Categorical Variables

Abstract

At the conceptual level continuous variables and categorical variables need not be distinguished but, at the practical level, the form which the analysis of latter takes needs to be spelt out. This is done in the present chapter where categorical variables appear in the standard data matrix. The key step is the replacement of a continuous variable by an indicator vector showing into which of a number of categories a sample member falls. In some cases more information is available in the shape of an ordering of the categories. This can be accommodated by introducing a further kind of unobserved hypothetical variable which is assumed to induce the ordering of the categories. The analysis can then be carried out as if these hypothetical variables had actually been observed. The same idea can be extended to other situations and the chapter concludes with one such example where it is assumed that there is an underlying model in continuous variables for which only categorical observed variables are available. This also provides another example of the lack of identifiability discussed in Chap. 7.