~ v14
f2_w4 =~ v24 + v34
f3_w4 =~ v44 + v54
f4_w4 =~ v64
f5_w4 =~ v74

#Defining indicators for week 5
f1_w5 =~ v15
f2_w5 =~ v25 + v35
f3_w5 =~ v45 + v55
f4_w5 =~ v65
f5_w5 =~ v75


#Specifying temporal dependencies & Structural relationships#
#Autoregressive effects for attitude
f1_w2 ~ f1_w1
f1_w3 ~ f1_w2
f1_w4 ~ f1_w3
f1_w5 ~ f1_w4

#Autoregressive effects for subjective norms
f2_w2 ~ f2_w1
f2_w3 ~ f2_w2
f2_w4 ~ f2_w3
f2_w5 ~ f2_w4

#Autoregressive effects for perceived behavioral control
f3_w2 ~ f3_w1
f3_w3 ~ f3_w2
f3_w4 ~ f3_w3
f3_w5 ~ f3_w4

#Autoregressive effects for intention
f4_w1 ~ f1_w1 + f2_w1 + f3_w1
f4_w2 ~ f1_w2 + f2_w2 + f3_w2 + alpha * f4_w1
f4_w3 ~ f1_w3 + f2_w3 + f3_w3 + beta* f4_w2
f4_w4 ~ f1_w4 + f2_w4 + f3_w4 + gamma * f4_w3
f4_w5 ~ f1_w5 + f2_w5 + f3_w5 + delta * f4_w4

#Autoregressive effects for actual consumption
f5_w1 ~ f4_w1 + f3_w1 + energypoverty_MEAN + initial_survey_age + initial_survey_hhsize + initial_survey_gender
f5_w2 ~ f4_w2 + epsilon * f5_w1 + f3_w2
f5_w3 ~ f4_w3 + zeta * f5_w2 + f3_w3
f5_w4 ~ f4_w4 + eta * f5_w3 + f3_w4
f5_w5 ~ f4_w5 + theta * f5_w4 + f3_w5


#Covariance between latent variables at the same time point
#Week 1
f1_w1 ~~ f2_w1
f1_w1 ~~ f3_w1
f2_w1 ~~ f3_w1

#Week 2
f1_w2 ~~ f2_w2
f1_w2 ~~ f3_w2
f2_w2 ~~ f3_w2

#Week 3
f1_w3 ~~ f2_w3
f1_w3 ~~ f3_w3
f2_w3 ~~ f3_w3

#Week 4
f1_w4 ~~ f2_w4
f1_w4 ~~ f3_w4
f2_w4 ~~ f3_w4

#Week5
f1_w5 ~~ f2_w5
f1_w5 ~~ f3_w5
f2_w5 ~~ f3_w5
'

