deviance issue

[C. Le Coeur]

Dear all,

I run two identical simple robust design models (from the same dataset) for which all parameters (S, gam”, gam’, p, c, N) were constrained to be a function of sex.
For one of these models, I created an additional factor variable in the data (cohort variable). Therefore, one had two groups (male and female) and the other had 4 groups (i.e sex and two cohorts). When I run the two models (sex-varying parameters), I obtained two huge different deviances : 3017.302 and 3970.949 respectively.

Why is there a difference in the deviance when additional groups were defined, as these are not involved in parameter specifications ?
If I understand well, the Mt+1 matrix and -2logL(saturated) were changed due to the two additional groups, so the deviance of the current model was changed too because it is defined as the difference in model likelihood of the current model and the saturated model, isn’t it ?

But what are the consequences for model selection then ? Should I predefined all my groups at the first step of the model selection to be able to compare them ?

For example, I begin the model selection by constraining all parameters by time, sex and cohort effects. Then, from my best model, I want to constrain the survival parameter by an additional age effect. If I define the age variable at this step (so a first selection has been done before the creation of age variable), I cannot compare this model to the previous models selection because the saturated model is not the same anymore, right ? If the age variable is created in the beginning, the saturated model is always the same (age models or not). Is it correct ?

Thank you for your answer,

C. Le Coeur

[gwhite]

You have effectively changed the data when you specify the attributes groups. Specifically, you have changed the saturated model. For example consider a known fate data set with a single group. The saturated model is the simplest model with just a single survival estimate. Now, you re-specify the data with 2 groups, males and females. Now the saturated model has 2 parameters, and allows evaluation of the sex differences.

Remember that deviance is the difference between the model of interest and the saturated model.

Gary