The future of dynamic factor analysis in psychology and biomedicine

The currently dominant approach to statistical analysis in psychology and biomedicine is based on analysis of inter-individual variation. Differences between subjects drawn from a population of subjects provide the information to make inferences about states of affairs at the population level (e.g., mean and/or covariance structure). Recently it has been shown that in general the inferred states of affairs at the population level do not apply at the level of intra-individual variation characterizing the life trajectories of individual subjects making up the population. This is a direct consequence of the so-called classical ergodic theorems of Birkhoff and Wiener which has important implications for the way in which psychological and biomedical processes have to be analyzed. The classical ergodic theorems are introduced below in order to show the necessity of using an alternative approach which is valid for the analysis of intra-individual variation. This approach has to be based on single-subject time series analysis. Next an overview is presented of dynamic factor models for the analysis of multivariate time series and the various ways to fit these models to the data. We then turn to an empirical application of factor analysis of personality data obtained in a replicated time series design, showing substantial heterogeneity in intra-individual factorial personality structure. The next topic is entirely innovative--for the first time I present my new dynamic factor model for the analysis of nonstationary time series. In the conclusion I will sketch some biomedical research initiatives in which this new model will be used.