It appears that the Hessian matrix generated in the present iteration has ill-conditioning ( near singularity) issues, inverting such an ill conditioned matrix is prone to numerical instability issues which manifest as large confidence intervals for one or more model parameters.

In such situation you can go with a modified Hessian (small perturbation incorporated to reduce the ill conditioning), an alternate approach it to update the current solution using an L=1 algorithm for feasible direction and the learning rate (for example, gradient descent, conjugate gradient etc.) and then from the next iteration onwards, switch over to the L=2 algorithms you are using for computation.

This message is telling you that:

Your model has unstable or invalid estimates due to mathematical issues in the regression — specifically, a singular Hessian matrix.

As a result, the regression has trouble computing valid standard errors, significance tests, and even coefficient estimates.

SPSS continues the procedure, but the message explicitly says:

“Validity of the model fit is uncertain.”

What’s Likely Going Wrong:

One or more of your predictor variables is redundant (highly correlated or linearly dependent with others).

Some categories in a categorical variable may have zero or very few cases, leading to empty or ill-conditioned cells in the model matrix.

This could also occur if there are dummy variables that are perfectly collinear (e.g., including all k dummies for a k-level factor without omitting one as reference).

What You Should Do:

Here’s a checklist to clean this up:

Check for collinearity

If you have many predictors, check if any are highly correlated (correlation matrix or use VIF in linear regression first).

Remove redundant or nearly collinear predictors.

Review categorical predictors

Are there categories with very few observations?

Merge sparse categories where it makes sense logically.

Avoid overparameterization

For k-level factors, ensure you're not including all k dummy variables — drop one as the reference category.

Rerun the model

After simplifying and cleaning the predictors/categories, rerun the NOMREG procedure.

Check if the warning disappears and if the model produces more stable results (with interpretable coefficients and standard errors).