A statistical model for the analysis of ordinal level dependent variables

TLDR

The model extends the dichotomous probit model, attributing ordinal data to methodological limitations that collapse an otherwise interval‑level variable into categories. This paper develops a linear‑model‑based framework for analyzing ordinal dependent variables. It assumes a linear effect of each independent variable and break points between categories, and derives maximum likelihood estimators with asymptotic sampling distributions, plus an R² analogue for goodness of fit. The framework is demonstrated on Congressional voting in the 1965 Medicare Bill, illustrating the estimators, asymptotic properties, and R² analogue.

Abstract

This paper develops a model, with assumptions similar to those of the linear model, for use when the observed dependent variable is ordinal. This model is an extension of the dichotomous probit model, and assumes that the ordinal nature of the observed dependent variable is due to methodological limitations in collecting the data, which force the researcher to lump together and identify various portions of an (otherwise) interval level variable. The model assumes a linear eflect of each independent variable as well as a series of break points between categories for the dependent variable. Maximum likelihood estimators are found for these parameters, along with their asymptotic sampling distributions, and an analogue of R 2 (the coefficient of determination in regression analysis) is defined to measure goodness of fit. The use of the model is illustrated with an analysis of Congressional voting on the 1965 Medicare Bill.