Comparing Two SAS-based Approaches to Latent Class Analysis for a Set of Binary Manifest Variables

• Activity Number: 133
• Type: Contributed
• Date/Time: Monday, August 4, 2003 : 12:00 PM to 1:50 PM
• Sponsor: Biometrics Section
• Author(s): David Thompson*+
• Companies: University of Oklahoma
• Keywords: SAS PROC CATMOD ; log-linear model ; simulation

Abstract

Latent class analysis (LCA) is a categorical analog to factor analysis (FA). Whereas FA attributes a multivariate sample's covariance structure to unobserved factors, LCA posits a latent structure to explain association in a multidimensional contingency table. LCA model parameters include LC prevalences and response probabilities conditional on LC membership. Parameter estimation assumes that, given LC membership, observed responses are independent. Although LCA is unavailable in conventional SAS, the presentation demonstrates two SAS-based LCA approaches. The first, an IML program, realizes Goodman's (1974) probabilistic parameterization. The second estimates logl-inear parameters in CATMOD, estimates response counts in conventional DATA steps, then resubmits the counts to CATMOD until the process arrives at LC parameter estimates. The presentation applies the approaches to published data by modeling a dichotomous LC variable to explain the association among four binary manifest variables. It also compares the approaches by simulating independent 2x2 contingency tables, merging them into a nonindependent table, then assigning LC membership and reconstructing the original tables.