Bayesian Estimation of a Continuous-Time Model for Discretely-Observed Panel Data

Abstract

Continuous-time models are used in many areas of science. However, in psychology and related fields, continuous-time models are often difficult to apply because only a small number of repeated observations are typically available. One promising model that has been suggested for such data is the Exact Discrete Model (EDM)—a set of mathematical relations that connect the discrete-time autoregressive cross-lagged (ARCL) panel model to an underlying continuous-time model. To date, several frequentist approaches have been developed for estimating the underlying continuous-time model parameters via the EDM. On the contrary, Bayesian approaches have not yet been explored. Therefore, the purpose of this project was to outline a Bayesian implementation of the EDM with non-informative priors and compare its performance to two frequentist approaches—EDM-SEM (Oud & Jansen, 2000) and Oversampling (Singer, 2012}—under proper model specification and variable experimental conditions. Data were generated under different combinations of sample size, number of time points, and population parameter values for a bivariate panel model. In addition, starting values for the frequentist methods were set to data generating values or randomly perturbed. Results from the three estimation approaches were equivalent at moderate and large sample sizes. The Bayesian implementation resulted in fewer non-converged and improper solutions compared to the frequentist approaches in nearly all experimental conditions. Parameter estimates were slightly less biased and less variable under frequentist estimation at small sample sizes. The Bayesian approach and Oversampling generally provided equivalent or better interval coverage compared to the EDM-SEM procedure across all conditions. Finally, model fit statistics calculated under the Bayesian approach via posterior predictive modeling checking were less sensitive to sample size than those calculated for the frequentist methods; however, proposed cutoff values did not correspond to Type I error rates. To summarize, preliminary support for a non-informative Bayesian implementation of the EDM was found. In addition, Oversampling appears to be a promising method for frequentist estimation of the EDM. Alternative prior specifications, modeling extensions, and the performance of these approaches under less ideal analytic conditions are important areas for further study.