State Space Dynamic Mixture Modeling: Finding People with Similar Patterns of Change

Abstract

Increasingly, psychologists encounter data in which several individuals have been measured on multiple variables over numerous occasions. Many of the current methods for this situation combine the data, assuming everyone is a randomly equivalent to everyone else. The extreme alternative on the other side is to separately analyze each person's data, assuming no one is similar to anyone else. This dissertation proposes a method as a compromise between these two extremes. The goal of the method is to find people in the data that are undergoing similar change processes over time. Data were simulated under various conditions to explore what factors influenced the ability of the method to correctly estimate the change process and accurately find people with the same process. It was found that sample size had the greatest positive influence on parameter estimation and the dimension of the change process had the greatest positive impact on correctly grouping people together, likely due to the distinctiveness of their patterns of change. With some success in simulation, the method was applied to an archival data source reflecting cognitive growth in the National Longitudinal Survey of Youth Children data. This analysis suggested that the genetic effects operating between people on their cognitive development may be quite different from their within-person effects, but also revealed a limitation for the method on large sample sizes. Once software improvements are made to the method, its applicability to large, real data should be reevaluated. State space mixture modeling, in its current form, offers one of the best-performing methods for simultaneously drawing conclusions about individual change processes while also analyzing multiple people.