some M-SURGE questions

[Fabienne Sutter]

Hello…
I’m a fairly new M-SURGE user. I’m working successfully with M-SURGE, but nevertheless there are still some open questions. I'm working with recapture only models with only one age class and one state.
I would be deeply grateful for any hints.

-estimated model rank: M-SURGE calculates the identifiable parameters for ten points near the MLE (10th at the MLE). Often it reports constant numbers in the first nine points, then the estimated number of identifiable parameters at the MLE drops down. What is the proposed model rank? It seems, that it is the maximum number of estimated parameters. Is that correct? Should I then modify the number of identifiable parameters to the number reported for the MLE?

-What does the figure show which is displayed after the optimisation procedure has stopped?

-I work with constrained design matrices. Some of the covariates have more then two digits after the comma. In the GEMACO it looks like if only a maximum of 2 digits after the comma were accepted? Is that correct? And if yes, is it okay to multiply the covariates by a constant number, so that only a maximum of two digits after the comma were left?

-An other problem occurred, when I tried to fit a model with a nonlinear (quadratic) time trend in the survival (phi(nonlineartimetrend.g).p(g.t)). The model never reached convergence, although the same model analysed in MARK fitted the data very well. Have you an idea what is going wrong?
A part of the design matrix (11 groups; 13 occasions)

g1 g2 g3... lin.timetrend quad.timetrend g1.linear ... g1.quadratic
1 0 0 1 1 1 1
1 0 0 2 4 2 4
1 0 0 3 9 3 9
....
0 1 0 1 1 0 0
0 1 0 2 4 0 0

- A more general question concerning the convergence of models. At the moment I’m working with the following numerical options: number of iterations: 1000 and Initial Values: multiple random 10. What is the recommendation with relative complex models based on a relatively sparse dataset?

Many thanks in advance
Fabienne

[CHOQUET]

1) Concerning the rank which is a crucial point for model selection.

In M-SURGE, the Catchpole-Morgan-Freeman(CMF) method is used to obtain estimates of the rank. The CMF approach is much more reliable than the Hessian approach. However, when estimates of parameter are on the boundaries then the estimate of the rank falls (this is the last estimate given by M-SURGE) and becomes less precise.
To get a reliable estimate of the rank, several points are taken in the neighborhood of the MLE far from the boundaries. If estimates of the MLE are strictly inside the domain then rank estimates at these nine new points are equals to the rank at the MLE. If not then the nine new rank estimates should be higher than the rank at the MLE. By default, M-SURGE takes the maximum of the ten estimates according to the CMF definition of the rank.

2) Concerning the figure show after the optimisation procedure has stopped

Another crucial point is what are the parameters involved in redundancy.
For each point used for the model rank estimates, a diagnostic tool based on the CMF theory is used in M-SURGE to show what are the parameters involved if any in the redundancy of the model considered. For the ten points (the last one is the MLE), lists of suspicious parameters are given.

3) Concerning the constrained design matrices

Two digits after the comma displayed by M-SURGE is only due to the display format.

4) Concerning co-variates

The convergence problem is due to the values of your covariates. To be free from convergence problems, you should normalize your covariates and start the fit (as you do) from random values.

5) Concerning the convergence of models with sparse dataset.

Fit relative complex models for sparse dataset is sometimes very difficult especially umbrella model. My recommendation is : Do not spent too much time on models with a lot of parameters as the data will not support such models. Ways to support time effect and group effects are for example to used co-variates on time, to make some constraints between groups. However if time, group effects are crucial and not related to anything, to used a Bayesian approach which will allowed to bring some extra informations.

[Fabienne Sutter]

Thanks for the answer, but I have some follow up questions…

1) Concerning the rank which is a crucial point for model selection.

In M-SURGE, the Catchpole-Morgan-Freeman(CMF) method is used to obtain estimates of the rank. The CMF approach is much more reliable than the Hessian approach. However, when estimates of parameter are on the boundaries then the estimate of the rank falls (this is the last estimate given by M-SURGE) and becomes less precise.
To get a reliable estimate of the rank, several points are taken in the neighborhood of the MLE far from the boundaries. If estimates of the MLE are strictly inside the domain then rank estimates at these nine new points are equals to the rank at the MLE. If not then the nine new rank estimates should be higher than the rank at the MLE. By default, M-SURGE takes the maximum of the ten estimates according to the CMF definition of the rank.

