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Ordinal Regression
Overview
Ordinal regression is used with ordinal dependent (response) variables, where the independents may be categorical factors or continuous covariates. Ordinal regression models are sometimes called cumulative logit models. Ordinal regression typically uses the logit link function, though other link functions are available. Ordinal regression with a logit link is also called a proportional odds model, since the parameters (regression coefficients) of the independent variable are independent of the levels (categories) of the ordinal dependent variable, and because these coefficients may be converted to odds ratios, as in logistic regression. 

Ordinal regression requires assuming that the effect of the independents is the same for each level of the dependent. Thus if an independent is age, then the effect on the dependent for a 10 year increase in age should be the same whether the difference is between age 20 to age 30, or from age 50 to age 60. In practice, researchers often consider it sufficiently "the same" if the slopes do not cross. The "test of parallel lines assumption" tests this critical assumption, which should not be taken for granted. In SPSS, select Analyze, Regression, Ordinal. 

See also the separate Statistical Associates "blue book" volume on generalized linear models. Ordinal regression is a special case of generalized linear modeling (GZLM). Identical parameter and model fit estimates can be obtained using the GZLM procedure, but options vary somewhat between PLUM (the ordinal regression procedure discussed here, standing for "polytomous universal model") and GZLM. Other coverage of ordinal regression is found in the separate Statistical Associates "Blue Book" on "Probit Regression and Response Models," which covers ordinal signal-response models.


Table of Contents

Overview	5
Key Terms and Concepts	6
Variables	6
The dependent variable	6
Factors	7
Covariates	8
Models	9
The location model	9
The default model	9
Interactions	10
Nested effects	10
Model Options	10
Statistics and saved variables for ordinal logistic regression	12
Output selections	12
SPSS Options	12
Example	13
The parallel lines test	14
Tests and effect size measures for model goodness of fit	15
Parameter estimates for the predictor variables and intercept	18
Odds ratios	20
Other output	24
Ordinal Regression for Signal-Response Models (Probit Link)	29
Overview	29
Assumptions	30
Parallel lines assumption	30
Adequate cell count	31
One ordinal dependent variable	33
Data level of predictor variables	33
Normal distribution of the dependent variable	33
Adequate sample size	33
No complete or quasi-complete separation	33
Frequently Asked Questions	34
Why not use multinomial logistic regression instead of ordinal (logit) regression?	34
Why not use ordinary least-squares regression instead of ordinal (logit) regression?	34
Why not use ANOVA instead of ordinal (logit) regression?	34
Why do SPSS and Stata parameter estimates differ, and what is "parameterization"?	35
Does the direction of coding of the ordinal dependent matter?	35
What is the SPSS syntax for ordinal regression models?	35
Bibliography	37