Time varying grouping variables in Markov latent class analysis

Abstract

Markov latent class analysis (MLCA) is a modeling technique for panel or longitudinal data that can be used to estimate the classification error rates (e.g., false positive and false negative rates for dichotomous items) for discrete outcomes with categorical predictors when gold-standard measurements are not available. Because panel surveys collect data at multiple time points, the grouping variables in the model may either be time varying or time invariant (static). Time varying grouping variables may be more correlated with either the latent construct or the measurement errors because they are measured simultaneously with the construct during the measurement process. However, they generate a large number of model parameters that can cause problems with data sparseness, model diagnostic validity, and model convergence. In this paper we investigate whether more parsimonious grouping variables that either summarize the variation of the time varying grouping variable or assume a structure that lacks memory of previous values of the grouping variables can be used instead, without sacrificing model fit or validity. We propose a simple diagnostic approach for comparing the validity of models that use time-invariant summary variables with their time-varying counterparts. To illustrate the methodology, this approach is applied to data from the National Crime Victimization Survey (NCVS) where greater parsimony and a reduction in data sparseness were achieved with no appreciable loss in model validity for the outcome variables considered. The approach is generalized for application to essentially any MLCA using time varying group variables and its advantages and disadvantages are discussed.