Comparing Revised Latent State-Trait Models Including Autoregressive Effects

Understanding the longitudinal dynamics of behavior, their stability and change over time, are of great interest in the social and behavioral sciences. Researchers investigate the degree to which an observed measure reflects stable components of the construct, situational fluctuations, method effects, or just random measurement error. An important question in such models is whether autoregressive effects occur between the residuals, as in the trait-state occasion model (TSO model), or between the state variables, as in the latent state-trait model with autoregression (LST-AR model). In this article, we compare the two approaches by applying revised latent state-trait theory (LST-R theory). Similarly to Eid et al. (2017) regarding the TSO model, we show how to formulate the LST-AR model using definitions from LST-R theory, and we discuss the practical implications. We demonstrate that the two models are equivalent when the trait loadings are allowed to vary over time. This is also true for bivariate model versions. The different but same approaches to modeling latent states and traits with autoregressive effects are illustrated with a longitudinal study of cancer-related fatigue in Hodgkin lymphoma patients. Understanding the longitudinal dynamics of behavior, its stability and change over time, are of great interest in the social and behavioral sciences. Researchers investigate the degree to which an observed measure reflects stable components of the construct, situational fluctuations, method effects, or just random measurement error. An important question in such models is whether carry-over effects from one time point to another occur between the residuals, as in the trait-state occasion model (TSO model), or between the state variables, as in the latent state-trait model with autoregression (LST-AR model). The residuals represent events at each measurement, such as situational influences and person-situation interactions, whereas the state variables depict the momentary state of the person. In this article, we compare both models by using a theory (latent state-trait theory revised, LST-R theory) that takes into account that a person is not static over time, but is allowed to change over the time of measurement. Contrary to the expectation, we show that the two models are equivalent. Our study is not only an essential contribution to the existing research of models investigating the longitudinal dynamics of behavior, but also helps applied researchers to interpret the results from LST-R models with autoregressive effects.