Multinomial logistic regression

When the dependent variable consists of several categories that are not ordinal (i.e., they have no natural ordering), the ordinary least square estimator cannot be used. Instead, a maximum likelihood estimator like multinomial logit or probit should be used.

The purpose of this article is to understand the multinomial logit model (MLM) that uses maximum likelihood estimator and its application in nursing research.

The research on "Racial differences in use of long-term care received by the elderly" (Kwak, 2001) is used to illustrate the multinomial logit model approach. This method assumes that the data satisfy a critical assumption called the "independence of irrelevant alternatives." A diagnostic developed by Hausman is used to test the independence of irrelevant alternatives assumption. Models in which the dependent variable consists of several unordered categories can be estimated with the multinomial logit model, and these models can be easily interpreted.

This method can handle situations with several categories. There is no need to limit the analysis to pairs of categories, or to collapse the categories into two mutually exclusive groups so that the (more familiar) logit model can be used. Indeed, any strategy that eliminates observations or combines categories only leads to less efficient estimates.