Logistic and probit regression fit a model to functions of the response level probabilities. For logistic regression, the response functions modeled are logits (log odds). For probit models, the functions are probits (inverse of the standard normal cumulative distribution function). Logistic and probit models are in the class of generalized linear models and these functions are known as the link functions for these models. Because of the natural constraint that the response level probabilities must sum to one, there is always one fewer response functions than there are response levels. For example, with a binary response in a logistic model, there is a single logit (log(p₁/p₂) and therefore one parameter for each continuous predictor rather than two. For a k-level response (with ordered or unordered levels), there are k–1 logits and k–1 parameters per predictor. For example, a logistic model for a three-level response with unordered levels models two logits: ln(p₁/p₃) and ln(p₂/p₃). A continuous predictor would therefore have two parameter estimates — the first measuring the predictor's effect on the log odds that compares levels 1 and 3, and the second measuring the effect on the log odds that compares levels 2 and 3. A positive parameter estimate for a continuous predictor on the first logit means that increasing the predictor increases the logit and therefore increases p₁ relative to p₃.

The estimated model is able to produce predicted probabilities for all response levels in each observation. You can request the predicted probabilities with the PREDPROBS=INDIVIDUAL option in the OUTPUT statement.