"Multinomial logit model" is a term often used to refer to a model for data in which the response is a set of unordered choices and with at least some of the independent variables indicating characteristics of the choices (examples are cost, size, and attractiveness) instead of characteristics of the subject or chooser (examples are age and income). This is also known as McFadden's conditional logit model and is in a class of models known as discrete choice models. In this model, the effect of an independent variable is conditional on the subject's choosing between two alternatives, and it depends on the distance between the variable's values that were assigned by the subject to the two alternatives.

This model can be fit by the SAS/STAT^® procedure BCHOICE (beginning with SAS^® 9.4 TS1M1) using Bayesian methods, or by the SAS/ETS^® procedure MDC, or by the SAS/STAT procedure PHREG using the STRATA statement and the TIES=BRESLOW option, or by the SAS/STAT procedure LOGISTIC using the STRATA statement. See examples in the BCHOICE and MDC documentation. Note that the multinomial probit model can also be fit using the BCHOICE and MDC procedures. Discussion and examples of fitting discrete choice models using PROC PHREG can be found in this paper. Related discussion is available in these documents. More discussion of the discrete choice models can be found in the book Logistic Regression Using SAS: Theory and Application, Second Edition.

Note that the LOGISTIC, PROBIT, and CATMOD procedures are generally used to fit a model in which all independent variables are characteristics of the choosers, not of the choices. For this case, you can use PROC LOGISTIC to model either a binary or multinomial response. A multinomial response variable can be either unordered (nominal) or ordered (ordinal). By default, PROC LOGISTIC fits an ordinal model to multinomial responses. Use the LINK=GLOGIT option in PROC LOGISTIC to fit a nominal model. While PROC CATMOD can also fit a nominal logistic model, PROC LOGISTIC is generally more efficient, easier to use, and offers more features when fitting these models (such as odds ratio estimation and saving predicted probabilities) than PROC CATMOD.

See this note for more information about the variety of logistic models that you can fit with SAS software.

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