Dynamic factor models (DFMs) have typically been applied to multivariate time series data collected from a single unit of study, such as a single individual or dyad. The goal of DFMs application is to capture dynamics of multivariate systems. When multiple units are available, however, DFMs are not suited to capture variations in dynamics across units. The aims of this study are (a) to propose a random coefficient DFM (RC-DFM) to statistically model variations of dynamics across multiple units using the Bayesian method, (b) to illustrate the use of the proposed procedure by applying RC-DFMs to affect data collected from multiple dyads in romantic relationships, and (c) to evaluate the performance of the RC-DFMs with Bayesian estimation through simulation analyses. The results from the simulation analyses show that the Bayesian estimation of RC-DFMs works well in recovering parameters including both fixed and random effects. A number of practical considerations are provided to guide future research on using Bayesian methods for estimating multivariate time series from multiple units. (Contains 2 figures, 8 tables and 9 footnotes.)