Switching Principal Component Analysis for Modeling Means and Covariance Changes Over Time

Many psychological theories predict that cognitions, affect, action tendencies, and other variables change across time in mean level as well as in covariance structure. Often such changes are rather abrupt, because they are caused by sudden events. To capture such changes, one may repeatedly measure the variables under study for a single individual and examine whether the resulting multivariate time series contains a number of phases with different means and covariance structures. The latter task is challenging, however. First, in many cases, it is unknown how many phases there are and when new phases start. Second, often a rather large number of variables is involved, complicating the interpretation of the covariance pattern within each phase. To take up this challenge, we present switching principal component analysis (PCA). Switching PCA detects phases of consecutive observations or time points (in single subject data) with similar means and/or covariation structures, and performs a PCA per phase to yield insight into its covariance structure. An algorithm for fitting switching PCA solutions as well as a model selection procedure are presented and evaluated in a simulation study. Finally, we analyze empirical data on cardiorespiratory recordings.