Maximum Likelihood Selection Skew-Normal Factor Analysis

• Activity Number: 498
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Beverly Gaucher*+
• Companies: Texas A&M University
• Keywords: skew ; factor analysis ; dimensionality reduction ; model fitting

Abstract

This research explores factor analysis applied to skewed distributions for the general skew model, the selection-elliptical model, the selection-normal model, the skew-elliptical model and the skew-normal model for finite sample sizes. The skewed models are formed using selection distribution theory, which is based on Rao's weighted distribution theory. The models assume the observed variable of the factor model is from a skewed distribution by defining the distribution of the unobserved common factors skewed and the unobserved unique factors symmetric. Additionally, the problem of "sign switching" is resolved in the selection skew-normal factor analysis model. Numerical examples are provided using maximum likelihood selection skew-normal factor analysis. Numerical examples such as maximum likelihood estimation, quasi-maximum likelihood estimation and model fitting illustrate the selection skew-normal factor model fits skew-normal data better than the normal factor model in the case of likelihood methods.