A Comparison of Stepwise Approaches in Latent Transition Analysis

• In Event: 61.063 - Mixture Modeling in Practice

Abstract

Applications of mixture modeling, which utilize categorical latent variables (i.e., latent class variables), in social science research have been increasing. However, it is still unclear how best to analyze models that include structural relations between latent class variables and auxiliary variables (i.e., covariates and distal outcomes) or models with multiple latent class variables. Recently, stepwise approaches have been preferred. These approaches first measure each latent class variable, followed by subsequent steps that analyze structural relations among auxiliary variables or multiple latent class variables.

Vermunt (2010) introduced a maximum likelihood based three-step method in which classification error from the first step (the measurement model) is entered into the model at the second step. He showed that accounting for classification error reduced bias when analyzing the structural parameters in the third step. Though his study focused on predictors of the latent class variable, the three-step method can also be used with latent transition analysis (LTA), which links two or more latent class variables. Recently, Bakk and Kuha (2017) introduced a two-step approach in which the parameters from the measurement model in the first step are fixed to their values in the second step. Once the measurement parameters are fixed, the second step allows for the inclusion of auxiliary variables or multiple latent class variables without affecting the measurement model(s). Their study showed this method reduced bias when analyzing covariates and distal outcomes of the latent class variable. Currently, these are the only two stepwise approaches that can be used to conduct LTA.

This paper builds upon Vermunt (2010) and Bakk and Kuha (2017) by comparing their methods in the context of LTA. First, a simulation study is presented. Data for an LTA (with sample sizes N = 500, 1000, and 2000) were generated in Mplus with a three-class model at each of two timepoints and longitudinal measurement invariance assumed. In addition to varying sample size, this study also varied the degree of class separation at each timepoint. For the three-step approach, the analysis was carried out in Mplus (Muthén & Muthén, 1998-2017). For the two-step approach, the first step was conducted in Mplus, but the second step was conducted in R (R Development Core Team, 2015). Each analysis utilized 500 replications. Initial results suggest that, in general, both methods perform similarly, but the two-step method performs slightly better with less bias when regressing the second latent class variable on the first, particularly as sample size and class separation increase.

Second, this paper provides an applied example using data collected from N = 965 students whose reading skills were assessed during fall and spring of first grade. Six variables assessing phonological awareness, word-level reading, and linguistic comprehension were used. This example uses LTA to link two latent class analyses. Each measurement model is briefly reviewed, while the focus is on how to implement steps 2 and 3 from each method. Syntax in both Mplus and R will be provided.

Authors

• Ryan Grimm, University of Virginia

• Karen L. Nylund-Gibson, University of California - Santa Barbara

• Emily Jane Solari, The University of Texas - Health Science Center at Houston