Hierarchically structured data sets are commonly encountered in many fields of scientific investigation. Hierarchical (Multilevel) linear models (HLM) provide effective ways of analyzing such data sets. Interpretations of parameters in these models become increasingly more difficult, however, as they accommodate more levels, more predictor variables, and more criterion variables. This paper presents a method of multilevel analysis with a dimension reduction feature to facilitate interpretations of model parameters such models. The method first decomposes variability in the criterion variables into several orthogonal components using predictor variables at different levels, and then applies singular value decomposition (SVD) to the decomposed parts to find more parsimonious representations. Examples are given to illustrate the method. Some possible extensions of the proposed method are also suggested.

Keywords: Clustered data; Projector; Dimension reduction; Singular value decomposition

Biography: Yoshio Takane is a professor of psychology at McGill University specializing quantitative psychology. He has developed many techniques of multivariate data analysis including Constrained Principal Component Analysis, regularized multivariate analysis, structural equation models, etc.