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Stochastic search item selection for factor analytic models.

Abstract

In this paper we implement a Markov chain Monte Carlo algorithm based on the stochastic search variable selection method of George and McCulloch (1993) for identifying promising subsets of manifest variables (items) for factor analysis models. The suggested algorithm is constructed by embedding in the usual factor analysis model a normal mixture prior for the model loadings with latent indicators used to identify not only which manifest variables should be included in the model but also how each manifest variable is associated with each factor. We further extend the suggested algorithm to allow for factor selection. We also develop a detailed procedure for the specification of the prior parameters values based on the practical significance of factor loadings using ideas from the original work of George and McCulloch (1993). A straightforward Gibbs sampler is used to simulate from the joint posterior distribution of all unknown parameters and the subset of variables with the highest posterior probability is selected. The proposed method is illustrated using real and simulated data sets.

Department of Primary Education, University of Ioannina, Greece; Department of Hygiene and Epidemiology, University of Ioannina School of Medicine, Greece.

TY - JOUR
T1 - Stochastic search item selection for factor analytic models.
AU - Mavridis,Dimitris,
AU - Ntzoufras,Ioannis,
Y1 - 2013/07/10/
PY - 2012/3/26/received
PY - 2013/5/17/revised
PY - 2013/7/10/aheadofprint
PY - 2013/7/11/entrez
PY - 2013/7/11/pubmed
PY - 2015/7/7/medline
KW - Gibbs sampling
KW - Markov Chain Monte Carlo
KW - Prior Specification
KW - Stochastic Search Variable Selection
KW - factor selection
SP - 284
EP - 303
JF - The British journal of mathematical and statistical psychology
JO - Br J Math Stat Psychol
VL - 67
IS - 2
N2 - In this paper we implement a Markov chain Monte Carlo algorithm based on the stochastic search variable selection method of George and McCulloch (1993) for identifying promising subsets of manifest variables (items) for factor analysis models. The suggested algorithm is constructed by embedding in the usual factor analysis model a normal mixture prior for the model loadings with latent indicators used to identify not only which manifest variables should be included in the model but also how each manifest variable is associated with each factor. We further extend the suggested algorithm to allow for factor selection. We also develop a detailed procedure for the specification of the prior parameters values based on the practical significance of factor loadings using ideas from the original work of George and McCulloch (1993). A straightforward Gibbs sampler is used to simulate from the joint posterior distribution of all unknown parameters and the subset of variables with the highest posterior probability is selected. The proposed method is illustrated using real and simulated data sets.
SN - 2044-8317
UR - https://www.unboundmedicine.com/medline/citation/23837882/Stochastic_search_item_selection_for_factor_analytic_models_
L2 - http://openurl.ebscohost.com/linksvc/linking.aspx?genre=article&sid=PubMed&issn=0007-1102&title=Br J Math Stat Psychol&volume=67&issue=2&spage=284&atitle=Stochastic search item selection for factor analytic models.&aulast=Mavridis&date=2014
ER -