#ANALYSIS#
#Fitting the PPLGM
original_longitudinal_model_fit <- sem(original_longitudinal_model, data = noneg_data_standardized, control = list(maxit = 10000), estimator = "MLR")
## Warning in lav_object_post_check(object): lavaan WARNING: some estimated lv
## variances are negative
summary(original_longitudinal_model_fit, fit.measures=TRUE, standardized=TRUE, rsquare=TRUE)
## lavaan 0.6.16 ended normally after 78 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                       119
## 
##                                                   Used       Total
##   Number of observations                          2352        2363
## 
## Model Test User Model:
##                                                Standard      Scaled
##   Test Statistic                              13047.475    7963.642
##   Degrees of freedom                                651         651
##   P-value (Chi-square)                            0.000       0.000
##   Scaling correction factor                                   1.638
##     Yuan-Bentler correction (Mplus variant)                        
## 
## Model Test Baseline Model:
## 
##   Test statistic                             66738.515   34860.589
##   Degrees of freedom                               735         735
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.914
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.812       0.786
##   Tucker-Lewis Index (TLI)                       0.788       0.758
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.817
##   Robust Tucker-Lewis Index (TLI)                            0.793
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -88377.250  -88377.250
##   Scaling correction factor                                  3.414
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -81853.513  -81853.513
##   Scaling correction factor                                  1.913
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                              176992.501  176992.501
##   Bayesian (BIC)                            177678.300  177678.300
##   Sample-size adjusted Bayesian (SABIC)     177300.213  177300.213
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.090       0.069
##   90 Percent confidence interval - lower         0.089       0.068
##   90 Percent confidence interval - upper         0.091       0.070
##   P-value H_0: RMSEA <= 0.050                    0.000       0.000
##   P-value H_0: RMSEA >= 0.080                    1.000       0.000
##                                                                   
##   Robust RMSEA                                               0.088
##   90 Percent confidence interval - lower                     0.087
##   90 Percent confidence interval - upper                     0.090
##   P-value H_0: Robust RMSEA <= 0.050                         0.000
##   P-value H_0: Robust RMSEA >= 0.080                         1.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.101       0.101
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   f1_w1 =~                                                              
##     v11               1.000                               1.000    1.000
##   f2_w1 =~                                                              
##     v21               1.000                               0.736    0.735
##     v31               0.854    0.043   19.658    0.000    0.628    0.629
##   f3_w1 =~                                                              
##     v41               1.000                               0.748    0.748
##     v51               0.686    0.050   13.717    0.000    0.513    0.513
##   f4_w1 =~                                                              
##     v61               1.000                               1.001    1.000
##   f5_w1 =~                                                              
##     v71               1.000                               1.001    1.000
##   f1_w2 =~                                                              
##     v12               1.000                               0.831    1.000
##   f2_w2 =~                                                              
##     v22               1.000                               0.735    0.744
##     v32               0.885    0.035   25.005    0.000    0.651    0.657
##   f3_w2 =~                                                              
##     v42               1.000                               0.783    0.791
##     v52               0.714    0.046   15.618    0.000    0.559    0.561
##   f4_w2 =~                                                              
##     v62               1.000                               0.992    1.000
##   f5_w2 =~                                                              
##     v72               1.000                               1.001    1.000
##   f1_w3 =~                                                              
##     v13               1.000                               0.858    1.000
##   f2_w3 =~                                                              
##     v23               1.000                               0.731    0.747
##     v33               0.936    0.039   24.271    0.000    0.684    0.698
##   f3_w3 =~                                                              
##     v43               1.000                               0.751    0.770
##     v53               0.766    0.044   17.302    0.000    0.575    0.583
##   f4_w3 =~                                                              
##     v63               1.000                               0.974    1.000
##   f5_w3 =~                                                              
##     v73               1.000                               1.001    1.000
##   f1_w4 =~                                                              
##     v14               1.000                               0.874    1.000
##   f2_w4 =~                                                              
##     v24               1.000                               0.737    0.760
##     v34               0.930    0.033   28.488    0.000    0.686    0.703
##   f3_w4 =~                                                              
##     v44               1.000                               0.769    0.794
##     v54               0.734    0.043   17.112    0.000    0.564    0.574
##   f4_w4 =~                                                              
##     v64               1.000                               0.971    1.000
##   f5_w4 =~                                                              
##     v74               1.000                               1.001    1.000
##   f1_w5 =~                                                              
##     v15               1.000                               0.856    1.000
##   f2_w5 =~                                                              
##     v25               1.000                               0.653    0.677
##     v35               0.955    0.036   26.265    0.000    0.624    0.645
##   f3_w5 =~                                                              
##     v45               1.000                               0.783    0.815
##     v55               0.706    0.057   12.463    0.000    0.552    0.563
##   f4_w5 =~                                                              
##     v65               1.000                               0.966    1.000
##   f5_w5 =~                                                              
##     v75               1.000                               0.998    1.000
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   f1_w2 ~                                                               
