The GENMOD Procedure

This type of model applies to cases where an observation can fall into one ofcategories. Binary data occur in the special case where. If there areobservations in a subpopulation, then the probability distribution of the number falling into thecategoriescan be modeled by the multinomial distribution, defined in the sectionResponse Probability Distributions, with. The multinomial model is anmodel if the categories have a natural order.



The GENMOD procedure supports only the ordinal multinomial model. Ifare the category probabilities, the cumulative category probabilities are modeled with the same link functions used for binomial data. Let,, be the cumulative category probabilities (note that). The ordinal model is

whereare intercept terms that depend only on the categories andis a vector of covariates that does not include an intercept term. The logit, probit, and complementary log-log link functionsare available. These are obtained by specifying the MODEL statement options DIST=MULTINOMIAL and LINK=CUMLOGIT (cumulative logit), LINK=CUMPROBIT (cumulative probit), or LINK=CUMCLL (cumulative complementary log-log). Alternatively,

whereis a cumulative distribution function for the logistic, normal, or extreme-value distribution.

PROC GENMOD estimates the intercept parametersand regression parametersby maximum likelihood.
