trouble replicating Phi(t) p(t*TSM) in design matrix

[Eric Janney]

I have a CJS dataset that GOF testing indicates a strong time since marking effect on recapture probability. Ultimately, I would like to run a Phi(sex+t) phi(t*time since marking) for this data set. So, I started by creating Phi(sex*t) p(t*TSM) using the PIMS. Then I was able to recreate this model using the design matrix. I checked AIC, Deviance, etc. between the PIM run and the Design run to make sure that I coded the design matrix correctly. Once I adjusted the # for K for the design matrix run, AIC etc. matched up indicating I coded the design matrix correctly. Then I dropped the sex effect on Phi using the PIMS and compared this model to the same model in which I dropped the sex effect on Phi using the design matrix (deleted the sex effect column and the interaction columns). The AIC, Deviance, etc. however, are slightly different between the PIM run and the Design Matrix run of this model. What could cause these two models runs to produce different results. Here is the model output. I'm probably overlooking something very obvious, but any help would be greatly appreciated!
Model QAICc K QDeviance

{Phi(t) p(t*TSM)} PIMS 16473.38 31 456.66

{Phi(sex*t) p(t*TSM)} PIMS 16473.66 42 434.82

{Phi(sex*t) p(t*TSM)} DESIGN 16473.66 42 434.82

{Phi(t) p(t*TSM)} DESIGN 16474.31 31 457.59

[cooch]

I The AIC, Deviance, etc. however, are slightly different between the PIM run and the Design Matrix run of this model.

Quick reply...

Slightly - indeed. I can't replicate it in a quick comparison of 5-6 different data sets parameterized the way you described (in fact, I get identical deviances regardless of whether or not I buld with PIMs, or the DM), but...

Try using the same link function (fiddling with PIMs defaults to sin link, anything other than identity DM defaults to logit link. Differences between models built with PIMs and DM are common if you have one or more parameters estimated near either 0 or 1 (owing to the different properties of the 2 link functions). If you have such estimates, or general 'data weirdness' (usually meaning 'sparseness'), this can happen.

Also, you might want to try using different reference cell coding, such the confounded parameters in the models aren't used as the reference cells in the DM. This is discussed in other posts, and in Chapter 7.

[Eric Janney]

Evan,

Thanks for the input. The data are indeed sparse in the early years of the study. I'll try using different cell coding and see if that works.