Median c-hat & general model question

[Andrea]

I estimated c-hat for the most general model in the candidate set using the median c-hat approach and obtained an estimate of 1.306, but with a SE of 0.0000. The SE of the intercept and the slope were also estimated to be 0.00. So I wonder if this indicates that I did something wrong. I have a couple of ideas of what this may be:
1-Perhaps, I should’ve not used an upper limit of 3 because I don’t know my data well enough to trust that the estimate would be below 3 (as was the case for the Dipper data in chapter 5).
2-My general model (not a full time-dependent model) has a total of 86 parameters, out of which 5 are non-estimable. I know that ideally you would use a general model with very few non-estimable parameters. But this model includes all possible interactions that seemed reasonable to expect based on what I know about the studied system. So, should I keep it in the candidate set? Or eliminate it, and have one of the simpler models (with fewer problems in estimability) be the most general one?
Thanks for any advice on this,
Andrea

[Doherty]

I estimated c-hat for the most general model in the candidate set using the median c-hat approach and obtained an estimate of 1.306, but with a SE of 0.0000. The SE of the intercept and the slope were also estimated to be 0.00. So I wonder if this indicates that I did something wrong. I have a couple of ideas of what this may be:
1-Perhaps, I should’ve not used an upper limit of 3 because I don’t know my data well enough to trust that the estimate would be below 3 (as was the case for the Dipper data in chapter 5).
2-My general model (not a full time-dependent model) has a total of 86 parameters, out of which 5 are non-estimable. I know that ideally you would use a general model with very few non-estimable parameters. But this model includes all possible interactions that seemed reasonable to expect based on what I know about the studied system. So, should I keep it in the candidate set? Or eliminate it, and have one of the simpler models (with fewer problems in estimability) be the most general one?
Thanks for any advice on this,
Andrea

Dear Andrea,

I think I would use a model without the estimation problems as your most general model.

Sincerley,

Paul

[Andrea]

I'm running a capture-recapture models on a set of data consisting of 110 occasions, 2 groups, and 1789 individuals. The effective sample size is 4609. But there is great temporal variation on the number of individuals that were present at times, with a couple of long stretches of time (lasting ca. 4-8 occasions) with very few animals present in the population.
In the output of every model that I've ran so far (even in the most simple ones) I see in that Pearson Chisquare = Not a number.
When I ran the median c-hat test in the most complex model in the set (with only 3 non-estimable parameters) I obtain a value for c-hat (1.42) but the SE, the values in the variance-covariance matrix, and the intercept and slope are all zero.
Are both of this problems related? What could be the cause?
Thanks,
Andrea
Bellow is part of the output from the model I used in the median c-hat estimation. And also part of the median c-hat output with a warning message that may be interpretable.

Number of Estimated Parameters {Phi(ss*sx+yr) p(ss+yr)} = 37
DEVIANCE {Phi(sea*sex+yr) p(sea+yr)} = 3900.5354
DEVIANCE Degrees of Freedom {Phi(sea*sex+yr) p(sea+yr)}= 492
c-hat {Phi(ss*sx+yr) p(ss+yr)} = 7.9279175
AIC {Phi(ss*sx+yr) p(ss+yr)} = 9005.2601
AICc {Phi(ss*sx+yr) p(ss+yr)} = 9005.8753
Pearson Chisquare {Phi(ss*sx+yr) p(ss+yr)} = Not a Number

Median c-hat output:

Estimated c-hat = 1.4193736 with SE = 0.0000000

Beta Variance-Covariance Matrix
0.0000000 0.0000000
0.0000000 0.0000000

MARK Logistic Regression Estimation Output follows...
INPUT --- icovariates Truth;
INPUT --- 10 10 1.00000;
INPUT --- 11 0 1.00000;
INPUT --- 10 0 1.81818;
INPUT --- 11 10 1.81818;
INPUT --- 10 0 2.63636;
INPUT --- 11 10 2.63636;
INPUT --- 10 0 3.45455;
INPUT --- 11 10 3.45455;
INPUT --- 10 0 4.27273;
INPUT --- 11 10 4.27273;
INPUT --- 10 0 5.09091;
INPUT --- 11 10 5.09091;
INPUT --- 10 0 5.90909;
INPUT --- 11 10 5.90909;
INPUT --- 10 0 6.72727;
INPUT --- 11 10 6.72727;
INPUT --- 10 0 7.54545;
INPUT --- 11 10 7.54545;
INPUT --- 10 0 8.36364;
INPUT --- 11 10 8.36364;
INPUT --- 10 0 9.18182;
INPUT --- 11 10 9.18182;
INPUT --- 10 0 10.00000;
INPUT --- 11 10 10.00000;

Number of unique encounter histories read was 24.
Variance Estimation Procedure Used is 2ndPart
-2logL(saturated) = 0.0000000
Effective Sample Size = 120

* * WARNING * * Error number 2 from VA09AD optimization routine.

Number of function evaluations was 40 for 2 parameters.
Time for numerical optimization was 0.01 seconds.
-2logL {c-hat logistic regression} = 0.3634164E-08
Penalty {c-hat logistic regression} = 0.0000000
Gradient {c-hat logistic regression}:
0.000000 0.000000
S Vector {c-hat logistic regression}:
0.2817038E-09 0.9810306E-12
Time to compute number of parameters was 0.01 seconds.
Threshold = 0.6000000E-07 Condition index = 0.3482490E-02
Conditioned S Vector {c-hat logistic regression}:
1.000000 0.3482490E-02
Number of Estimated Parameters {c-hat logistic regression} = 2
DEVIANCE {c-hat logistic regression} = 0.3634164E-08
DEVIANCE Degrees of Freedom {c-hat logistic regression} = 118
c-hat {c-hat logistic regression} = 0.3079800E-10
AIC {c-hat logistic regression} = 4.0000000
AICc {c-hat logistic regression} = 4.1025641
Pearson Chisquare {c-hat logistic regression} = 1210.0000

LOGIT Link Function Parameters of {c-hat logistic regression}
95% Confidence Interval
Parameter Beta Standard Error Lower Upper

1:Intercept Truth 86.363142 0.0000000 86.363 86.363
2:Slope Truth -60.845953 0.0000000 -60.845 -60.845

[Andrea]

Hi,
I went ahead an re-ran the median c-hat test with a smaller upper bound. I chose 1.6 to encompass the value estimated in the previous run (1.42) even though it had the weird output (SE and other parameters estimated to be 0). This time the output looks fine. I obtained a reasonable estimate for c-hat (1.33), its SE (0.011), and all the other parameters in the model. So, I guess the problem is solved.
Is it common, then, that when you use a high upper bound (10 in my case) to make it greater than the observed c-hat (7 in my case) and you only have a few design points (10 in my initial simulation) then you may end up with zeros for all those parameters?
I see that the strategy of using an upper bound greater than the observed value is recommended, but it has also been suggested to use a maximum of 3. See the post bellow...

http://www.phidot.org/forum/viewtopic.p ... pper+bound

I'm still a little concerned about the fact that the Pearson Chisquare is "not a number" in the output of all of my models. Any insights on this will be highly appreciated!
Thanks,
Andrea