Hi Guillaume,
Thank you again for your willingness to help. Below there are answer to your comments and some other detail on this case study. In italic are my previous commentaries.
By checking the output file for the same model without individual covariate testing (the other one has only info on beta estimates),Guillaume Souchay wrote:The Output file from a model with individual covariate only included the estimation of the beta. The beta are the estimated parameters and the biological parameters are only backtransformation of the beta. Thus, even if there is only beta, you have all the information you need :)
Yes, I wasn't clear enough, I was just referring to the fact that for model with individual covariate there is no info on which parameters are not identifiable and other details.
How could I know if the slope associated to body mass is at the boundary? there is no information on which parameter is at the boundary from the output of a model with individual covariate.Guillaume Souchay wrote:A parameter estimated at the boundary will have either the value of 0 or 1 on the biological scale, thus either -36 or +36 on R scale. When a parameter is estimated at these values, it's possible that the SE is not calculated. Remi could say more about that.
R scale refers to the mathematical parameter scale, isn't it? You are right I should have checked it as the first thing. As said in the previous post, my estimates (from different non-linear solver) on the mathematical scale are far beyond -36 and it does mean they are at the boundary. The strange thing, and this is why I haven't paid much attention to the boundary issue, is that the QAICc and Deviance of the model with the individual covariate is much better than the model without. I would believe that if deviance is much better, it is because body mass is absorbing deviance and this is not very coherent with the slope of body mass being very very close to zero (as it would be my case).
Guillaume Souchay wrote:Usually, you have some information about the number of parameters estimated at the boundary in the output text file, with the information of the number of mathematical/estimated parameters. However, you don't have all the parameters involved.
By the way, any reference on how to do it in R is very welcome from me and, probably, other E-Surge users.Guillaume Souchay wrote:Concerning the Delta Method, you can find lots of information in the MARK BOOK, which is the link between a program manual and an handbook of CMR method. See Appendix B about the Delta Method, section B.4. Cooch and White provided several examples of back-transformation
Thanks for the tip, I forgot about that chapter in MARK manual (read quite a long time ago): it is clear enough to be easily implemented in R (or even in Excel itself).
I have nine case studies, each one with a different data set and I have seen that this happens in most of but not all the cases. To add details or confusion: I have also noticed that body mass slope values yielded by using different Non-linear solvers (Quasi-Newton, EM, and PEM) can be quite different (e.g. respectively: -77.2, -38.5, -56.8). This is not the case for the other betas.Guillaume Souchay wrote:My first guess would be related to local minima. Using different solvers should lead to different solutions but to different method to achieve the unique convergence point. Another care is to standardize the individual covariate before using it within E-SURGE.
Did you run your model without ind covariate several time with the Multiple-Random option?
Did your model well converge when you found these different values for the slope? Was the optimization achieved rather than the number of iterations/function value was exceeded? (information from the DOS-Windows).
Answering this:
1. Yes, Individual covariates were standardized before running the model (mean=0, SE=1).
2. Yes, I run the model without individual covariate (also the one with individual covariate) by checking "Multiple Random" initial values = 6 (made some trial before and saw this was a value big enough to get the same value of deviance).
3. Yes, my model converged without any at least apparent problem either by using Quasi-Newton, EM or PEM.
4. Regarding last question, I didn't pay to much attention to this because in my experience when some problem occurs with that, a pop up window advises you. However, I have seen that in many cases (from the MS-DOS window) the optimization was reached at the 201th iteration (the cycle is set on default value=200) and then started the next cycle (remember I had Multiple Random activated). I have been doing some trial by excluding a few individuals for which the body mass was a clear outlier (likely due to field work errors) and saw that the slope is a bit better from a boundary issue perspective, i.e. -39.4 vs prior -77.2 (Quasi-Newton). However, it is still beyond the -32 limit you mentioned for the Logit link estimates, and still have SE=0. On the other hand, I have seen that last iteration used to be around the 90th, far before the 200th.
Do you believe the number of iteration at which model stops running is an important point to be considered, also in case no warning is given?
Guillaume Souchay wrote:A good way is to run several time your model without the body mass covariate, and to use the result from this best model as the Initial Value for your model with the covariate: After running your model without the cov, use the "from Last Model" option for IVFV, include the covariate in GEMACO, fixed the parameters, if needed (be sure to be on the biological scale!) and run your model.
In the past I have never been lucky with the "from last model" option to get rid of local minima. However, I have tried to make what you suggest but the deviance I get results to be higher than the model without the individual covariate (should be equal or less than that). It doesn't seem to work in my case.
Guillaume Souchay wrote:I just noticed this point: From previous model I have no serious concerns on parameter estimability.
Is your model full-ranked? Do you have some identifiability issues related to the parameters with ind covariate?
Considering the model without the individual covariate: it has three parameters that are not identifiable which are two Initial State (for occasion 5th and 6th as mentioned in the previous post) and one that is quite logic since it refers to the probability a previously captured individual is seen at occasion 1th. I have tried to fix it to zero and nothing changes except this parameter is no more in the parameter estimability list.
From the *.out file of this model results that:
No. of mathematical parameters: 46
Estimated model rank applicable to the data: 44
Estimated No. of boundary parameters: 2
About the model with individual covariate: this is the problem I was referring to in the first point, i.e. as far as I know there is no info about which specific parameters are not estimable. However, from the *out file results that:
No. of mathematical parameters: 46
Estimated model rank applicable to the data: 47
Estimated No. of boundary parameters: 4
Really I would have thought it has only one more parameter than the model without the individual covariate and therefore I manually modified no. of parameters of individual covariate model to be 45.
Then, in conclusion I have not yet a clear idea where the problem is coming from. The strangest thing for me is that the individual covariate model would seem to perform consistently better but still the apparent slope for body mass is very close to zero boundary (no effect at all).
Simone