Structural Models for Binary Repeated Measures: Linking Modern Longitudinal Structural Equation Models to Conventional Categorical Data Analysis for Matched Pairs

The current widespread availability of software packages with estimation features for testing structural equation models with binary indicators makes it possible to investigate many hypotheses about differences in proportions over time that are typically only tested with conventional categorical data analyses for matched pairs or repeated measures, such as McNemar's chi-square. The connection between these conventional tests and simple longitudinal structural equation models is described. The equivalence of several conventional analyses and structural equation models reveals some foundational concepts underlying common longitudinal modeling strategies and brings to light a number of possible modeling extensions that will allow investigators to pursue more complex research questions involving multiple repeated proportion contrasts, mixed between-subjects x within-subjects interactions, and comparisons of estimated membership proportions using latent class factors with multiple indicators. Several models are illustrated, and the implications for using structural equation models for comparing binary repeated measures or matched pairs are discussed.