7 Cluster analysis for segmentation

In this chapter, you will learn how to carry out a cluster analysis and a linear discriminant analysis.

A cluster analysis works on a group of observations that differ from each other on a number of dimensions. It will find clusters of observations in the n-dimensional space such that the similarity of observations within clusters is as high as possible and the similarity of observations between clusters is as low as possible. You can always carry out a cluster analysis and you can ask for any number of clusters. The maximum number of clusters is the total number of observations. In that case each observation will be a cluster, but that would not be a very useful clustering, however. The goal of clustering is to find a small number of clusters that can be meaningfully described by their average scores on the n dimensions. In other words, the goal is to find different ‘profiles’ of observations.

Linear discriminant analysis tries to predict a categorical variable on the basis of a number of continuous or categorical independent variables. It is similar to logistic regression. We’ll use it to predict an observation’s cluster membership (as established by the cluster analysis) based on a few segmentation variables (i.e., other information we have on the observations that did not serve as input in the cluster analysis).

We will analyze data from 40 respondents who rated the importance of a number of store attributes when buying office equipment. We will use cluster analysis to find clusters of observations, in this case, clusters of respondents. These clusters will have different profiles (e.g., one cluster may attach importance to price and return policy, the other may attach importance to variety of choice and quality of service). We will then use linear discriminant analysis to test whether we can predict cluster membership (i.e., what type of office equipment shopper someone is) based on a number of respondent characteristics (e.g., their income).