More Stable Estimation of the STARTS Model: A Bayesian Approach Using Markov Chain Monte Carlo Techniques

The STARTS (Stable Trait, AutoRegressive Trait, and State) model decomposes individual differences in psychological measurement across time into 3 sources of variation: a time-invariant stable component, a time-varying autoregressive component, and an occasion-specific state component. Previous simulation research and applications of the STARTS model have shown that serious estimation problems such as nonconvergence or inadmissible estimates (e.g., negative variances) frequently occur for STARTS model parameters. This article introduces a general approach to estimating the parameters of the STARTS model by employing Bayesian methods that use Markov Chain Monte Carlo (MCMC) techniques. With the specification of appropriate prior distributions, the Bayesian approach offers the advantage that the model estimates will be within the admissible range, and it should be possible to avoid estimation problems. Furthermore, we show how Bayesian methods can be used to stabilize STARTS model estimates by specifying weakly informative prior distributions for the model parameters. In a simulation study, the statistical properties (bias, root mean square error, coverage rate) of the parameter estimates obtained from the Bayesian approach are compared with those of the maximum-likelihood approach. A data example is presented to illustrate how the Bayesian approach can be used to estimate the STARTS model. Finally, further extensions of the STARTS model are discussed, and suggestions for applied research are made. Translational Abstract Studying stability and change in psychological constructs (e.g., self-esteem, depression) across time is a central topic of longitudinal research. The STARTS (Stable Trait, AutoRegressive Trait, and State) model offers great potential for researchers interested in the question which portion of individual differences across time in a psychological construct is explained by stable factors that are completely unchanging across time (e.g., genes), which portion is due to the effects of changing factors that are only partly stable and endure across time (e.g., relationship satisfaction), and which portion reflects the effects of transient factors that are completely occasion specific (e.g., mood). Previous research has revealed that the applicability of the STARTS model is limited by the fact that large data sets with many measurement points are needed to obtain valid estimates of the model parameters. In this article, we demonstrate that a Bayesian estimation approach has the potential to solve some of these estimation problems (e.g., variances that are negative). The basic idea of the proposed Bayesian approach is to add a small amount of information to the model that provides some direction for the estimation of the model parameters. It is shown with simulated and real data that compared to previous estimation approaches (e.g., maximum likelihood estimation), the Bayesian approach needs less demanding longitudinal designs in order to obtain reliable estimates of STARTS model parameters. We hope that the proposed approach allows for better understanding of stability and change in psychological constructs across time.