You can model to a binomial (two level) response in PROC GENMOD by specifying the DIST=BINOMIAL option in the MODEL statement. The default link function is the logit link yielding a logistic model. Specify LINK=PROBIT in the MODEL statement to request a probit model or LINK=CLOGLOG to use the complementary log log link (useful when the shape of the model is not symmetric). By default, the probability of the lower response level is modeled as in the LOGISTIC and PROBIT procedures. Use the DESCENDING response variable option in the MODEL statement to reverse the response order and model the probability of the higher level. Always check the Response Profile table and messages in the log and displayed results to verify that the desired level is modeled.

You can also use PROC GENMOD to model an ordinal multinomial response (that is, categorical response data with more than two levels that are ordered) by specifying the DIST=MULTINOMIAL option in the MODEL statement. PROC GENMOD cannot model an unordered (nominal) multinomial response. With the DIST=MULTINOMIAL option, GENMOD fits a model that treats the response as an ordinal variable by modeling a set of cumulative response probabilities through a link function (LINK=CLOGIT for cumulative logits, LINK=CPROBIT for cumulative probits, or LINK=CLOGLOG for cumulative complementary log-log functions). The default cumulative logit link fits the same model that PROC LOGISTIC and PROC PROBIT fit by default to multinomial data. The cumulative logit link produces an ordinal logistic model that assumes proportional odds. A test of this assumption is not available in PROC GENMOD as it is in PROC LOGISTIC. Specify LINK=CPROBIT in the MODEL statement to request an ordinal probit model. By default, the probabilities of lower response levels are modeled as in the LOGISTIC and PROBIT procedures. Use the DESCENDING response variable option in the MODEL statement to reverse the response order and model the probabilities of the higher levels. Always check the Response Profile table to verify that the response levels are in logical ascending or descending order and that the desired order is used.

If your multinomial response is not ordered (is nominal, rather than ordinal), you can use the LINK=GLOGIT option in the MODEL statement of PROC LOGISTIC or PROC GLIMMIX to fit a generalized logit model appropriate for a nominal response.

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