Rank and Set Restrictions for Homogeneity Analysis in R

• Activity Number: 61
• Type: Contributed
• Date/Time: Sunday, August 3, 2008 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Patrick Mair*+ and Jan de Leeuw
• Companies: Wirtschaftsuniversität Wien and University of California, Los Angeles
• Keywords: Gifi-models ; homogeneity analysis ; nonlinear principal component analysis ; nonlinear canonical correlation analysis ; multiple correspondence analysis

Abstract

The model family proposed by Gifi (1990) is a flexible framework for the analysis of multivariate data. The common properties shared by all Gifi-models are the specification of a loss function solved by ALS and transformations of the variables which lead to quantifications of the categories. The latter issue implies the concept of "optimal scaling" and allows to account for the variables scaling level. Starting from the basic model called homals (homogeneity analysis aka multiple CA) we present various extensions in terms of rank restrictions (nonlinear PCA) and restrictions on sets of variables (nonlinear canonical correlation analysis). We focus on recent methodological developments and on the R package "homals" (de Leeuw & Mair, 2008) which allows for the computation of these models and provides new visualization techniques of the results.