Modeling Heterogeneity in Transitions: A Confirmatory Higher Order Latent Transition Analysis

• In Event: Recent Developments in Multiple-Group, Multilevel, and Longitudinal Mixture Modeling

Abstract

The mover-stayer LTA model is the most commonly used higher-order LTA model, sometimes called a mixed Markov models. The key feature of this model is that it allows researchers to model heterogeneity in transitions across time by specifying a higher order latent class variable, which partitions individuals into different classes based on their transitions across time. As the name suggests, in the mover-stayer model, there are two classes in the higher-order latent class variable, those who “stay” in the same latent class over time and a second class comprised of those who “move” among the latent classes over time. For example, Neundorf, Stegmueller, Scotto (2011) used the mover-stayer LTA Markov process show that distinct patterns of political party affiliations exists by estimating distinctive subpopulations that follow different patterns of partisan stability and instability over a 24-year period.

This paper introduces a generalized framework for estimating a confirmatory higher-order LTA model. This model builds off the mover-stayer model, but provides a more general framework for modeling heterogeneity in transition patterns. For example, in many developmental contexts there is a desire to separate different stayers, e.g., stayers at a “high” class would be very different from stayers at a “low” class. In a confirmatory framework, it is possible to estimate more classes in the higher-order latent class variable, where the classes of the higher-order variable have very specific transition probability patterns. Given the confirmatory nature, the specification of the classes must be driven by developmental theory. LTA models with different specifications at the higher-order can be tested against each other. This model also provides a natural way to include distal outcomes into the LTA model, where the three-step method (Nylund-Gibson, Grimm, Quirk, and Furlong, 2014) can be used to estimate distal outcome means.

This paper will present the confirmatory higher-order LTA (Figure 1) model and demonstrate the utility of the model using an application with a 6-class higher order LTA model to capture changes in peer victimization experiences of middle schools students. In this application, the six classes are all substantively motivated (stay victimization, stay sometimes-victimized, stay non-victimized, transition to more victimization, transition to less victimization, flip-flop in victimization experiences). The specification of this model in Mplus will be highlighted. This application includes distal outcomes.

Authors

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

• Cecile Binmoeller, University of California - Santa Barbara

• Adrienne Nishina, University of California - Davis

• Amy Bellmore, University of Wisconsin - Madison