The Ordinal Controversy Revisited

We present a discussion of the different dimensions of the ongoing controversy about the analysis of ordinal variables. The source of this controversy is traced to the earliest possible stage, measurement theory. Three major approaches in analyzing ordinal variables, called the non-parametric, the parametric, and the underlying variable approach, are identified and the merits and drawbacks of each of these approaches are pointed out. We show that the controversy on the exact definition of an ordinal variable causes problems with regard to defining ordinal association, and therefore to the interpretation of many recently designed models for ordinal variables, e.g., structure equation models using polychoric correlations, latent class models and ordinal response models. We conclude that the discussion with regard to ordinal variable modeling can only be fruitful if one makes a distinction between different types of ordinal variables. Five types of ordinal variables were identified. The problems concerning the analysis of these five types of ordinal variables are solved in some cases and remain a problem for others.