I am wondering if there are cases when a model with a smaller number of estimated parameters may have lower deviance of another with more parameters. This is the specific case I have in mind:

Mod1: {phi(g x IndCov) p(.)} np = 7 Deviance = 580

Mod2: {phi(g + IndCov) p(.)} np = 5 Deviance = 585

Mod3: {phi(g + t) p(.)} np = 9 Deviance = 581

Where IndCov is an individual covariate, g is a group of three levels and t are seven occasions.

This is from a paper I have read and I have been surprised by that because a priori I would have expected that Mod3 cannot have a deviance value higher than that of Mod1.

I wonder if this can be something related to what discussed in the sidebar at page 11-10 of MARK manual about standardization of individual covariates when there is a common intercept and 2 or more slopes.

Or am I missing the point? Any commentary on it would be really appreciated.