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

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Abstract

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.

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