##     f1_w1             0.457    0.018   25.205    0.000    0.550    0.550
##   f1_w3 ~                                                               
##     f1_w2             0.658    0.021   31.681    0.000    0.637    0.637
##   f1_w4 ~                                                               
##     f1_w3             0.683    0.019   35.646    0.000    0.671    0.671
##   f1_w5 ~                                                               
##     f1_w4             0.707    0.017   40.421    0.000    0.721    0.721
##   f2_w2 ~                                                               
##     f2_w1             0.834    0.035   23.837    0.000    0.835    0.835
##   f2_w3 ~                                                               
##     f2_w2             0.944    0.028   33.534    0.000    0.950    0.950
##   f2_w4 ~                                                               
##     f2_w3             0.963    0.027   36.349    0.000    0.955    0.955
##   f2_w5 ~                                                               
##     f2_w4             0.923    0.025   36.262    0.000    1.042    1.042
##   f3_w2 ~                                                               
##     f3_w1             0.783    0.039   20.062    0.000    0.748    0.748
##   f3_w3 ~                                                               
##     f3_w2             0.844    0.031   27.286    0.000    0.880    0.880
##   f3_w4 ~                                                               
##     f3_w3             0.917    0.028   32.989    0.000    0.895    0.895
##   f3_w5 ~                                                               
##     f3_w4             0.864    0.027   31.834    0.000    0.848    0.848
##   f4_w1 ~                                                               
##     f1_w1             0.022    0.031    0.714    0.476    0.022    0.022
##     f2_w1             0.260    0.057    4.591    0.000    0.191    0.191
##     f3_w1             0.597    0.066    9.005    0.000    0.446    0.446
##   f4_w2 ~                                                               
##     f1_w2             0.081    0.038    2.130    0.033    0.067    0.067
##     f2_w2             0.172    0.053    3.237    0.001    0.128    0.128
##     f3_w2             0.559    0.058    9.666    0.000    0.441    0.441
##     f4_w1   (alph)    0.121    0.026    4.711    0.000    0.122    0.122
##   f4_w3 ~                                                               
##     f1_w3             0.161    0.032    4.992    0.000    0.142    0.142
##     f2_w3             0.252    0.047    5.335    0.000    0.189    0.189
##     f3_w3             0.397    0.061    6.523    0.000    0.306    0.306
##     f4_w2   (beta)    0.217    0.029    7.418    0.000    0.221    0.221
##   f4_w4 ~                                                               
##     f1_w4             0.119    0.034    3.517    0.000    0.107    0.107
##     f2_w4             0.118    0.046    2.554    0.011    0.090    0.090
##     f3_w4             0.474    0.063    7.502    0.000    0.375    0.375
##     f4_w3   (gamm)    0.284    0.030    9.562    0.000    0.285    0.285
##   f4_w5 ~                                                               
##     f1_w5             0.073    0.031    2.336    0.019    0.065    0.065
##     f2_w5             0.064    0.059    1.082    0.279    0.043    0.043
##     f3_w5             0.551    0.069    8.031    0.000    0.446    0.446
##     f4_w4   (delt)    0.289    0.032    9.057    0.000    0.291    0.291
##   f5_w1 ~                                                               
##     f4_w1             0.106    0.033    3.209    0.001    0.105    0.105
##     f3_w1            -0.344    0.049   -7.024    0.000   -0.257   -0.257
##     en_MEAN           0.069    0.021    3.223    0.001    0.069    0.063
##     intl_s_          -0.009    0.002   -5.085    0.000   -0.009   -0.116
##     intl_s_          -0.111    0.016   -6.752    0.000   -0.111   -0.140
##     intl_s_          -0.009    0.040   -0.210    0.834   -0.008   -0.004
##   f5_w2 ~                                                               
##     f4_w2             0.007    0.011    0.614    0.539    0.007    0.007
##     f5_w1   (epsl)    0.931    0.035   26.402    0.000    0.932    0.932
##     f3_w2             0.005    0.018    0.269    0.788    0.004    0.004
##   f5_w3 ~                                                               
##     f4_w3             0.002    0.011    0.210    0.834    0.002    0.002
##     f5_w2   (zeta)    0.958    0.017   54.936    0.000    0.957    0.957
##     f3_w3             0.008    0.014    0.528    0.598    0.006    0.006
##   f5_w4 ~                                                               
##     f4_w4             0.016    0.011    1.471    0.141    0.016    0.016
##     f5_w3    (eta)    0.928    0.036   26.061    0.000    0.928    0.928
##     f3_w4            -0.030    0.020   -1.535    0.125   -0.023   -0.023
##   f5_w5 ~                                                               
##     f4_w5            -0.028    0.012   -2.242    0.025   -0.027   -0.027
##     f5_w4   (thet)    0.939    0.026   36.740    0.000    0.942    0.942
##     f3_w5            -0.004    0.017   -0.243    0.808   -0.003   -0.003
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   f1_w1 ~~                                                              
##     f2_w1             0.286    0.022   12.922    0.000    0.389    0.389
##     f3_w1             0.384    0.027   14.107    0.000    0.513    0.513
##   f2_w1 ~~                                                              
##     f3_w1             0.377    0.025   15.108    0.000    0.685    0.685
##  .f1_w2 ~~                                                              
##    .f2_w2             0.106    0.012    8.909    0.000    0.380    0.380
##    .f3_w2             0.176    0.016   10.802    0.000    0.489    0.489
##  .f2_w2 ~~                                                              
##    .f3_w2             0.148    0.016    9.170    0.000    0.705    0.705
##  .f1_w3 ~~                                                              
##    .f2_w3             0.071    0.010    7.256    0.000    0.471    0.471
##    .f3_w3             0.148    0.015    9.675    0.000    0.626    0.626
##  .f2_w3 ~~                                                              
##    .f3_w3             0.077    0.011    7.110    0.000    0.947    0.947
##  .f1_w4 ~~                                                              
##    .f2_w4             0.075    0.010    7.548    0.000    0.528    0.528
##    .f3_w4             0.138    0.015    9.143    0.000    0.619    0.619
##  .f2_w4 ~~                                                              
##    .f3_w4             0.061    0.011    5.747    0.000    0.811    0.811
##  .f1_w5 ~~                                                              
##    .f2_w5             0.080    0.012    6.667    0.000    0.707    0.707
##    .f3_w5             0.140    0.016    8.563    0.000    0.570    0.570
##  .f2_w5 ~~                                                              
##    .f3_w5             0.085    0.016    5.359    0.000    1.069    1.069
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .v11               0.000                               0.000    0.000
