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Modified versions of the Bayesian Information Criterion for sparse Generalized Linear Models

Zak-Szatkowska, Małgorzata and Bogdan, Malgorzata LU (2011) In Computational Statistics and Data Analysis 55(11). p.2908-2924
Abstract

The classical model selection criteria, such as the Bayesian Information Criterion (BIC) or Akaike information criterion (AIC), have a strong tendency to overestimate the number of regressors when the search is performed over a large number of potential explanatory variables. To handle the problem of the overestimation, several modifications of the BIC have been proposed. These versions rely on supplementing the original BIC with some prior distributions on the class of possible models. Three such modifications are presented and compared in the context of sparse Generalized Linear Models (GLMs). The related choices of priors are discussed and the conditions for the asymptotic equivalence of these criteria are provided. The performance... (More)

The classical model selection criteria, such as the Bayesian Information Criterion (BIC) or Akaike information criterion (AIC), have a strong tendency to overestimate the number of regressors when the search is performed over a large number of potential explanatory variables. To handle the problem of the overestimation, several modifications of the BIC have been proposed. These versions rely on supplementing the original BIC with some prior distributions on the class of possible models. Three such modifications are presented and compared in the context of sparse Generalized Linear Models (GLMs). The related choices of priors are discussed and the conditions for the asymptotic equivalence of these criteria are provided. The performance of the modified versions of the BIC is illustrated with an extensive simulation study and a real data analysis. Also, simplified versions of the modified BIC, based on least squares regression, are investigated.

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publishing date
type
Contribution to journal
publication status
published
subject
keywords
Bayesian Information Criterion, Generalized Linear Models, Model selection, Sparse linear models
in
Computational Statistics and Data Analysis
volume
55
issue
11
pages
17 pages
publisher
Elsevier
external identifiers
  • scopus:79959704858
ISSN
0167-9473
DOI
10.1016/j.csda.2011.04.016
language
English
LU publication?
no
id
df03a372-7b3e-491b-a840-11391486530d
date added to LUP
2023-12-08 09:25:37
date last changed
2023-12-11 11:39:18
@article{df03a372-7b3e-491b-a840-11391486530d,
  abstract     = {{<p>The classical model selection criteria, such as the Bayesian Information Criterion (BIC) or Akaike information criterion (AIC), have a strong tendency to overestimate the number of regressors when the search is performed over a large number of potential explanatory variables. To handle the problem of the overestimation, several modifications of the BIC have been proposed. These versions rely on supplementing the original BIC with some prior distributions on the class of possible models. Three such modifications are presented and compared in the context of sparse Generalized Linear Models (GLMs). The related choices of priors are discussed and the conditions for the asymptotic equivalence of these criteria are provided. The performance of the modified versions of the BIC is illustrated with an extensive simulation study and a real data analysis. Also, simplified versions of the modified BIC, based on least squares regression, are investigated.</p>}},
  author       = {{Zak-Szatkowska, Małgorzata and Bogdan, Malgorzata}},
  issn         = {{0167-9473}},
  keywords     = {{Bayesian Information Criterion; Generalized Linear Models; Model selection; Sparse linear models}},
  language     = {{eng}},
  month        = {{11}},
  number       = {{11}},
  pages        = {{2908--2924}},
  publisher    = {{Elsevier}},
  series       = {{Computational Statistics and Data Analysis}},
  title        = {{Modified versions of the Bayesian Information Criterion for sparse Generalized Linear Models}},
  url          = {{http://dx.doi.org/10.1016/j.csda.2011.04.016}},
  doi          = {{10.1016/j.csda.2011.04.016}},
  volume       = {{55}},
  year         = {{2011}},
}