On Multinomial Regression
Output Warning interpretation

When a multinomial regression is fitted using NOMREG (SPSS) or GENMOD (SAS) then the model parameters (intercept and regression parameters) are estimated based on the maximum likelihood method. The latter method involves first computing the Hessian matrix that is, a matrix of all second derivatives of a certain function.  Next, it inverts the matrix, i.e., calculates the inverse of the Hessian matrix. This step requires the matrix to be nonsingular (of full rank).
Then each regression parameter estimate is based on the previous estimated parameter, i.e., by iteration. So the SPSS’s warning “Unexpected singularities in the Hessian matrix are encountered. The NOMREG procedure continues despite the above warning(s). Subsequent results shown are based on the last iteration. Validity of the model fit is uncertain” just states that the iteration process of calculating the parameter estimates could not be complete so that the results provided in the output are doubtable.
The warning also provides some suggestions on how to deal with that situation: “This indicates that either some predictor variables should be excluded or some categories should be merged.”
In general, a multinomial model is sensitive in terms of the number of parameters and number of categories of a dependent variable, both should not be very large. I would suggest to start with simple multinomial models and build the final model in a step-wise forward manner by “hand”. One of the approaches can be first to model the outcome based on a single predictor. Again, here depending on whether your predictor is continuous or a categorical you may get different results. Then you will get some information on what variables are associated with the outcome and include in the final model only those which were significant in the simple models.
The other general suggestion is whenever it is appropriate, keep the number of categories of the dependent variable as small as possible.