##    .v21               0.461    0.029   16.135    0.000    0.461    0.460
##    .v31               0.604    0.029   20.902    0.000    0.604    0.605
##    .v41               0.441    0.028   15.846    0.000    0.441    0.441
##    .v51               0.737    0.034   21.767    0.000    0.737    0.737
##    .v61               0.000                               0.000    0.000
##    .v71               0.000                               0.000    0.000
##    .v12               0.000                               0.000    0.000
##    .v22               0.436    0.025   17.618    0.000    0.436    0.446
##    .v32               0.557    0.025   22.007    0.000    0.557    0.568
##    .v42               0.366    0.024   15.067    0.000    0.366    0.374
##    .v52               0.679    0.035   19.171    0.000    0.679    0.685
##    .v62               0.000                               0.000    0.000
##    .v72               0.000                               0.000    0.000
##    .v13               0.000                               0.000    0.000
##    .v23               0.423    0.023   18.203    0.000    0.423    0.442
##    .v33               0.492    0.026   19.082    0.000    0.492    0.513
##    .v43               0.386    0.025   15.670    0.000    0.386    0.407
##    .v53               0.642    0.034   18.650    0.000    0.642    0.660
##    .v63               0.000                               0.000    0.000
##    .v73               0.000                               0.000    0.000
##    .v14               0.000                               0.000    0.000
##    .v24               0.398    0.022   18.150    0.000    0.398    0.423
##    .v34               0.481    0.024   20.043    0.000    0.481    0.506
##    .v44               0.347    0.024   14.530    0.000    0.347    0.370
##    .v54               0.648    0.034   18.839    0.000    0.648    0.671
##    .v64               0.000                               0.000    0.000
##    .v74               0.000                               0.000    0.000
##    .v15               0.000                               0.000    0.000
##    .v25               0.502    0.026   19.616    0.000    0.502    0.541
##    .v35               0.545    0.025   21.449    0.000    0.545    0.584
##    .v45               0.310    0.043    7.264    0.000    0.310    0.336
##    .v55               0.658    0.039   16.877    0.000    0.658    0.683
##    .v65               0.000                               0.000    0.000
##    .v75               0.000                               0.000    0.000
##     f1_w1             1.000    0.029   34.965    0.000    1.000    1.000
##     f2_w1             0.541    0.033   16.211    0.000    1.000    1.000
##     f3_w1             0.559    0.035   16.173    0.000    1.000    1.000
##    .f4_w1             0.635    0.038   16.558    0.000    0.634    0.634
##    .f5_w1             0.913    0.058   15.633    0.000    0.911    0.911
##    .f1_w2             0.481    0.020   23.898    0.000    0.697    0.697
##    .f2_w2             0.163    0.020    8.139    0.000    0.302    0.302
##    .f3_w2             0.270    0.029    9.232    0.000    0.440    0.440
##    .f4_w2             0.584    0.035   16.845    0.000    0.594    0.594
##    .f5_w2             0.134    0.029    4.654    0.000    0.134    0.134
##    .f1_w3             0.438    0.020   21.493    0.000    0.594    0.594
##    .f2_w3             0.052    0.013    4.191    0.000    0.098    0.098
##    .f3_w3             0.127    0.022    5.689    0.000    0.225    0.225
##    .f4_w3             0.504    0.026   19.068    0.000    0.532    0.532
##    .f5_w3             0.085    0.011    7.896    0.000    0.085    0.085
##    .f1_w4             0.420    0.020   21.430    0.000    0.550    0.550
##    .f2_w4             0.048    0.012    3.870    0.000    0.089    0.089
##    .f3_w4             0.117    0.022    5.344    0.000    0.199    0.199
##    .f4_w4             0.470    0.028   17.034    0.000    0.498    0.498
##    .f5_w4             0.136    0.023    6.053    0.000    0.136    0.136
##    .f1_w5             0.352    0.017   20.157    0.000    0.480    0.480
##    .f2_w5            -0.037    0.020   -1.805    0.071   -0.086   -0.086
##    .f3_w5             0.172    0.044    3.924    0.000    0.281    0.281
##    .f4_w5             0.447    0.033   13.388    0.000    0.478    0.478
##    .f5_w5             0.108    0.019    5.644    0.000    0.109    0.109
## 
## R-Square:
##                    Estimate
##     v11               1.000
##     v21               0.540
##     v31               0.395
##     v41               0.559
##     v51               0.263
##     v61               1.000
##     v71               1.000
##     v12               1.000
##     v22               0.554
##     v32               0.432
##     v42               0.626
##     v52               0.315
##     v62               1.000
##     v72               1.000
##     v13               1.000
##     v23               0.558
##     v33               0.487
##     v43               0.593
##     v53               0.340
##     v63               1.000
##     v73               1.000
##     v14               1.000
##     v24               0.577
##     v34               0.494
##     v44               0.630
##     v54               0.329
##     v64               1.000
##     v74               1.000
##     v15               1.000
##     v25               0.459
##     v35               0.416
##     v45               0.664
##     v55               0.317
##     v65               1.000
##     v75               1.000
##     f4_w1             0.366
##     f5_w1             0.089
##     f1_w2             0.303
##     f2_w2             0.698
##     f3_w2             0.560
##     f4_w2             0.406
##     f5_w2             0.866
##     f1_w3             0.406
##     f2_w3             0.902
##     f3_w3             0.775
##     f4_w3             0.468
##     f5_w3             0.915
##     f1_w4             0.450
##     f2_w4             0.911
##     f3_w4             0.801
##     f4_w4             0.502
##     f5_w4             0.864
##     f1_w5             0.520
##     f2_w5                NA
##     f3_w5             0.719
##     f4_w5             0.522
##     f5_w5             0.891
mod_ind_pplgm <- modificationindices(original_longitudinal_model_fit)
## Warning in sqrt(var.lhs.value * var.rhs.value): NaNs produced
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply NaN for a correlation value;
##                   variables involved are: f1_w5 f2_w5
# spotting the top 10
head_mod_pplgm <- head(mod_ind_pplgm[order(mod_ind_pplgm$mi, decreasing=TRUE), ], 10)
head_mod_pplgm
##      lhs op rhs      mi    epc sepc.lv sepc.all sepc.nox
## 1566 v54 ~~ v55 883.003  0.435   0.435    0.666    0.666
## 1475 v53 ~~ v54 708.106  0.382   0.382    0.593    0.593
## 1349 v52 ~~ v55 706.124  0.396   0.396    0.592    0.592
## 1482 v53 ~~ v55 690.958  0.381   0.381    0.587    0.587
## 1335 v52 ~~ v53 641.690  0.374   0.374    0.566    0.566
## 128  v15 ~~ v15 638.855 -0.759   0.000    0.000    0.000
## 1342 v52 ~~ v54 630.056  0.369   0.369    0.556    0.556
## 1153 v51 ~~ v53 586.494  0.370   0.370    0.538    0.538
## 1146 v51 ~~ v52 559.556  0.373   0.373    0.528    0.528
## 1160 v51 ~~ v54 533.185  0.353   0.353    0.511    0.511