For example I’ve a model where the estimate for the ten points are 57 57 …. 57 47. The proposed model rank is 57. So I have not to adjust the rank but have to be aware of the imprecise estimate of the number of parameter. Is that right?

2) Concerning the figure show after the optimisation procedure has stopped

Another crucial point is what are the parameters involved in redundancy.
For each point used for the model rank estimates, a diagnostic tool based on the CMF theory is used in M-SURGE to show what are the parameters involved if any in the redundancy of the model considered. For the ten points (the last one is the MLE), lists of suspicious parameters are given.

After the procedure has stopped, the sheet with the parameters involved in redundancy and a histogram occur. The histogram consists of two or more blue columns. The x-axis is for example 0 to 2 x105 and the y- axis 0 to 10. What does this figure show?


4) Concerning co-variates

The convergence problem is due to the values of your covariates. To be free from convergence problems, you should normalize your covariates and start the fit (as you do) from random values.
Do I not change the meaning of the constraint when normalizing the covariates? When normalising the covariate by log- transforming it, does it not change the linear constraint to a log-linear constraint?


Another open question:
I compared different models in M-SURGE and in MARK. For example: phi(mean temperature+ t).p(g.t) (mean temperature is a continuous variable). The AIC as well as the deviance are quite different for this model in the two programs (difference in deviance of 45) . Other models like phi(pondtype+t).p(g.t) (pondtype is a discrete variable) are exactly the same in both programs. Models with some discrete variables (but also combined with continuous variables) are most of the time equal in both programs, whereas models with only continuous variables are different.
The values are always higher in M-SURGE.
The constraint DM for phi (mean temperature +t) looks like the following:
0.1388 0 0 ….
0.1388 1 0
0.1388 0 1
….
0.1636 0 0
0.1636 1 0
0.1636 0 1
…
The covariate is normally distributed. In MARK the covariate is exactly the same.

Many thanks in advance for any help…

Fabienne

[CHOQUET]

1) Concerning the rank which is a crucial point for model selection.
For example I’ve a model where the estimate for the ten points are 57 57 …. 57 47. The proposed model rank is 57. So I have not to adjust the rank but have to be aware of the imprecise estimate of the number of parameter. Is that right?

In this case, the value 57 is quite reliable as 9 estimates over 10 give this rank.

2) Concerning the figure show after the optimisation procedure has stopped. After the procedure has stopped, the sheet with the parameters involved in redundancy and a histogram occur. The histogram consists of two or more blue columns. The x-axis is for example 0 to 2 x105 and the y- axis 0 to 10. What does this figure show?

This figure show the histogram of the deviances obtained for the different starting points.

4) Concerning co-variates
Do I not change the meaning of the constraint when normalizing the covariates? When normalising the covariate by log- transforming it, does it not change the linear constraint to a log-linear constraint?

Of course with covariates, applying the identity link or the logit link to the same constraint lead to two different models.

5) I compared different models in M-SURGE and in MARK. For example: phi(mean temperature+ t).p(g.t) (mean temperature is a continuous variable). The AIC as well as the deviance are quite different for this model in the two programs (difference in deviance of 45) . Other models like phi(pondtype+t).p(g.t) (pondtype is a discrete variable) are exactly the same in both programs. Models with some discrete variables (but also combined with continuous variables) are most of the time equal in both programs, whereas models with only continuous variables are different.
The values are always higher in M-SURGE.
The constraint DM for phi (mean temperature +t) looks like the following:
0.1388 0 0 ….
0.1388 1 0
0.1388 0 1
….
0.1636 0 0
0.1636 1 0
0.1636 0 1

There is something strange in your matrix. I think that the first column for
time is missing.

However, perhaps starting points are not optimal in this case. I recommend two approachs to avoid this problem.
1) add the intercept by using the following sentence [i+g*x]+t where x is the co-variates of mean temperature for each group.
2) start from the estimates of the model phi(t) p(g.t) by using the option start from last model.

Rémi