Clusterwise and switching component models for modeling between- and within-block structural differences in multivariate multiblock data

Behavioral researchers are often interested in the underlying structure of multivariate data. For instance, if one has a multivariate data block consisting of multiple ratings of a set of emotions by one subject, one may wonder whether some of the emotions covary across time. To explore this covariation structure, dimension reduction techniques such as principal component analysis (PCA) are often used. PCA reduces the variables to a few dimensions that summarize the variance in the data block and that yield insight into which variables covary strongly and which do not. For the emotion example, many researchers postulate that pleasantness-unpleasantness and arousal-sleepiness are the relevant dimensions.Research questions are often more complex, however. On the one hand, one may dispose of multivariate time series data of more than one subject (i.e., multiblock data) and wonder whether the underlying structure is the same for all subjects. For example, subjects may differ with respect to so-called emotional granularity, i.e., for subjects low on emotional granularity negative or positive emotional states are highly correlated across time, whereas subjects high on emotional granularity experience emotions in a more fine-grained way. This type of research questions pertains to between-block differences in underlying structure. On the other hand, even the data of a single subject can be scrutinized in more detail, investigating whether the underlying structure is the same across all measurements or varies over time. For example, when physiological parameters (e.g., blood pressure, heart rate, etc.) are measured across time for a single subject, it is expected that (some of) these parameters take on extreme values (response patterning) and covary stronger (synchronicity) when an emotion-eliciting event occurs, to enable a fast and efficient reaction of the organism. This type of research questions concerns within-block differences in underlying structure.There are some component models available for answering these types of questions, but they all have important limitations. Therefore, in this doctoral dissertation, we present a family of Clusterwise Simultaneous Component Analysis (SCA) models for studying between-block structural differences, on the one hand, and Switching Principal Component Analysis (PCA) for studying within-block structural differences, on the other hand.Clusterwise SCA captures the most important between-block structural differences in multiblock data by assigning the data blocks to a limited number of mutually exclusive clusters and modeling the data within each cluster by a separate set of dimensions. This implies that data blocks with a similar covariation structure are grouped in the same cluster. Chapter 1 introduces Clusterwise SCA-ECP for modelling differences in correlation structure, imposing the number of dimensions to be equal across clusters. Chapter 2 describes software for performing Clusterwise SCA-ECP analyses. Chapter 3 presents Clusterwise SCA-P for modelling differences in covariance structure, also using the same number of dimensions in all clusters. Chapter 4 discusses a Clusterwise SCA-ECP variant in which the number of dimensions may differ across clusters. Chapter 5 presents Common and Cluster-specific SCA-ECP for distinguishing among dimensions that are common in that they show up in each cluster, and dimensions that are cluster-specific.Switching PCA, described in Chapter 6, models within-block structural differences in single subject data, as well as within-block differences in means. Switching PCA clusters the time points into a few phases of consecutive time points with similar means and/or covariation structure and performs a PCA per phase to yield insight into the covariation structure.

Publication year:2013

Accessibility:Open