Design matrix and PIM yielding very different deviance

[simone77]

Hi all,

I know this is a topic that has been treated quite a few times and also that GI gives many details on this.
As far as I know, different deviance obtained from the same model in PIM and in DM may arise from these situations:
1) The DM is built wrong
2) You don't specify the last interval as the reference cell (PIM in MARK uses the last interval as reference cell - in general something that should be avoided).
3) Different link functions in DM and PIM

I am dealing with models from the Robust Design Multi-state with Mis-Classification context in order to approximate a multi-event approach that allow to improve precision (with respect to data censoring and other procedures) in the estimates of the parameters by keeping in the data set the observation of individuals whose state is unknown.
In my case there are nine primary occasion each one with two secondary occasion. Capture and identification rates for the last secondary occasions are set to zero as explained in Kendall et al. (in press).
I have several data sets I am analyzing with this procedure.

In one case I have found that DM and PIM of a specific model yield very different values of deviance (5491 vs 5501) leading to very different AIC values.

This specific model has been run under other data sets with the same identical structure in DM and PIM and it gets very close results between them, so I can exclude the (1).
I have changed the reference cell, for instance I have set the last interval as reference cell and it makes no difference so that the (2) can be excluded.
I have tried to use the SIN or the LOGIT link in both the DM and PIM and it makes almost no difference so that the (3) can be excluded.

After these trials I have compared the DM and PIM results by starting from a very simple model without time variation and increasing the complexity of the models step by step.
I have found that initially the results are identical. Introducing time variation in omega (probability an individual has to be in state s) gives no changes, but when I introduce time variation in pi (probability an unclassified individual has to be in state state s at initial capture) the results begin to differ and, finally, when I add time variation to survival rate I get those very different results I am speaking about.

The data set that works well, i.e. no difference between DM and PIM results, is the best one (less sparseness): I believe it must be an important factor in this but cannot see how.
I would like to know what is going on and how to proceed with model selection given this situation. DM may be essential to me because sometimes I am interested in modeling additivity between factors.

Any commentary/suggestion on this?

Simone