Design matrices for transient models

[annaren]

The problem is that the parameter estimates for the same model:

Phi (m2*s*h*t) p(m*s*h*t)
where m2 indicates transience
s = sex (wide or narrow)
h = habitat (wide or narrow)
t = time ( four trap occassions so t1 and t2)
m indicates trap dependence

constructed using the PIMS are not the same as those from the design matrix although the AIC, deviance and number of parameters are the same.

Additionally, the number of parameters estimated is 26 and no matter how much I read all the information in the book on counting parameters I can not see why it is 26 and not 32.

THank you so much for all your kind help so far. I really appreciate it as I know you must be very busy yourself.
Best,
Anna

[jlaake]

You should never create your groups or any other predictor based on the results of capture (eg once or more than once). Doing so confuses your explanatory variables (predictors/independent variables) and the data (dependent variables). For example, consider what would happen if you split your groups as recaptured at least once versus not recaptured.

As Evan said the transience model simply sets the "apparent survival" rate of "newly caught" to be different than "previously caught". TSM=0 versus TSM >0. The concept is that transient animals will not be seen again so that is absorbed into apparent survival.

--jeff

[jlaake]

> The problem is that the parameter estimates for the same model:
>
> Phi (m2*s*h*t) p(m*s*h*t)
> where m2 indicates transience
> s = sex (wide or narrow)
> h = habitat (wide or narrow)
> t = time ( four trap occassions so t1 and t2)
> m indicates trap dependence
>
How is m being used in p? Transience models have an effect in Phi but not in p. Are you also trying to model a trap dependence(happy/shy) effect such that capture in occasion t affects p(t+1)? These are not likely to fit well together in the same model.

Also are you fitting Phis and ps for each time? That would be 3 rather than just t1,t2. If you are fitting a full time model then the values for the last time are confounded. Not sure what you are doing for p but for Phi, the full interaction transience model would have 5 Phi parameters for each group and would then have 20 (4*5) for your 4 groups. Sounds like you are using the additive model with 4 Phi parameters so 16 in total for Phi and the additive model for p somehow for a total of 32. My guess is that you have a combination of truly confounded parameters for the last occasion and parameters that are hitting a boundary. I suggest that you drop the m in the p model and then look at which parameters are still showing as singular. My guess is that they would be for the last occasion because of true confounding.

--jeff

[annaren]

Yes I am trying to fit a model with both transience and trap dependence and have 20 phi and 20 p's in the design matrix. The reason for this was when I used U-CARE both transience adn trap dependence were significant. The reason I thought that 32 parameters would be estimated as I took of the 2 beta terms for each of the 4 groups I have. I will run a model without the m term in the model and see what I find.
Thanks so much

[cooch]

> The problem is that the parameter estimates for the same model:
>
> Phi (m2*s*h*t) p(m*s*h*t)
> where m2 indicates transience
> s = sex (wide or narrow)
> h = habitat (wide or narrow)
> t = time ( four trap occassions so t1 and t2)
> m indicates trap dependence
>
How is m being used in p? Transience models have an effect in Phi but not in p. Are you also trying to model a trap dependence(happy/shy) effect such that capture in occasion t affects p(t+1)? These are not likely to fit well together in the same model.

Jeff is entirely correct, of course. For a model with TSM structure in both phi and p, you have several confounded terminal parameters (what Lebreton et al. unfortunately called 'beta terms'). For each 'age' class, the terminal phi(p) parameters are estimated only as a function of their product. So, for example, if you had one group, 7 occasion study, you'd have

phi(1) -> phi(5) (5 parameters)
phi(6) would be confounded with p(7) (1 parameter)

phi(7) -> phi(10) (4 parameters)
phi(11) would be confounded with p(22) (1 parameter)

p(12) -> p(16) (5 parameters)
p(18) -> p(21) (4 parameters)

So, even though the DM has 22 columns - suggesting 22 estimable parameters - in fact only (5+1+4+1+5+4)=20 estimable parameters.

If the deviances for the PIM and DM versions are the same, then you're good to go.

[annaren]

Ok I have got back to basics and am looking at the data NOT divided into sex or habitat. The GOF test shows significant transience so I have a model phi (m2*t) p (t) which is non-significant and thus fits the data.
Next I used MARK and constructed the model usiing the PIMS and then the design matrix.

Phi
1 4 5
2 5
3

p
6 7 8
7 8
8

This is where the problem lies. Somehow MARK does not like making transient models using PIMS as it then can't build a design matrix as it says there are more (8) parameters in the PIMS than should be (6).
When I then look at the parameter estimates for the same model constructed using the PIMS and design matrix they are different for both the end terminal phi and p values when normally it is only the end p value that is unestimatable (see below).


Real Function Parameters of {phi m*t p t}Design Matrix}

Parameter Estimate Standard Error
------------------------- -------------- --------------
1:Phi 0.2334532 0.0284160
2:Phi 0.2559661 0.0286167
3:Phi 0.4254893 0.0000000
4:Phi 0.4019668 0.0778906
5:Phi 0.5709824 0.0000000
6:p 0.9090909 0.0612909
7:p 0.7941177 0.0693445
8:p 0.4184684 0.0000000



Real Function Parameters of {phi m*t p t}using PIMS

Parameter Estimate Standard Error
------------------------- -------------- --------------
1:Phi 0.2334532 0.0284160
2:Phi 0.2559662 0.0286167
3:Phi 0.4066062 126.38807
4:Phi 0.4019670 0.0778908
5:Phi 0.5456421 169.60553
6:p 0.9090910 0.0612909
7:p 0.7941176 0.0693446
8:p 0.4379024 136.11604


So even know MARK says it can estimate 7 parameters only 5 are comparable between the two models.
Does anybody know why is this is and if both the end phi and p are therefore both unestimatable.

Anna

[jlaake]

Anna-

Spend some more time reading the guide or go to one of the workshops and you'll save your self time and grief. The real parameters are confounded as a product. If I tell you the product of two numbers x and y is 42, can you tell me what either number is? They could be x=6,y=7 or the opposite or 2 and 21 etc. Get the idea? All you can do is estimate the product and NEITHER p nor Phi is useful in that case. You can change the values so the product is the same and the model will fit the same.

--jeff

[cooch]

Ok I have got back to basics and am looking at the data NOT divided into sex or habitat. The GOF test shows significant transience so I have a model phi (m2*t) p (t) which is non-significant and thus fits the data.
Next I used MARK and constructed the model usiing the PIMS and then the design matrix.

Phi
1 4 5
2 5
3

p
6 7 8
7 8
8

This is where the problem lies. Somehow MARK does not like making transient models using PIMS as it then can't build a design matrix as it says there are more (8) parameters in the PIMS than should be (6).

As explained in several points in 'the book', you can have MARK automatically build the full design matrix only for a fully time-dependent model. A transient model isn't a simple full-time model. So, you need to select 'reduced', and build it by hand. When you select 'reduced', it will give you an empty DM that you then construct manually.

When I then look at the parameter estimates for the same model constructed using the PIMS and design matrix they are different for both the end terminal phi and p values when normally it is only the end p value that is unestimatable (see below).

This is very basic - at this point, I suggest putting away your data, and work through Chapters 1 -> 8 in their entirety. If you don't know why terminal phi and p parameters are confounded in a time-dependent model (of any flavour), you really aren't ready to starting working with your data - or anything as nuanced as transience and trap-dependent models.