Updated Longitudinal MODEL

updated_longitudianl_model <- '#Defining latent variables#
#Defining indicators for week 1
f1_w1 =~ v11
f2_w1 =~ v21 + v31
f3_w1 =~ v41 + v51
f4_w1 =~ v61
f5_w1 =~ v71

#Defining indicators for week 2
f1_w2 =~ v12
f2_w2 =~ v22 + v32
f3_w2 =~ v42 + v52
f4_w2 =~ v62
f5_w2 =~ v72

#Defining indicators for week 3
f1_w3 =~ v13
f2_w3 =~ v23 + v33
f3_w3 =~ v43 + v53
f4_w3 =~ v63
f5_w3 =~ v73

#Defining indicators for week 4
f1_w4 =~ v14
f2_w4 =~ v24 + v34
f3_w4 =~ v44 + v54
f4_w4 =~ v64
f5_w4 =~ v74

#Defining indicators for week 5
f1_w5 =~ v15
f2_w5 =~ v25 + v35
f3_w5 =~ v45 + v55
f4_w5 =~ v65
f5_w5 =~ v75
#look at whats going on in week five, especially for f2

#Specifying temporal dependencies & Structural relationships#
#Autoregressive effects for attitude
f1_w2 ~ f1_w1
f1_w3 ~ f1_w2
f1_w4 ~ f1_w3
f1_w5 ~ f1_w4

#Autoregressive effects for subjective norms
f2_w2 ~ f2_w1
f2_w3 ~ f2_w2
f2_w4 ~ f2_w3
f2_w5 ~ f2_w4

#Autoregressive effects for perceived behavioral control
f3_w2 ~ f3_w1
f3_w3 ~ f3_w2
f3_w4 ~ f3_w3
f3_w5 ~ f3_w4

#Autoregressive effects for intention
f4_w1 ~ f1_w1 + f2_w1 + f3_w1
f4_w2 ~ f1_w2 + f2_w2 + f3_w2 + alpha * f4_w1
f4_w3 ~ f1_w3 + f2_w3 + f3_w3 + beta* f4_w2
f4_w4 ~ f1_w4 + f2_w4 + f3_w4 + gamma * f4_w3
f4_w5 ~ f1_w5 + f2_w5 + f3_w5 + delta * f4_w4

#Autoregressive effects for actual consumption
f5_w1 ~ f4_w1 + energypoverty_MEAN + initial_survey_age + initial_survey_hhsize + initial_survey_gender + f3_w1
f5_w2 ~ f4_w2 + epsilon * f5_w1 + f3_w2
f5_w3 ~ f4_w3 + zeta * f5_w2 + f3_w3
f5_w4 ~ f4_w4 + eta * f5_w3 + f3_w4
f5_w5 ~ f4_w5 + theta * f5_w4 + f3_w5


#Covariance between latent variables at the same time point
#Week 1
f1_w1 ~~ f2_w1
f1_w1 ~~ f3_w1
f2_w1 ~~ f3_w1

#Week 2
f1_w2 ~~ f2_w2
f1_w2 ~~ f3_w2
f2_w2 ~~ f3_w2

#Week 3
f1_w3 ~~ f2_w3
f1_w3 ~~ f3_w3
f2_w3 ~~ f3_w3

#Week 4
f1_w4 ~~ f2_w4
f1_w4 ~~ f3_w4
f2_w4 ~~ f3_w4

#Week5
f1_w5 ~~ f2_w5
f1_w5 ~~ f3_w5
f2_w5 ~~ f3_w5

#V5 Covariance
v51 ~~ v52
v52 ~~ v53
v53 ~~ v54
v54 ~~ v55

v51 ~~ v53
v51 ~~ v54
v51 ~~ v55

v52 ~~ v54
v52 ~~ v55

v53 ~~ v55
'

