Measurement Error and Penalized Likelihoods for Variable and Factor Selection in Factor Analysis

• Activity Number: 441
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Social Statistics Section
• Author(s): Alana Unfried* and Dennis Boos and Leonard Stefanski
• Companies: North Carolina State University and North Carolina State University and North Carolina State University
• Keywords: Factor Analysis ; Variable Selection ; Measurement Error ; Penalized Likelihood

Abstract

Factor analysis is commonly used to describe the covariance structure for a group of variables through a set of underlying latent factors. Variables loading on the same factor are correlated with one another, and it is often desirable to remove variables from the model that are uncorrelated with any others. Another issue in factor analysis is choosing the appropriate number of factors, which must be specified prior to estimating factor loadings. We use measurement error methods introduced in Stefanski, Wu, and White (2014, JASA) to identify and eliminate marginally correlated variables prior to choosing the number of factors. A new penalized likelihood, which forces sparse columns in the factor loading matrix, is then used for selecting the number of factors and fitting the factor model.