Multidimensional Scaling

This chapter discusses the use of multidimensional scaling and begins with making a comparison of MDS with principal components analysis, cluster analysis and discriminant analysis. The chapter discusses two approaches to MDS: metric (used with data measured on interval/ratio scale) and non-metric (used with data measured on ordinal scale). It is important to note that the data for MDS requires to be in a matrix form, and the metric approach to MDS requires it to be a matrix object too. We therefore explain to first coerce the object of “dist” type into a matrix object and then undertake metric MDS using the dataset on paired distances between some European cities. A perceptual map is generated based on the Euclidean distance between the cities. We then take an example of the quality of life of breast cancer patients, measured on an ordinal scale, to explain the non-metric MDS and generate a perceptual map of patients with similar qualities of life. We finally explain Shephard's diagram to examine the goodness-of-fit of the non-metric MDS. The chapter ends with a note on missing values.