#ANALYSIS#
#Fitting the PPLGM
updated_longitudianl_model <- sem(updated_longitudianl_model, data = noneg_data_standardized, control = list(maxit = 10000), estimator = "MLR")
## Warning in lav_object_post_check(object): lavaan WARNING: some estimated lv
## variances are negative
summary(updated_longitudianl_model, fit.measures=TRUE, standardized=TRUE, rsquare=TRUE)
## lavaan 0.6.16 ended normally after 87 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                       129
## 
##                                                   Used       Total
##   Number of observations                          2352        2363
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                              8320.083    5089.184
##   Degrees of freedom                               641         641
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.635
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                             66738.515   34860.589
##   Degrees of freedom                               735         735
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.914
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.884       0.870
##   Tucker-Lewis Index (TLI)                       0.867       0.851
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.889
##   Robust Tucker-Lewis Index (TLI)                            0.872
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -86013.554  -86013.554
##   Scaling correction factor                                  3.294
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -81853.513  -81853.513
##   Scaling correction factor                                  1.913
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                              172285.109  172285.109
##   Bayesian (BIC)                            173028.539  173028.539
##   Sample-size adjusted Bayesian (SABIC)     172618.679  172618.679
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.071       0.054
##   90 Percent confidence interval - lower         0.070       0.053
##   90 Percent confidence interval - upper         0.073       0.055
##   P-value H_0: RMSEA <= 0.050                    0.000       0.000
##   P-value H_0: RMSEA >= 0.080                    0.000       0.000
##                                                                   
##   Robust RMSEA                                               0.069
##   90 Percent confidence interval - lower                     0.068
##   90 Percent confidence interval - upper                     0.071
##   P-value H_0: Robust RMSEA <= 0.050                         0.000
##   P-value H_0: Robust RMSEA >= 0.080                         0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.098       0.098
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   f1_w1 =~                                                              
##     v11               1.000                               1.000    1.000
##   f2_w1 =~                                                              
##     v21               1.000                               0.737    0.736
##     v31               0.857    0.044   19.387    0.000    0.631    0.631
##   f3_w1 =~                                                              
##     v41               1.000                               0.781    0.781
##     v51               0.549    0.031   17.586    0.000    0.428    0.430
##   f4_w1 =~                                                              
##     v61               1.000                               1.001    1.000
##   f5_w1 =~                                                              
##     v71               1.000                               0.999    1.000
##   f1_w2 =~                                                              
##     v12               1.000                               0.826    1.000
##   f2_w2 =~                                                              
##     v22               1.000                               0.732    0.743
##     v32               0.887    0.036   24.873    0.000    0.649    0.657
##   f3_w2 =~                                                              
##     v42               1.000                               0.827    0.836
##     v52               0.510    0.028   18.099    0.000    0.422    0.430
##   f4_w2 =~                                                              
##     v62               1.000                               0.991    1.000
##   f5_w2 =~                                                              
##     v72               1.000                               0.999    1.000
##   f1_w3 =~                                                              
##     v13               1.000                               0.848    1.000
##   f2_w3 =~                                                              
##     v23               1.000                               0.726    0.745
##     v33               0.939    0.039   24.306    0.000    0.682    0.698
##   f3_w3 =~                                                              
##     v43               1.000                               0.789    0.812
##     v53               0.577    0.027   21.062    0.000    0.455    0.466
##   f4_w3 =~                                                              
##     v63               1.000                               0.970    1.000
##   f5_w3 =~                                                              
##     v73               1.000                               1.000    1.000
##   f1_w4 =~                                                              
##     v14               1.000                               0.862    1.000
##   f2_w4 =~                                                              
##     v24               1.000                               0.729    0.755
##     v34               0.936    0.033   28.783    0.000    0.682    0.703
##   f3_w4 =~                                                              
##     v44               1.000                               0.815    0.841
##     v54               0.546    0.026   20.897    0.000    0.445    0.457
##   f4_w4 =~                                                              
##     v64               1.000                               0.968    1.000
##   f5_w4 =~                                                              
##     v74               1.000                               0.999    1.000
##   f1_w5 =~                                                              
##     v15               1.000                               0.846    1.000
##   f2_w5 =~                                                              
##     v25               1.000                               0.643    0.671
##     v35               0.963    0.036   26.555    0.000    0.619    0.644
##   f3_w5 =~                                                              
##     v45               1.000                               0.860    0.892
##     v55               0.526    0.030   17.338    0.000    0.453    0.463
##   f4_w5 =~                                                              
##     v65               1.000                               0.967    1.000
##   f5_w5 =~                                                              
##     v75               1.000                               0.996    1.000
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   f1_w2 ~                                                               
##     f1_w1             0.449    0.018   24.602    0.000    0.544    0.544
##   f1_w3 ~                                                               
##     f1_w2             0.641    0.021   30.496    0.000    0.625    0.625
##   f1_w4 ~                                                               
##     f1_w3             0.671    0.019   34.598    0.000    0.660    0.660
##   f1_w5 ~                                                               
##     f1_w4             0.699    0.018   39.569    0.000    0.713    0.713
##   f2_w2 ~                                                               
##     f2_w1             0.818    0.034   23.710    0.000    0.823    0.823
##   f2_w3 ~                                                               
##     f2_w2             0.940    0.028   33.634    0.000    0.948    0.948
##   f2_w4 ~                                                               
##     f2_w3             0.953    0.026   36.023    0.000    0.949    0.949
##   f2_w5 ~                                                               
##     f2_w4             0.916    0.025   36.123    0.000    1.039    1.039
##   f3_w2 ~                                                               
##     f3_w1             0.753    0.033   23.004    0.000    0.711    0.711
##   f3_w3 ~                                                               
##     f3_w2             0.785    0.029   27.447    0.000    0.823    0.823
##   f3_w4 ~                                                               
##     f3_w3             0.875    0.027   32.722    0.000    0.846    0.846
##   f3_w5 ~                                                               
##     f3_w4             0.824    0.028   28.997    0.000    0.780    0.780
##   f4_w1 ~                                                               
##     f1_w1             0.003    0.031    0.105    0.916    0.003    0.003
##     f2_w1             0.260    0.052    4.987    0.000    0.191    0.191
##     f3_w1             0.600    0.063    9.540    0.000    0.468    0.468
##   f4_w2 ~                                                               
##     f1_w2             0.052    0.036    1.426    0.154    0.043    0.043
##     f2_w2             0.155    0.049    3.165    0.002    0.114    0.114
##     f3_w2             0.596    0.052   11.384    0.000    0.497    0.497
##     f4_w1   (alph)    0.111    0.025    4.413    0.000    0.112    0.112
##   f4_w3 ~                                                               
##     f1_w3             0.128    0.032    4.013    0.000    0.112    0.112
##     f2_w3             0.241    0.044    5.439    0.000    0.180    0.180
##     f3_w3             0.443    0.055    7.996    0.000    0.360    0.360
##     f4_w2   (beta)    0.202    0.029    7.039    0.000    0.206    0.206
##   f4_w4 ~                                                               
##     f1_w4             0.099    0.032    3.091    0.002    0.088    0.088
##     f2_w4             0.124    0.042    2.964    0.003    0.094    0.094
##     f3_w4             0.496    0.054    9.233    0.000    0.417    0.417
##     f4_w3   (gamm)    0.269    0.029    9.292    0.000    0.269    0.269
##   f4_w5 ~                                                               
##     f1_w5             0.084    0.029    2.936    0.003    0.073    0.073
##     f2_w5             0.087    0.047    1.864    0.062    0.058    0.058
##     f3_w5             0.509    0.050   10.128    0.000    0.453    0.453
##     f4_w4   (delt)    0.290    0.031    9.408    0.000    0.291    0.291
##   f5_w1 ~                                                               
##     f4_w1             0.144    0.032    4.446    0.000    0.144    0.144
##     en_MEAN           0.070    0.021    3.325    0.001    0.071    0.065
##     intl_s_          -0.009    0.002   -5.065    0.000   -0.009   -0.115
##     intl_s_          -0.102    0.016   -6.325    0.000   -0.102   -0.129
##     intl_s_          -0.011    0.040   -0.271    0.786   -0.011   -0.006
##     f3_w1            -0.406    0.048   -8.473    0.000   -0.317   -0.317
##   f5_w2 ~                                                               
##     f4_w2             0.007    0.012    0.578    0.563    0.007    0.007
##     f5_w1   (epsl)    0.931    0.036   26.025    0.000    0.932    0.932
##     f3_w2             0.004    0.019    0.192    0.848    0.003    0.003
##   f5_w3 ~                                                               
##     f4_w3             0.002    0.012    0.136    0.892    0.002    0.002
##     f5_w2   (zeta)    0.958    0.018   54.471    0.000    0.957    0.957
##     f3_w3             0.008    0.015    0.564    0.573    0.007    0.007
##   f5_w4 ~                                                               
##     f4_w4             0.021    0.011    1.877    0.061    0.021    0.021
##     f5_w3    (eta)    0.927    0.036   25.892    0.000    0.928    0.928
##     f3_w4            -0.036    0.020   -1.850    0.064   -0.030   -0.030
##   f5_w5 ~                                                               
##     f4_w5            -0.016    0.012   -1.351    0.177   -0.015   -0.015
##     f5_w4   (thet)    0.938    0.026   36.574    0.000    0.941    0.941
##     f3_w5            -0.023    0.016   -1.428    0.153   -0.020   -0.020
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   f1_w1 ~~                                                              
