Multinomial logistic regression is a type of logistic regression that deals with dependent variables that are nominal – that is, there are multiple response levels and they have no specific order..  For example, you might be interested in type of residence (e.g. private house, shared house, apartment,, etc) with demographic and other variables.

The main problem with multinomial logistic regression is the enormous amount of output it generates; but there are ways to organize that output, both in tables and in graphs, that can make interpretation easier.  Multinomial logistic regression must sometimes be used with ordinal data, if none of the ordinal logistic regression methods can be used because of poor fit or violation of assumptions.