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Recent methodological developments in the area of how to include auxiliary variables (e.g., covariates and distal outcomes) in mixture models have proposed methods that allow for the estimation of relationships with latent class variables while preserving the measurement parameters of the latent class variable. These preferred approaches (e.g., ML three-step, BCH, etc.) overcome the problem of measurement parameters of the latent class variable being unintentionally influenced by the auxiliary variables. Some shifts in the measurement parameters may occur due to differential item functioning (DIF; Masyn, 2017), the multi-step auxiliary methods aim to overcome changes due to other relationships and have the flexibility to accommodate DIF if warranted. The landscape of auxiliary variable approaches are actively in flux due to new developments by statistical methodologists, these methods will need to be tested and studied across a range of modeling conditions before we are confident in their performance in practice. The majority of these auxiliary variable methods, however, have been explored in the cross-sectional mixture modeling context (e.g., LCA and LPA). The use of auxiliary variables in longitudinal models, such as the latent transition analysis model, is understudied.
This paper presents the use of the newer auxiliary variable methods for use in the LTA modeling context where covariates and distal outcomes are included. These methodological approaches, in theory, can be used in the modeling context of multiple latent class variables, such as with LTA, however, their implementation in common statistical software packages have yet to be extended to accommodate multiple latent class variables, such as in the case with LTA models. The ML three-step approach (Vermunt, 2010) as implemented in Mplus can accommodate multiple latent class variables and newer two-step approach can accommodate multiple latent class variable but can only be used in a very limited capacity.
This paper will present the modeling possibilities for including covariates in LTA models and how to specify them with the current best practices. Further, using an applied example using a longitudinal study of heterogeneity in high school social-emotional strengths across time, we will demonstrate the use of the auxiliary variable methods. An important aspect of these modeling capabilities is not only how to specify the models in commonly used software packages (Mplus and Latent Gold), but knowing how to make meaning of the results. We will focus on gender differences in transitions over time, using gender as covariate and linking transitions to graduation rates and college-going choices. Limitations and future directions for auxiliary variables in LTA models will be discussed.