**1. Introduction**

Principal components analysis (PCA) is a popular dimension reduction method and is applied to analyze quantitative data. For PCA to qualitative data, the data are quantified by using optimal scaling that nonlinearly transforms qualitative data into quantitative data. The PCA with optimal scaling is called nonlinear PCA. Nonlinear PCA reveals all qualitative variables uniformly as numerical variables by using optimal scaling quantifiers in the analysis, that is, it can deal with nonlinear relationships among variables with different measurement levels.

Using this quantification, we can consider variable selection in the context of PCA for qualitative data. In PCA for quantitative data, Tanaka and Mori discussed a method called modified PCA (M.PCA) that can be used to compute principal components (PCs) using only a selected subset of variables that represents all of the variables, including those not selected [1]. Since M.PCA includes variable selection procedures in the analysis, if we quantify all the qualitative variables by using the

optimal scaling and then apply M.PCA to the quantified data, we can select a reasonable subset of variables from the qualitative data.

In this chapter, we refer to Mori et al. [2] to revisit a variable selection problem in PCA for qualitative data. The proposed method here (we call it nonlinear M.PCA or NL.M.PCA) is an extension of M.PCA so as to deal with a mixture of quantitative and qualitative data. In Section 2 we provide the overview of NL.M.PCA (optimization, the original M.PCA and NL.M.PCA for qualitative data) based on studies by Mori et al. [2], and in Section 3, we apply this method to the customer engagement data [3] to show how it works in the real data and how you use the output from the method for variable selection, and to evaluate the performance of the method.
