Switching principal component analysis for modeling means and covariance changes over time.

Abstract

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.

Improved Insight into and Prediction of Network Dynamics by Combining VAR and Dimension Reduction

“…Of course, it is possible that this is not the case. The current PC-VAR(1) approach might be extended based on the principles behind switching PCA (De Roover, Timmerman, Van Diest, Onghena, & Ceulemans, 2014), in which divides the time series is divided into separate phases that are each characterized by a separate set of component loadings. In this regard, change point detection methods for signaling correlation change might be a useful screening tool to decide on an appropriate modeling strategy (Cabrieto, Tuerlinckx, Kuppens, Hunyadi, & Ceulemans, 2018;.…”

Latent Markov Factor Analysis for Exploring Measurement Model Changes in Time-Intensive Longitudinal Studies

“…to retain an expected variance of 1 (De Roover, Timmerman, Van Diest, Onghena, & Ceulemans, 2014). Finally, the data-matrices Y i were again merged into one data set Y .…”

MultiLevel simultaneous component analysis: A computational shortcut and software package

“…Therefore, researchers should decide whether or not such variance differences are meaningful. For instance, when analyzing physiological measures such as heart rate, respiratory volume, and blood pressure, variance differences are at least partly arbitrary because the variables are measured on a different scale (see e.g., De Roover, Timmerman, Van Diest, Onghena, & Ceulemans, 2014). Thus, it makes sense to give each variable the same weight in the analysis by scaling each variable to a variance of one across all data blocks.…”