Zero-intercept poisson regression model predicts better than a model with an intercept?

Question

I have read some blogs/articles saying that intercept should not be suppressed. Recently, I used glmm.admb to model a ZIP (Zero-inflated Poisson) model which is giving better results without an intercept rather than with an intercept. I was surprised to find that the model without an intercept predicts better than that with an intercept. Is the prediction accuracy one of the reasons that I should use zero-intercept models?

Zero-intercept in my case means fixed effects have zero intercept while it is having a random intercept. Does this really make sense to include intercept in random effects but not in fixed effects?

Kindly assist me in regard to this.

Answer 1

Generally, you cannot get better in-sample fit by eliminating features from the model, and the intercept is a feature. Si, if your description of what you did was accurate, I would say there must be a user error (or software error, but user error is more probable ...) But then you say:

Zero-intercept in my case means fixed effects have zero intercept while it is having a random intercept

so you do have intercepts in the model. There should be no surprise that (random) intercepts for some groups can fit better than a common intercept.