Alternatives to the multinomial logit model I am trying to estimate a model of occupational choice with three choices. Are there any alternatives to using the multinomial logistic regression when handling such unordered categorical outcomes?
When dealing with binary dependent variables there seems to be several choices such as the LPM model as well as the binary probit and logit model. When dealing with unordered categorical variables the literature however keeps recommending the multinomial logit model without comparing it to alternatives.
 A: There is a variety of models available to model multinomial models.
I recommend Cameron & Trivedi Microeconometrics Using Stata for an easy and excellent introduction or take a look at the Imbens & Wooldridge Lecture Slides or here which are available online.
Widely used models include:
multinomial logistic regression or mlogit in Stata
multinomial conditional logit (allows to easily include not only individual-specific but also choice-specific predictors) or asclogit in Stata
nested logit (relax the independence from irrelevant alternatives assumption (IIA) by grouping/ranking choices in an hierarchical way) or nlogit in Stata
mixed logit (relaxes the IIA assumption by assuming e.g. normal distributed parameters) or mixlogit in Stata. 
multinomial probit model (can further relax the IIA assumption but you should have choice-specific predictors available) 
mixed logit (relaxes the IIA assumption assuming e.g. normal distributed parameters), use asmprobit in Stata (mprobit does not allow to use choice-specific predictors but you should use them to relax the IIA asumption) 
A: If you're wanting options quite different from a logistic regression, you could use a neural net. For example, R's nnet package has a multinom function. Or you could use a Random Forest (R's randomForest package, and others). And there are several other Machine Learning alternatives, though options like an SVM tend to not be well-calibrated which makes their outputs inferior -- in my opinion -- to a logistic regression.
[Actually, a logit is probably being used under the hood by the neurons in the neural net. So it's quite different, but not quite different at the same time.]
A: Also, think Neural Nets (with softmax activation), Decision Trees (or Random Forests) do not require the IIA assumption to be met considering the unreliability of these tests concerned with checking the IIA assumption. So this might be an advantage compared to the multinomial logistic if all we are concerned is only predictions. 
Alternatively, multiple logistic models can be built for the K-1 categories with the Kth category as the reference. This also allows for different predictors to be plugged for each of the equations in contrast to the multinomial 
