Homogeneity Assumptions in the Analysis of Dynamic Processes

With the increased use of time series data in human research, ranging from ecological momentary assessments to data passively obtained, researchers can explore dynamic processes more than ever before. An important question researchers must ask themselves is, do I think all individuals have similar processes? If not, how different, and in what ways? Dr. Peter Molenaar's work set the foundation to answer these questions by providing insight into individual-level analysis for processes that are assumed to differ across individuals in at least some aspects. Currently, such assumptions do not have a clear taxonomy regarding the degree of homogeneity in the patterns of relations among variables and the corresponding parameter values. This paper provides the language with which researchers can discuss assumptions inherent in their analyses. We define strict homogeneity as the assumption that all individuals have an identical pattern of relations as well as parameter values; pattern homogeneity assumes the same pattern of relations but parameter values can differ; weak homogeneity assumes there are some (but not all) generalizable aspects of the process; and no homogeneity explicitly assumes no population-level similarities in dynamic processes across individuals. We demonstrate these assumptions with an empirical data set of daily emotions in couples.