Which c-hat to use in age model and Test 2.CL not running

questions concerning analysis/theory using programs M-SURGE, E-SURGE and U-CARE

Which c-hat to use in age model and Test 2.CL not running

Postby monicaarso » Thu Jun 24, 2021 11:07 am

Hi ,
I have a dataset of 4 years of annual sightings for harbour seals (n = 381 animals), from which I want to estimate survival. The GOF sum of tests denotes the presence of transients (P-level <0.00001), but no trap-dependence (P-level = 0.47). The calculated c-hat from the sum of test is 5.11, which I suspect is primarily due to the transients (when I exclude first encounter, the c-hat becomes 1.99).
I have two questions:
1) My plan is to run age-models to get survival for these transients and for the rest. However, which c-hat should I apply to account for the presence of overdispersion? Still the 5.11 or 1.99? (I would go for the latter given that the age model accounts for the initial lack of fit to the general model)
2) I was also trying to calculate the individual components that make up the global chi-square and df for the calculation of c-hat (to make sure the overdispersion was due to transience), as explained in Choquet et al 2009 for multistate models, but the Test 2.CL does not run (an error message prompts up to say that the test cannot be run if the number of occasions is <5, which is this case). Summing up the other 3 components (Test 3.SR, 3.SM and 2.CT) produce a c-hat of 3.4 (which is lower than the global of 5.11). Anyway, I was just curious if there is anything to be done and also how are the chi-square and df then computed in the sum of tests if Test 2.CL does not run?
Many thanks,
Monica
monicaarso
 
Posts: 20
Joined: Wed Feb 22, 2012 2:58 pm

Re: Which c-hat to use in age model and Test 2.CL not runnin

Postby simone77 » Fri Jun 25, 2021 11:49 am

monicaarso wrote:Hi ,
I have a dataset of 4 years of annual sightings for harbour seals (n = 381 animals), from which I want to estimate survival. The GOF sum of tests denotes the presence of transients (P-level <0.00001), but no trap-dependence (P-level = 0.47). The calculated c-hat from the sum of test is 5.11, which I suspect is primarily due to the transients (when I exclude first encounter, the c-hat becomes 1.99).

According to some hidden group you are not considering, different apparent survival rates could be a source of overdispersion. Females and males, for example, or juveniles and adults. If you have data on groups that may absorb some variance in apparent survival, you should try to run the GOF tests separately.

monicaarso wrote:I have two questions:
1) My plan is to run age-models to get survival for these transients and for the rest. However, which c-hat should I apply to account for the presence of overdispersion? Still the 5.11 or 1.99? (I would go for the latter given that the age model accounts for the initial lack of fit to the general model)

If you're using the Time-Since-Marking model (where "Marking" refers to the first individual sighting), you should definitely use the 1.99 c-hat. I prefer this definition over the age model because it does not complicate the often useful distinction between mortality and permanent emigration. This is most likely "apparent survival" (an animal can die or permanently move out of the study area). In that case, the apparent survival estimate for the first interval following the first observation (say, Phi1st ) should not be interpreted as "survival for these transients". Phi1st includes the proportion of transients, which can be calculated as 1 – (phi1st /phi2nd>) (Pradel et al., 1997)* where phi2nd> is the apparent survival after the first interval (of each individual encounter history).
monicaarso wrote:2) I was also trying to calculate the individual components that make up the global chi-square and df for the calculation of c-hat (to make sure the overdispersion was due to transience), as explained in Choquet et al 2009 for multistate models, but the Test 2.CL does not run (an error message prompts up to say that the test cannot be run if the number of occasions is <5, which is this case). Summing up the other 3 components (Test 3.SR, 3.SM and 2.CT) produce a c-hat of 3.4 (which is lower than the global of 5.11). Anyway, I was just curious if there is anything to be done and also how are the chi-square and df then computed in the sum of tests if Test 2.CL does not run?

I'm afraid I can't answer this (I'm hoping someone with a more technical/statistical background will chime in).

