User Guide

79
Chapter
8
Ordinal Regression
Ordinal Regression allows you to model the dependence of a polytomous ordinal
response on a set of predictors, which can be factors or covariates. The design of
Ordinal Regression is based on the methodology of McCullagh (1980, 1998), and the
procedure is referred to as
PLUM in the syntax.
Standard linear regression analysis involves minimizing the sum-of-squared
differences between a response (dependent) variable and a weighted combination of
predictor (independent) variables. The estimated coefficients reflect how changes in
the predictors affect the response. The response is assumed to be numerical, in the
sense that changes in the level of the response are equivalent throughout the range of
the response. For example, the difference in height between a person who is 150 cm
tall and a person who is 140 cm tall is 10 cm, which has the same meaning as the
difference in height between a person who is 210 cm tall and a person who is 200 cm
tall. These relationships do not necessarily hold for ordinal variables, in which the
choice and number of response categories can be quite arbitrary.
Example. Ordinal Regression could be used to study patient reaction to drug dosage.
The possible reactions may be classified as “none,” “mild,” “moderate,” or “severe.”
The difference between a mild and moderate reaction is difficult or impossible to
quantify and is based on perception. Moreover, the difference between a mild and
moderate response may be greater or less than the difference between a moderate and
severe response.
Statistics and plots. Observed and expected frequencies and cumulative frequencies,
Pearson residuals for frequencies and cumulative frequencies, observed and expected
probabilities, observed and expected cumulative probabilities of each response
category by covariate pattern, asymptotic correlation and covariance matrices of
parameter estimates, Pearson’s chi-square and likelihood-ratio chi-square, goodness-
of-fit statistics, iteration history, test of parallel lines assumption, parameter estimates,