Proc LOGISTIC, PROC GENMOD, PROC GLIMMIX to fit Binary Logit, Cumulative Logit and Cumulative Probit Models

Binary Logit Models

Suppose there are J-levels of the outcome Yi, 1..J. The cumulative probabilities of Yi, pj(xi)=Pr(Yi<=j|xi), reflect the ordering, with p1(xi)<=p2(xi)<=...<=pJ(xi)=1.

Proc logistic, genmod and glimmix with the option link=cumlogit will fit the cumulative logit model s.t. log(pj(xi)/(1-pj(xi))=aj+xi.beta. The parameter beta describe the effect of a covariate on the log odds of response in the category j or below.

proc logistic data=test;
class vn0476_M(ref='female') vn0435_34(ref='rent') vn0455_1(ref='unmarried')/param=ref;
model product_pref=&numeric &norminal/link=cumlogit;
format vn0476_M gender. vn0435_34 rent. vn0455_1 marital.;
run;

Cumulative Probit Models

Proc logistic, genmod and glimmix with the option link=cumprobit will fit the cumulative probit model s.t. Pi^(-1)=ai+xi.beta.

proc logistic data=test;
class vn0476_M(ref='female') vn0435_34(ref='rent') vn0455_1(ref='unmarried')/param=ref;
model product_pref=&numeric &norminal/link=cumprobit;
format vn0476_M gender. vn0435_34 rent. vn0455_1 marital.;
run;

Cumulative logit and cumulative probit models assume the effect of a covariate is identical for all J-1 cumulative logits, which is called the proportional odds property.