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Research on stage-sequential shifts across multiple latent classes can be challenging in part because it may not be possible to observe the particular stage-sequential pattern of a single latent class variable directly. In addition, one latent class variable may affect or be affected by other latent class variables and the associations among multiple latent class variables are not likely to be directly observed either. To address this difficulty, we propose a multivariate latent class analysis for longitudinal data, joint latent class profile analysis (JLCPA), which provides a principle for the systematic identification of not only associations among multiple discrete latent variables but sequential patterns of those associations. We also propose the recursive formula to the EM algorithm to overcome the computational burden in estimating the model parameters, and our simulation study shows that the proposed algorithm is much faster in computing estimates than the standard EM method. In this work, we apply a JLCPA using data from the National Longitudinal Survey of Youth 1997 in order to investigate the multiple drug-taking behavior of early-onset drinkers from their adolescence, via young adulthood, to adulthood.

Latent Class Analysis for Repeatedly Measured Multiple Latent Class Variables