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Additive and bilinear models to unravel multivariate experimental design effects

Marieke Timmerman


In many experiments, data are collected on a large number of variables. Typically, the manipulations involved yield differential effects on subsets of variables and on the associated individual differences. The key challenge is to unravel the nature of these differential effects. An effective approach to achieve this goal is to analyse the data with a combined additive and bilinear model. Well-known examples are principal component analysis, reduced rank regression analysis and simultaneous component analysis (SCA). In this talk, I will show how various existing models fit into the model framework, and discuss the type of insights that can be obtained witht the different variants. I will discuss into more detail simultaneous component modeling, where the multivariate data are structured in blocks with respect to the different levels of the experimental factors. Herewith, it is important to express that the dominant sources of variance in the observed data may differ across blocks. This can be done via SCA, presuming that the structure is equal across all blocks, or clusterwise SCA, which aims at identifying both similarities and differences in structure between the blocks. As with any component analysis, (clusterwise) SCA results heavily on the scaling applied. I will discuss the basic principles relevant for scaling, yielding the tools for a rational selection of scaling for a data analytic problem at hand. To illustrate the power of the approach, I will present analysis results from real-life data, and show that insight can be obtained into multivariate experimental effects, in terms of similarities and differences across individuals. The latter is highly relevant for subtyping.



Marieke Timmerman ( is a professor in multivariate data analysis at the Heymans Institute for Psychological Research at the University of Groningen, the Netherlands. Her research focuses on the development of models for multivariate data with complex structures, to achieve an understanding of the processes underlying these data. Her research interests are data reduction methods, including multi-set models, latent variable modelling and classification.