Which Procedure Is Best for Your Application?

The techniques embodied in four of these procedures (Correspondence Analysis, Multiple Correspondence Analysis, Categorical Principal Components Analysis, and Nonlinear Canonical Correlation Analysis) fall into the general area of multivariate data analysis known as dimension reduction. That is, relationships between variables are represented in a few dimensions—say two or three—as often as possible. This enables you to describe structures or patterns in the relationships that would be too difficult to fathom in their original richness and complexity. In market research applications, these techniques can be a form of perceptual mapping. A major advantage of these procedures is that they accommodate data with different levels of optimal scaling.

Categorical Regression describes the relationship between a categorical response variable and a combination of categorical predictor variables. The influence of each predictor variable on the response variable is described by the corresponding regression weight. As in the other procedures, data can be analyzed with different levels of optimal scaling.

Multidimensional Scaling and Multidimensional Unfolding describe relationships between objects in a low-dimensional space, using the proximities between the objects.

Following are brief guidelines for each of the procedures:

• Use Categorical Regression to predict the values of a categorical dependent variable from a combination of categorical independent variables.
• Use Categorical Principal Components Analysis to account for patterns of variation in a single set of variables of mixed optimal scaling levels.
• Use Nonlinear Canonical Correlation Analysis to assess the extent to which two or more sets of variables of mixed optimal scaling levels are correlated.
• Use Correspondence Analysis to analyze two-way contingency tables or data that can be expressed as a two-way table, such as brand preference or sociometric choice data.
• Use Multiple Correspondence Analysis to analyze a categorical multivariate data matrix when you are willing to make no stronger assumption that all variables are analyzed at the nominal level.
• Use Multidimensional Scaling to analyze proximity data to find a least-squares representation of a single set of objects in a low-dimensional space.
• Use Multidimensional Unfolding to analyze proximity data to find a least-squares representation of two sets of objects in a low-dimensional space.