ABSTRACT
So far, we have assumed that the variables we analyze by generalized structured component analysis are all quantitative, that is, they are measured on relatively continuous scales and are linearly related to their latent variables. However, not all variables satisfy these conditions. Some variables are purely qualitative in the sense that no a priori quantications are given. Some other variables are relatively continuous, but are nonlinearly related to their latent variables. In this chapter, we discuss extensions of generalized structured component analysis, called “nonlinear” generalized structured component analysis (Hwang and Takane 2010), that allow optimal quantications (scaling, transformations) of the observed variables. The word “nonlinear” here refers to the nonlinearity of the data transformations, and not to the nonlinearity in the structural model.
