Logistic Regression Models
If the response categories of the response variable 
can be restricted to a number of ordinal values, you can fit cumulative probabilities of the response categories with a cumulative logit model, a complementary log-log model, or a probit model. Details of cumulative logit models (or proportional odds models) can be found in McCullagh and Nelder (1989). If the response categories of are nominal responses without natural ordering, you can fit the response probabilities with a generalized logit model. Formulation of the generalized logit models for nominal response variables can be found in Agresti (2002). For each model, the procedure estimates the model parameter 
by using a pseudo-log-likelihood function. The procedure obtains the pseudo-maximum likelihood estimator 
by using iterations described in the section Iterative Algorithms for Model Fitting and estimates its variance described in the section Variance Estimation.
Cumulative Logit Model
A cumulative logit model uses the logit function
as the link function.
Denote the cumulative sum of the expected proportions for the first 
categories of variable by
for 
Then the cumulative logit model can be written as
with the model parameters
Complementary Log-Log Model
A complementary log-log model uses the complementary log-log function
as the link function. Denote the cumulative sum of the expected proportions for the first categories of variable by
for Then the complementary log-log model can be written as
with the model parameters
Probit Model
A probit model uses the probit (or normit) function, which is the inverse of the cumulative standard normal distribution function,
as the link function, where
Denote the cumulative sum of the expected proportions for the first categories of variable by
for Then the probit model can be written as
with the model parameters
be the reference category for the response variable 
as in the section Notation. Then the generalized logit model can be written as 
with the model parameters 