##     f2_w1             0.284    0.022   12.754    0.000    0.385    0.385
##     f3_w1             0.415    0.024   17.183    0.000    0.531    0.531
##   f2_w1 ~~                                                              
##     f3_w1             0.383    0.024   15.766    0.000    0.666    0.666
##  .f1_w2 ~~                                                              
##    .f2_w2             0.104    0.012    8.716    0.000    0.362    0.362
##    .f3_w2             0.189    0.016   11.763    0.000    0.469    0.469
##  .f2_w2 ~~                                                              
##    .f3_w2             0.163    0.016   10.048    0.000    0.673    0.673
##  .f1_w3 ~~                                                              
##    .f2_w3             0.070    0.010    7.134    0.000    0.458    0.458
##    .f3_w3             0.168    0.015   11.203    0.000    0.569    0.569
##  .f2_w3 ~~                                                              
##    .f3_w3             0.097    0.011    8.984    0.000    0.939    0.939
##  .f1_w4 ~~                                                              
##    .f2_w4             0.074    0.010    7.455    0.000    0.498    0.498
##    .f3_w4             0.151    0.015   10.371    0.000    0.537    0.537
##  .f2_w4 ~~                                                              
##    .f3_w4             0.073    0.011    6.389    0.000    0.728    0.728
##  .f1_w5 ~~                                                              
##    .f2_w5             0.080    0.012    6.652    0.000    0.745    0.745
##    .f3_w5             0.146    0.016    9.022    0.000    0.458    0.458
##  .f2_w5 ~~                                                              
##    .f3_w5             0.095    0.016    5.801    0.000    0.971    0.971
##  .v51 ~~                                                                
##    .v52               0.430    0.024   17.886    0.000    0.430    0.540
##  .v52 ~~                                                                
##    .v53               0.441    0.025   17.719    0.000    0.441    0.576
##  .v53 ~~                                                                
##    .v54               0.450    0.025   18.304    0.000    0.450    0.602
##  .v54 ~~                                                                
##    .v55               0.489    0.026   18.520    0.000    0.489    0.651
##  .v51 ~~                                                                
##    .v53               0.433    0.023   18.788    0.000    0.433    0.558
##    .v54               0.420    0.023   18.602    0.000    0.420    0.540
##    .v55               0.395    0.023   17.320    0.000    0.395    0.507
##  .v52 ~~                                                                
##    .v54               0.444    0.024   18.445    0.000    0.444    0.579
##    .v55               0.469    0.024   19.466    0.000    0.469    0.611
##  .v53 ~~                                                                
##    .v55               0.453    0.025   18.283    0.000    0.453    0.605
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .v11               0.000                               0.000    0.000
##    .v21               0.459    0.029   16.004    0.000    0.459    0.458
##    .v31               0.601    0.029   20.653    0.000    0.601    0.601
##    .v41               0.391    0.026   15.010    0.000    0.391    0.391
##    .v51               0.807    0.028   29.362    0.000    0.807    0.815
##    .v61               0.000                               0.000    0.000
##    .v71               0.000                               0.000    0.000
##    .v12               0.000                               0.000    0.000
##    .v22               0.436    0.025   17.491    0.000    0.436    0.448
##    .v32               0.556    0.025   22.008    0.000    0.556    0.569
##    .v42               0.294    0.020   15.021    0.000    0.294    0.301
##    .v52               0.784    0.030   26.559    0.000    0.784    0.815
##    .v62               0.000                               0.000    0.000
##    .v72               0.000                               0.000    0.000
##    .v13               0.000                               0.000    0.000
##    .v23               0.422    0.023   18.144    0.000    0.422    0.444
##    .v33               0.488    0.026   19.017    0.000    0.488    0.512
##    .v43               0.322    0.021   15.500    0.000    0.322    0.341
##    .v53               0.746    0.029   25.883    0.000    0.746    0.783
##    .v63               0.000                               0.000    0.000
##    .v73               0.000                               0.000    0.000
##    .v14               0.000                               0.000    0.000
##    .v24               0.400    0.022   18.057    0.000    0.400    0.429
##    .v34               0.476    0.024   20.049    0.000    0.476    0.506
##    .v44               0.276    0.020   13.970    0.000    0.276    0.293
##    .v54               0.750    0.029   26.123    0.000    0.750    0.791
##    .v64               0.000                               0.000    0.000
##    .v74               0.000                               0.000    0.000
##    .v15               0.000                               0.000    0.000
##    .v25               0.504    0.026   19.738    0.000    0.504    0.549
##    .v35               0.540    0.025   21.337    0.000    0.540    0.585
##    .v45               0.191    0.027    7.123    0.000    0.191    0.205
##    .v55               0.752    0.031   24.105    0.000    0.752    0.786
##    .v65               0.000                               0.000    0.000
##    .v75               0.000                               0.000    0.000
##     f1_w1             1.000    0.029   34.965    0.000    1.000    1.000
##     f2_w1             0.543    0.034   16.050    0.000    1.000    1.000
##     f3_w1             0.610    0.034   17.953    0.000    1.000    1.000
##    .f4_w1             0.623    0.037   16.639    0.000    0.623    0.623
##    .f5_w1             0.892    0.058   15.374    0.000    0.893    0.893
##    .f1_w2             0.481    0.020   23.908    0.000    0.704    0.704
##    .f2_w2             0.173    0.020    8.508    0.000    0.323    0.323
##    .f3_w2             0.338    0.029   11.761    0.000    0.494    0.494
##    .f4_w2             0.556    0.034   16.519    0.000    0.567    0.567
##    .f5_w2             0.134    0.029    4.654    0.000    0.134    0.134
##    .f1_w3             0.438    0.020   21.511    0.000    0.609    0.609
##    .f2_w3             0.054    0.013    4.214    0.000    0.102    0.102
##    .f3_w3             0.200    0.022    8.920    0.000    0.322    0.322
##    .f4_w3             0.487    0.026   18.618    0.000    0.517    0.517
##    .f5_w3             0.085    0.011    7.898    0.000    0.086    0.086
##    .f1_w4             0.419    0.020   21.453    0.000    0.564    0.564
##    .f2_w4             0.053    0.013    4.152    0.000    0.100    0.100
##    .f3_w4             0.188    0.023    8.300    0.000    0.284    0.284
##    .f4_w4             0.450    0.027   16.616    0.000    0.480    0.480
##    .f5_w4             0.136    0.022    6.063    0.000    0.136    0.136
##    .f1_w5             0.352    0.017   20.180    0.000    0.492    0.492
##    .f2_w5            -0.033    0.020   -1.626    0.104   -0.079   -0.079
##    .f3_w5             0.290    0.031    9.326    0.000    0.391    0.391
##    .f4_w5             0.429    0.028   15.472    0.000    0.459    0.459
##    .f5_w5             0.108    0.019    5.657    0.000    0.109    0.109
## 
## R-Square:
##                    Estimate
##     v11               1.000
##     v21               0.542
##     v31               0.399
##     v41               0.609
##     v51               0.185
##     v61               1.000
##     v71               1.000
##     v12               1.000
##     v22               0.552
##     v32               0.431
##     v42               0.699
##     v52               0.185
##     v62               1.000
##     v72               1.000
##     v13               1.000
##     v23               0.556
##     v33               0.488
##     v43               0.659
##     v53               0.217
##     v63               1.000
##     v73               1.000
##     v14               1.000
##     v24               0.571
##     v34               0.494
##     v44               0.707
##     v54               0.209
##     v64               1.000
##     v74               1.000
##     v15               1.000
##     v25               0.451
##     v35               0.415
##     v45               0.795
##     v55               0.214
##     v65               1.000
##     v75               1.000
##     f4_w1             0.377
##     f5_w1             0.107
##     f1_w2             0.296
##     f2_w2             0.677
##     f3_w2             0.506
##     f4_w2             0.433
##     f5_w2             0.866
##     f1_w3             0.391
##     f2_w3             0.898
##     f3_w3             0.678
##     f4_w3             0.483
##     f5_w3             0.914
##     f1_w4             0.436
##     f2_w4             0.900
##     f3_w4             0.716
##     f4_w4             0.520
##     f5_w4             0.864
##     f1_w5             0.508
##     f2_w5                NA
##     f3_w5             0.609
##     f4_w5             0.541
##     f5_w5             0.891
#Modification Indices

