Methods: PCM employ a latent class analysis (LCA) framework, a cross-sectional method that estimates and characterizes subgroups within a population. Latent transition analysis (LTA) extends LCA via autoregressive modeling to estimate the transition probabilities between classes across data waves. When continuous measures are used, models are known as latent profiles. The LCA framework derives discrete latent class means dependent upon model constraints. LCA is estimated using gamma parameters (γ; proportion of participants in each latent class), and rho parameters (ρ; measurement error). When extending LCA to multiwave data, LTA integrates autoregressive modeling to generate delta parameters (δ; proportion of individuals in each class at each wave), and tau parameters (τ; transition probabilities between time t latent class to time t+1 latent class).
PCM are useful in examining treatment effects on class membership over time. The transition probability for individual i is estimated by τikm = P(Cit = k | Cit+1 = m, xit). In this equation, the latent variable Cit+1 with m classes is regressed on the latent variable Cit with k classes. Thus, τikm is probability for individual i to be in latent class m at time point t +1, conditional upon membership in latent class k at time point t. When covariate xit is introduced, the probability for individual i to be in latent class m is conditioned on both prior class membership and covariates, including treatment assignment.
PCM may be estimated using Mplus (Muthén & Muthén, 2011). To help symposium participants build skills in conducting PCM, we will share code and demonstrate options for nested data, sequential steps for model building, and the evaluation of model fit (e.g., BLRT, LMR, BIC, and entropy) as well as the importance of substantive validation. Follow-up analyses, conducted by exporting posterior probabilities from Mplus into any statistical software, will be discussed.
Results: Although promising, PCM is conditioned by strong assumptions and limitations. Models might not be stable with small sample sizes and violations of distributional assumptions. We will discuss both strengths and limitations of the PCM approach.
Implications: Biological, family, peer, school, neighborhood, and other risk factors co-vary, and this correlated risk affects life course outcomes (Cicchetti, 1993; Jessor & Jessor, 1977; Kazdin & Weisz, 2010). In everyday parlance, practitioners and policymakers acknowledge correlated risk as person-level risk status. Presenting research findings in a person-centered manner clearly communicates the impact of interventions. PCM have been underutilized as analytic tools to investigate the effects of interventions in holistic ways. Thus, PCM complement variable-centered analysis and provide researchers with an alternative means for both estimating and communicating findings.