Latent Class Models for Stage-Sequential Dynamic Latent Variables

Stage-sequential dynamic latent variables are of interest in many longitudinal studies. Measurement theory for these latent variables, called Latent Transition Analysis (LTA), can be found in recent generalizations of latent class theory. LTA expands the latent Markov model to allow applications to more complex latent variables and the use of multiple indicators. Because complex latent class models result in sparse contingency tables, that may lead to poor parameter estimation, a simulation study was conducted in order to determine whether model parameters are recovered adequately by LTA, and whether additional indicators result in better measurement or in impossibly sparse tables. The results indicated that parameter recovery was satisfactory overall, although as expected the standard errors were large in some conditions with few subjects. The simulation also indicated that at least within the conditions examined here, the benefits of adding indicators outweigh the costs. Additional indicators improved standard errors, even in conditions producing extremely sparse tables. An example of LTA analysis of empirical data on math skill development is presented.