ABSTRACT
This chapter presents several approaches to predicting ordinal relations, of the kind described by the hypothetical investigator, on a dependent variable Y from several predictor variables. Ordinal methods are used for analyzing data in only a few instances, becoming almost unknown once the data go beyond the simplest kinds of bivariate correlations or one-way comparisons of location. One approach to more sophisticated analyses of ordinal data, dating from the early 1960s, has been to assume a particular model fits the data and then transform the observed scale so that it optimally fits the model. An LSMR analysis may satisfy the ordinal goal reasonably, or it may not, but a more strictly ordinal analysis, designed to minimize an ordinal loss function, seems more likely to do so. As an alternative to applying LSMR to variables that are ordinal, several writers proposed applying LSMR methodology to tau correlations.
