Ordinal Regression

Abstract

Many variables of interest are ordinal. That is, you can rank the values, but the real distance between categories is unknown. Diseases are graded on scales from least severe to most severe. Survey respondents choose answers on scales from strongly agree to strongly disagree. Students are graded on scales from A to F. You can use ordinal categorical variables as predictors, or factors, in many statistical procedures, such as linear regression. However, you have to make difficult decisions. Should you forget the ordering of the values and treat your categorical variables as if they are nominal? Should you substitute some sort of scale (for example, numbers 1 to 5) and pretend the variables are interval? Should you use some other transformation of the values hoping to capture some of that extra information in the ordinal scale? When your dependent variable is ordinal you also face a quandary. You can forget about the ordering and fit a multinomial logit model that ignores any ordering of the values of the dependent variable. You fit the same model if your groups are defined by color of car driven or severity of a disease. You estimate coefficients that capture differences between all possible pairs of groups. Or you can apply a model that incorporates the ordinal nature of the dependent variable. The SPSS Ordinal Regression procedure, or PLUM (Polytomous Universal Model), is an extension of the general linear model to ordinal categorical data. You can specify five link functions as well as scaling parameters. The procedure can be used to fit heteroscedastic probit and logit models.