Latent class and transition models for modeling qualitative individual differences: An application on longitudinal resilience data

Longitudinal studies are becoming increasingly popular because "change" is of central interest in many areas like educational, and social sciences. The notion of change can be regarded as quantitative or qualitative, the former referring to that which is observed as a degree or an amount (e.g., increase/decrease in test scores) while the latter referring to that which is observed as a form or a kind (e.g., change in problem solving strategies). While the methodology and the applications for tracking change for continuous variables of interest are relatively familiar to researchers, there still remains a need for research studies providing methodological guidance for making use of longitudinal statistical techniques when measuring and modeling categorical variables. This study takes on the challenge and focuses on the use of latent transition analysis, a longitudinal extension of latent class analysis, from a measurement perspective. An overview and an application were provided addressing some of the potential issues when using the latent transition analysis. The study presents a model building strategy for the purpose of integrating a latent transition analysis into the study of repeated assessment data. An illustration is provided where a longitudinal measurement model is formulated into a latent transition model to estimate the relationships between a latent and several observed variables over time. The presented strategy encompasses model building and analysis processes and is presented in five steps: Step-0) studying descriptive statistics, Step-1) testing latent class model alternatives for each time point, Step-2) exploring transitions based on cross-sectional results, Step-3) examining longitudinal measurement invariance across time points, and Step-4) testing latent transition model alternatives and exploring transitions. Application data were collected from the same 360 volunteered college students at three equally – spaced (four weeks apart) time points using an on-line measure consisting of five items asking about students' adversity exposure and resilience levels. After the completion of preliminary Step-0, several latent class model alternatives were considered for the data collected at each of the three time points. In Step-1, 1-class to 5-class models were tested for each time point. The results suggested a better fit for a four-class model for all time points. In accordance with the literature, these classes are labeled with respect to the adversity and resilience levels, namely Resilience, Competence, Maladaptation, and Vulnerability. In Step-2, individuals were assigned to their most likely class for each time point, and cross-tabulations of these class memberships were constructed from Time t to Time t+1. It was found that there are various movement paths between classes across time points. In Step-3, measurement invariance (full- and non-invariance) of those classes was tested and the results indicated that the meaning (characteristics) of latent classes remained constant over all time points. In Step-4, four latent transition model alternatives were tested: (1) model including only first order effect, (2) model with stationary transition probabilities, (3) model including first and second order effects, and (4) model with a higher-order latent class variable involving two classes as mover and stayer. The model with stationary transition probabilities (Model-2) was the best fitting model and the results showed that the individuals who are in the classes with low adversity (i.e., competence and vulnerability) tend to remain within the same class whereas the members of the classes with high adversity (i.e., resilience and maladaptation) tend to move to the classes with less adversity. While the focus of the current study was to provide an overview and an application on latent transition analysis which examines qualitative changes, the provided application also presents significant findings regarding the change patterns in resilience classes of the pre-service teachers. It should be noted that although an illustrative example using resilience data was presented here to show how to conduct latent class and transition analyses, these statistical models can be easily applied to other research topics as well as various extensions of these models (such as adding auxiliary variables, multi-group analysis) might be studied.