The assumptions behind multinomial regression are similar to the ones for logistic regression. Since the y-variable has multiple categories, model diagnostics are nonetheless slightly more complicated.
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Checklist
Categorical outcome
The y-variable should be categorical (and non-binary). Check whether it is possible to group similar categories (cf. the Blue bus/Red bus problem). Although it makes most sense to use multinomial regression analysis if the y-variable is nominal with more than two categories, it is possible to use a binary outcome – however, then you could just as well go with a plain logistic regression (unless you want to obtain some of the test available for multinomial regression analysis). It is also possible to have an ordinal y-variable (e.g., if the assumptions for ordinal regression were violated, you can try a multinomial regression instead; the latter does not assume parallel lines).
Independence of errors
Data should be independent, i.e. not derived from any dependent samples design, e.g. before-after measurements/paired samples.
No multicollinearity
Multicollinearity may occur when two or more x-variables that are included simultaneously in the model are strongly correlated with each another. Actually, this does not violate the assumptions, but is does create greater standard errors which makes it harder to reject the null hypothesis.