mod_ind_pplgm <- modificationindices(updated_longitudianl_model)
## Warning in sqrt(var.lhs.value * var.rhs.value): NaNs produced
## Warning in lav_start_check_cov(lavpartable = lavpartable, start = START): lavaan WARNING: starting values imply NaN for a correlation value;
##                   variables involved are: f1_w5 f2_w5
# spotting the top 10
head_mod_pplgm <- head(mod_ind_pplgm[order(mod_ind_pplgm$mi, decreasing=TRUE), ], 10)
head_mod_pplgm
##        lhs op   rhs      mi    epc sepc.lv sepc.all sepc.nox
## 138    v15 ~~   v15 639.569 -0.759   0.000    0.000    0.000
## 29   f1_w5 =~   v15 528.516 -0.331  -0.280   -0.331   -0.331
## 2354 f5_w1  ~ f5_w5 500.068  1.453   1.447    1.447    1.447
## 1239   v12 ~~   v13 457.764 -0.171  -0.171       NA       NA
## 1383   v72 ~~   v73 356.701 -0.028  -0.028       NA       NA
## 2398 f5_w3  ~ f5_w4 339.639 -0.315  -0.315   -0.315   -0.315
## 1845 f5_w3 ~~ f5_w4 338.729 -0.043  -0.397   -0.397   -0.397
## 130    v73 ~~   v73 338.578  0.046   0.000    0.000    0.000
## 838  f5_w4 =~   v73 338.138 -0.314  -0.314   -0.314   -0.314
## 2423 f5_w4  ~ f5_w2 337.400  0.479   0.479    0.479    0.479
#Making a graph?
png("updated_longitudinal_SEM_diagram.png", width = 800, height = 600)
semPlot::semPaths(updated_longitudianl_model, whatLabels = "std", layout = "tree", rotation = 2)
dev.off()
## png 
##   2