Due to its capability of modeling dynamics of psychological processes, the Dynamic Factor Model (DFM) has gained popularity in psychological research during the past few decades. DFMs have been traditionally applied to time series data collected from a single unit of study, such as a single individual or dyad. As a single-unit based approach, however, DFMs are limited to study inter-unit differences in the dynamical system of interest when cross-sectional multivariate time series data are available. The aims of the present study are to (a) propose a Random Coefficient DFM (RC-DFM) to statistically describe random variations of the dynamics in the population, (b) derive a Bayesian procedure to estimate model parameters in RC-DFMs, and (c) evaluate the performance of the Bayesian procedure for estimating RC-DFMs under different data conditions. As to aim (c), both empirical application and simulation analyses are performed. More specifically, RC-DFMs are applied to real-life data on affect variability so as to examine inter-individual or -dyad differences in within-individual or -dyad dynamics of affect. A series of simulation analyses were carried out to systematically evaluate the performance of the Bayesian procedure for estimating RC-DFMs under different experimental conditions.

The results from both the empirical and simulation analyses show that the Bayesian estimation procedure work well in estimating parameters of RC-DFMs, including both fixed and random effects. In particular, the simulation analyses offer greater evidence for the feasibility of Bayesian estimation of RC-DFMs, in which the experimental conditions are created by varying the number of units, number of measurement occasions, population-average dynamics, and variability of such dynamics.

Further, the results and their implications are discussed with respect to the advantages of Bayesian methods to statistical inference and the applicability of RC-DFMs. A number of practical considerations are provided to guide future research on using the Bayesian method for estimating complex models. In conclusion, some important questions are broached for future research to address.