Solved – Unexpected singularities in the Hessian matrix error in multinomial logistic regression

Question

I have been doing multinomial logistic regression analysis using SPSS 19.
I have encountered the following problem when I run the analysis procedure:

"Unexpected singularities in the
Hessian matrix are encountered. This
indicates that either some predictor
variables should be excluded or some
categories should be merged."

A little background about my data used. I have four categorical predictors with two levels each, 1 or 2. The response variable in my model is a three-level categorical variable. I used the last level as the reference category. I tried to compare the coefficients of the intercept with that of the four predictors in the two logits so as to find which level of the response variable may cause this problem. The big differences in coefficients between the intercept and three of the predictors suggest that it might be the reference category that has the problem. However, I could not combine the levels of the response variable (which I'm not allowed for my research).

I have also tried to exclude the predictors one by one, but still got the same problem.

Could anyone please tell me what I should do to solve this problem?

Answer 1

I the key you may be looking for can be found on the UCLA website for Multinomial Logistic Regression where it states:

Perfect prediction: Perfect prediction means that only one value of a predictor variable is associated with only one value of the response variable. You can tell from the output of the regression coefficients that something is wrong. You can then do a two-way tabulation of the outcome variable with the problematic variable to confirm this and then rerun the model without the problematic variable.

I would recommend running a two-way table for each of the predictors (vs. the response) to determine if one level of the response occurs with only one level of your predictor.