age/sex models using design matrices

[shelly]

I am a newbie to MARK. To test my understanding of model building using design matrices I have been comparing the output of models I've built using PIMs versus the same models built using the design matrix. I have noticed that sometimes the output (particularly the number of estimable parameters but also the model deviance and Akaike scores) is different when I build (what i think is) the same model with a PIM versus a design matrix.

For example, I have a dataset of 7 years of captures for males and females all captured as sub-adults, with males and females input as two groups in the .inp file. Ignoring sex differences(for the moment) I want to build a 2-age class model (1st age class = 1yr, 2nd age class = remaining years with time variation in both age classes and recapture rate varying by time only). The PIMS are
(one each for males and females)
1 7 8 9 10 11
2 8 9 10 11
3 9 10 11
4 10 11
5 11
6
The design matrix coding I have tried is the following (recapture part not included)
111000000000
110100010000
110010001000
110001000100
110000100010
110000000000
100100000000
100010000000
100001000000
100000100000
100000000000
But this doesn’t give the same output as the model based on the PIMs.

I have a feeling this is due to the different link function that two approaches use to estimate the parameters. The logit function seems to be much worse in estimating (resolving) parameters than does the sin link for the same model, therefore the same model built with a design matrix (as opposed to PIMs) ends up better supported in the final results(has fewer parameters). But it is quite likely that I’m doing something fundamentally wrong.

Any assistance with what is going wrong and how to correct this problem would be greatly appreciated.

Also I do eventually want to look at differences between males and females (particularly in the first age class). I have had a go at coding the design matrix for this but I am not sure I have the interactions correct as the same problem happens as above. What does the design matrix look like for the full parameterized model with sex, 2 age classes and 6 time intervals? (Intercept = 1 column, sex = 1 column, age = 1 column, time = 5 columns, age*time = 4 columns, sex*time = 5 columns, age*sex = 1 column, age*sex*time = 4 columns)??

1111000000001100000000
1110100010001010001000
1110010001001001000100
1110001000101000100010
1110000100011000010001
1110000000001000000000
1100100000000100000000
1100010000000010000000
1100001000000001000000
1100000100000000100000
1100000000000000010000
1011000000000000000000
1010100010000000000000
1010010001000000000000
1010001000100000000000
1010000100010000000000
1010000000000000000000
1000100000000000000000
1000010000000000000000
1000001000000000000000
1000000100000000000000
1000000000000000000000

[cooch]

I am a newbie to MARK.
...

Any assistance with what is going wrong and how to correct this problem would be greatly appreciated.

Your questions are already answered for you in various chapters in 'the book'. Hard to know what you have, or haven't read, but I'd suggest careful study of chapters 7 and 8 will provide answers to most (probably all) of your questions. There are specific sections dealing with link functions, parameter counting.

As for age models, covered in some detail in chapter 8 - including many examples of building corresponding design matrices.