Leveraging component-based methods to improve MTMM analysis

The chapter describes an approach for detecting outliers in MTMM data. This approach relies on a component-based method that accounts for the multiple-source structure of data and enables estimation of a T² statistic, which is analogous to the squared Mahalanobis distance. Moreover, the technique results in a useful visualization plot that also helps in identifying outliers. The component-based method is known in the consumer science literature as multiple factor analysis (MFA; Escofier & Pagès, 1983, 2008), yet a more appropriate label is multiple principal components analysis (MPCA). I argue that MPCA offers a number of advantages for specific problems scientists working with MTMM data face. After providing a preliminary review of the singular value decomposition, principal components analysis (PCA), and MPCA, I show how to obtain the T² statistic from MPCA along with confidence intervals to flag potential outliers. Two simulated data examples showed that using this approach in conjunction with the consensus map produced by MPCA, was useful to identify unusual observations. Two types of MTMM outliers were identified in the examples: method-consistent and method-specific outliers. Suggestions for finding and handling outliers in MTMM data and instances in which MPCA might be preferred over standard MTMM models are discussed.