Multinomial (or multigroup) logistic regression is a generalization of binary logistic regression applied to finding which variables best discriminate between three or more groups. It is available in most statistics software including SPSS.

The procedure produces regression estimates of form a(j) + b(kj) for the j-th group where a(j) is a constant term related to the relative sizes of the groups and b(kj) is the k-th predictor coefficient. As in ordinary (linear) regression a group predictor with s levels will be decomposed into s-1 dummy variables. For one of the groups, R, a(R) = b(kR) = 0 since group R is used as a reference group. R is usually taken to be the first or the last category.

These regression estimates are then used to compute a score in each group for each individual of form a(j) + b(j)xi where xi is the score for individual, I in group j. The score for all individuals in group R is zero.

The individual is then classified into the group for which they have the highest score.

Reference

Garson GD (2014) Logistic regression: binary and multinomial. Statistical Associates Publishers:Asheboro, NC. This illustrated tutorial introduces multinomial logistic regression. Contains SPSS (and SAS) examples. This is a major revision of the 2012 and 2013 texts. The attachment consists of the first 25 pages of text only.