Design matrix and PIM with different deviances

[CBardier]

Hi, I have a discrepancy similar to that raised by simone77 in 2011:

viewtopic.php?f=1&t=2031&p=6144&hilit=+PIM#p6144

Same kind of data (12 primary encounter occasions each with two secondary occasions) but in Multi-State Closed Robust Design (MSCRD). I have three states: juveniles, adult males, adult females, so the global model already has some restrictions because not all the psis between the three states are possible.

When I build the global model (which also has p=c) the deviances for the same model structure using PIM and DM are slightly different (-1054.9360 in DM and -1054.9269 in PIM), and estimations are close, but never the same as the examples in the GI book.
To match these models as much as possible, I used only the logit link function in both PIM and DM, I also changed the reference cell in the DM to be the first and not the last, and followed the instructions to equal p and c from chapter 14. So I am not sure about what else should I check (assuming the structure of the DM is correct).

Also, consider that for the DM, as rows cannot be deleted, for the psis I have to fix 44 parameters to 0 (the "unreal" psis), and for the PIM I only have to fix 11 to 0, would this be involved in the difference between PIM and DM?
Two of the primary occasions were not achieved, so my EH has two columns of dots "..", would this also be involved?

Moreover, when I run again each model (DM or PIM), even using the alt. opt. method, they give different deviations and AICc (because they estimate different number of parameters each time). I am not sure if this is usual with the logit link funtion, could this be the root of the whole problem?

Thanks in advance,

CBardier

[cooch]

Your attempt to get help would be aided considerably if you provide the page(s) you refer to in the 'book', which example data set, and which model(s) you're trying to build. Without the above, there isn't much to go on (i.e., no one is going to try to answer the question, because we don't have precise information indicating what the question actually is).

But, generally, if you're sure the PIM is right, and the DM attempt gives you different (but close) estimates of one thing or another, then (short of difference in the link function), the chances are very high the problem lies in the DM structure, somewhere. For high-dimensional problems (say, multi-age class models), these DM issues invariably involve structuring the interaction terms for the different age classes. Getting them wrong often yields answers that are 'close but not exactly the same' as those from the PIM.

[CBardier]

Thank you very much for your quick response!

My data set is not an example from the GI book, it is a database of frogs that consists of 12 primary (seasonal) encounter occasions (two of them could not be achieved, so they're represented with dots), each of them with two secondary (daily) encounter occasions. And I have one group with three observable states: juveniles, males and females.
So my EH looks like this:

J0000000F0..00000000..F0 1;
J0M0M00000..0M000000..00 1;

I thought the best approach would be a MSCRD (clousure would be assumed for the population), I am interested in obtaining the best models for S, the transitions from J to F and from J to M, and the population sizes. By now I am using the model type "Full Likelihood p and c", it seems simpler to me (I am sticking to the example of the MSCRD in page 15-30), but I am not sure if it the best specification.

So, my initial global model is S(state*t)psi(state*t)p(state*t). Either in PIM or DM, this model has four transitions fixed to 0, and p=c. I want to build DMs because I want to use correclty the MLogit link function for the transition parameters (when time is involved).

When building the DM, I followed the coding for p=c of the model {f0, p(.)=c(.)} described in page 14-19, so it would be the model M0 of the Otis notation. This is because I know that in the robust design, the final capture probability is confounded with recapture probability, solutions would be assuming capture probability is equal within a primary period (pi1 = pi2) or assuming capture probability is equal to recapture probability (pi2 = ci2). I have no reasons to assume different capture probabilities within secondary occasions, and I don't want to assume the same capture probability between primary sessions, so I chose pi2 = ci2 which I think is p(.)=c(.) in my case.

Also, when building the DM, I changed the reference cell in the DM to be the first and not the last. Although the DM is quite big, I think I specified it correctly. Before building more models, I want to be sure of it by emulating with the DM the models initialy built using PIM. I am using the same link function for all the parameters in PIM and DM (logit) to be sure that it is not the problem.

My questions would be two right now:

1) Why results are always close but not identical when I run the same model using PIM and DM (e.g., deviances of -1054.9360 in DM and -1054.9269 in PIM)? Now I am trying simpler models to start with: S(.)psi(.)p=c(state*t)... and the same happens.

2) Why when I run a given model in DM over and over again it keeps giving different deviances and estimates each time? It also happens with any given model of the PIM. I get the same level of difference as in question 1 but between several runnings of the same PIM or DM model. This happens even if I use the alt. opt. method.

In a reply to a similar post but with CJS (viewtopic.php?f=1&t=2115&p=6437&hilit=+discrepancy#p6437) you said "Problem is specific to your data. Structurally, the models are equivalent. If you get differences in deviance among the models you've tried, its because of issues with the data. This commonly occurs when you have one or more parameters that are poorly estimated. Nothing more. "

I have some poor estimates for some parameters (near boundary 0,1), is this affecting all my deviances and estimations?

Thanks in advance!

CB