ABSTRACT
The subject of this chapter lies, in a sense, between that of Chapter 7 on factor analysis and Chapter 8 on factor analysis for binary data. It differs from both of these earlier kinds of factor analysis principally in that the manifest variables are ordered categorical variables; that is, the response will be in one of a number of ordered categories. For example, if we ask someone whether they enjoyed a meal, “very much”, “a little”, or “not very much”, we would be observing an ordered categorical variable. The answer can fall into only one category and those categories are ordered according to strength of approval. Any ordered categorical variable can be reduced, of course, to a binary variable by amalgamating categories. For example, if we were to amalgamate “a little” and “very much”, we would have a binary variable. In fact, we did this in the analysis of the sexual attitudes data in Section 8.8, where three of the items had four categories. These were amalgamated into two pairs so that all variables could be treated as binary. In doing this, we are losing information and that provides the motivation for the present chapter. Categorical variables with more than two categories are often referred to as polytomous, where they are ordered they may be called ordinal.
