Can anyone explain me the differences between Multinomial Logit Model and Conditional Multinomial Logit Model?
Multinomial Logit Model $$P(y_n=j|z_n=z)=\frac{exp(z'a_j)}{1+\sum exp(z'a)}$$
Conditional Multinomial Logit Model $$P(y_n=j|x_n)=\frac{exp(x_n'\beta_j)}{\sum exp(x_n'\beta_j)}$$
The ordinal logistic regression is also a multinomial model?
I'm using this reference Categorical Data Analysis, Alan Agresti, if anyone has another references I appreciate.
As I explained yesterday in another post, the conditional multinomial logit extends the multinomial logit by including characteristics of the alternatives (as well as characteristics of the individuals). Multinomial logit models allow to include only individual predictors but not alternative-specific regressors (except for more complicated re-parameterizing). An excellent introduction can be found in Cameron & Trivedi Microeconometrics Using Stata or online here or here.
