Response-Level Ordering and Referencing |
In models for binary and multinomial data, the response-level ordering is important because it reflects the following:
which probability is modeled with binary data
how categories are ordered for ordinal data
which category serves as the reference category in nominal generalized logit models (models for nominal data)
You should view the "Response Profile" table to ensure that the categories are properly arranged and that the desired outcome is modeled. In this table, response levels are arranged by Ordered Value. The lowest response level is assigned Ordered Value 1, the next lowest is assigned Ordered Value 2, and so forth. In binary models, the probability modeled is the probability of the response level with the lowest Ordered Value.
You can change which probability is modeled and the Ordered Value in the "Response Profile" table with the DESCENDING, EVENT=, ORDER=, and REF= response variable options in the MODEL statement. See the section Response Level Ordering in Chapter 53, The LOGISTIC Procedure, for examples about how to use these options to affect the probability being modeled for binary data.
For multinomial models, the response-level ordering affects two important aspects. In cumulative link models the categories are assumed ordered according to their Ordered Value in the "Response Profile" table. If the response variable is a character variable or has a format, you should check this table carefully as to whether the Ordered Values reflect the correct ordinal scale.
In generalized logit models (for multinomial data with unordered categories), one response category is chosen as the reference category in the formulation of the generalized logits. By default, the linear predictor in the reference category is set to 0, and the reference category corresponds to the entry in the "Response Profile" table with the highest Ordered Value. You can affect the assignment of Ordered Values with the DESCENDING and ORDER= options in the MODEL statement. You can choose a different reference category with the REF= option. The choice of the reference category for generalized logit models affects the results. It is sometimes recommended that you choose the category with the highest frequency as the reference (see, for example, Brown and Prescott 1999, p. 160). You can achieve this with the GLIMMIX procedure by combining the ORDER= and REF= options, as in the following statements:
proc glimmix; class preference; model preference(order=freq ref=first) = feature price / dist=multinomial link=glogit; random intercept / subject=store group=preference; run;
The ORDER=FREQ option arranges the categories by descending frequency. The REF=FIRST option then selects the response category with the lowest Ordered Value—the most frequent category—as the reference.