title: 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.
authors.affiliation: Department of Primary Education, University of Ioannina, Greece; Department of Hygiene and Epidemiology, University of Ioannina School of Medicine, Greece.
authors.forename: Dimitris
authors.initials: D
authors.lastname: Mavridis
authors.forename: Ioannis
authors.initials: I
authors.lastname: Ntzoufras
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005163:Factor Analysis, Statistical; D016014:Linear Models; D008390:Markov Chains; D015233:Models, Statistical; D009010:Monte Carlo Method; D010555:Personality Inventory / Q000706:statistics & numerical data; D011581:Psychological Tests / Q000706:statistics & numerical data*; D011594:Psychometrics / Q000706:statistics & numerical data*; D013269:Stochastic Processes
keywords: Gibbs sampling; Markov Chain Monte Carlo; Prior Specification; Stochastic Search Variable Selection; factor selection