Nonlinear Principal Component Analysis

In this chapter we present a technique for the analysis of customer satisfaction based on a dimensionality reduction approach. This technique, usually referred to as Nonlinear Principal Component Analysis (NPCA), assumes that the observed ordinal variables can be mapped into a one-dimensional quantitative variable, but unlike Linear Principal Component Analysis, does not require the adoption of an a priori difference between classification categories and does not presuppose a linear relation among the observed variables. So, neither the weights of the variables nor the differences between their categories are assumed, and both are suitably determined through the data as the solution of an optimization problem. The main features of Nonlinear Principal Component Analysis are illustrated, the problem of missing data is dealt with, and several methods for their treatment are described and assessed. Nonlinear Principal Component Analysis is also compared with the Rasch model (Chapter 14) and Linear Principal Component Analysis, two direct competitors for studying customer satisfaction data. Finally, the method is applied to the ABC ACSS data, and its applicability and findings are discussed.