Is there a difference between a multinomial logit model and a non-binary logistic regression model? If yes, then what is the difference?

Answer

Dear Sarah,

Non-binary logistic regression is a more general term than multinomial logit models. You now quote the multivariate case, but the situation is completely similar to the univariate case.

When you talk about logistic regression you are always talking about a dummy or binary random variable where you want to explain its probability of success on the basis of measured variables. In your multinomial case, you have a categorical variable that you wish to declare. Now if I designate y as variable to be explained (categorical) and x1,…,xn the measured or explanatory variables (If the dependent variable is categorical, actually several dummies are created because this is statistically better). If G is a function from the real numbers to the interval [0,1]then is

y=G(∑θixi) a non-binary logistic regression model. If you now equate the function G(u) with the Logit function:

G(u)=1/(1+e^-you)

are called multinomial logit models. If you equate the function G(u) with the Probit function, ie the cumulative distribution function of the normal distribution, then one speaks of a multinomial probit model.

I should note that, strictly speaking, multinomial logit models are made for nominal variables. For ordinal variables such as someone’s opinion (0=worst, 1=bad, 2=better,3=best) you have to use a so-called ordered logit model and not a multinomial logit model.

More about the differences in use in the appendix.

In summary: A multinomial logit model is part of the larger class of non-binary logistic regression models, which in turn are part of the even larger class of generalized multilinear regression models.

Can you choose any function for G? Actually yes, but you can show that the Logit function has the best properties for explaining categorical data. The probit function can be explained well for absolutely continuous data, although this is a less robust choice.

Hope this is a bit clear,

Regards,

Kurt.