* Pradel, R., Hines, J. E., Lebreton, J. D., & Nichols, J. D. (1997). Capture-recapture survival models taking account of transients. Biometrics, 60-72.
simone77
 
Posts: 184
Joined: Mon Aug 10, 2009 2:52 pm

Re: Which c-hat to use in age model and Test 2.CL not runnin

Postby simone77 » Sun Jun 27, 2021 10:38 am

An idea regarding your second question: when the data are sparse, U-CARE employs the Fisher exact test rather than directly calculating the Chi2. The Chi2 is then back-calculated as the value of a Chi2(1) distribution, which yields the corresponding p-value. I'm curious if, when the data are sparse, the Chi2 that you see in the output of each test is the same as the Chi2 values that U-CARE adds up in the "Sum of TESTs over groups." I don't know. Anyway, if you find out what happens there, please share the solution here as it will undoubtedly be of interest to others...
simone77
 
Posts: 184
Joined: Mon Aug 10, 2009 2:52 pm

Re: Which c-hat to use in age model and Test 2.CL not runnin

Postby monicaarso » Wed Sep 08, 2021 1:10 pm

Hi Simone (et al)
Sorry I've been a bit slow on this. In summary:
1)
According to some hidden group you are not considering, different apparent survival rates could be a source of overdispersion. Females and males, for example, or juveniles and adults. If you have data on groups that may absorb some variance in apparent survival, you should try to run the GOF tests separately.

I did fit TSM models to those data that showed evidence for transience, and then recalculated the c-hat by removing the GOF 3.SR test component as suggested in Pradel et al 2005. All good here, but see bit on sex-specific survival further below.

2)
An idea regarding your second question: when the data are sparse, U-CARE employs the Fisher exact test rather than directly calculating the Chi2. The Chi2 is then back-calculated as the value of a Chi2(1) distribution, which yields the corresponding p-value. I'm curious if, when the data are sparse, the Chi2 that you see in the output of each test is the same as the Chi2 values that U-CARE adds up in the "Sum of TESTs over groups."

If I have understood this correctly, YES, they match:

Sum of TESTs over groups Chi2 = 20.4419
Test 3.SR Chi2 = 18.916 + Test3.SM Chi2 = 1 + Test2.CT Chi2 = 0.51026 = Chi2 of 20.43
(note that the Test 2.CL is not calculated in this case because the number of occasions < 5

3) You were also right in saying that in some cases, part of the heterogeneity might be due to differences between groups, in this case sexes. For a reduced dataset only containing Males and Females with an adhoc approach (i.e. sightings previous to the assignment of the sex are ignored, see Nichols et al 2004) GOF for the full-time dependent CJS is accepted (in U-CARE, with two groups for male/female and doing the sum of tests over groups); df =8, Quadratic Chi2 = 10.61, p-level = 0.225; not significant for transients (p-value = 0.19) or for trap-dep (p-value = 1). However, looking further into the individual test components shows that there is some evidence for transience in the females only (p-level, one-sided test for transience = 0.044)

I tested this same dataset in R2ucare, and followed the advice given in the documentation for the package, which says "For groups, just treat the group separately as in the Dipper example below". So I did split my dataset into Females and Males and ran separate GOF tests for each. When doing this, the general GOF test was rejected for the Female data, with the individual 3.SR test for transience being significant:

Code: Select all
> overall_CJS(SkAdL_sex.fem.hist, SkAdL_sex.fem.freq)
                          chi2 degree_of_freedom p_value
Gof test for CJS model: 10.328                 4   0.035
> test3sr_females
$test3sr
     stat        df     p_val sign_test
    9.471     2.000     0.009     1.704

$details
  component  stat p_val signed_test  test_perf
1         2 9.102 0.003       3.017 Chi-square
2         3 0.369 0.544      -0.607 Chi-square


The GOF test and individual components were fine for the male dataset.

Three questions here regarding groups and testing:
A) Why would the sum of tests over groups accept a general model for the male/female data (2 groups) if one of the tests (3SR in this case) is significant for one of the groups?
B) If following the advice given in the R2ucare package to split data into the two groups, how does one calculate the c-hat in R2ucare to apply to sex-specific survival models (in MARK/RMark) which will contain both groups?
C) and related to the previous one: if fitting sex-specific models with transience (TSM) only affecting one group (i.e. females in this case), how do I recalculate the c-hat (in U-CARE or in R2ucare) to exclude the 3SR component when there are two groups in the data?

Any advice on these last questions would be highly appreciated.

Many thanks,
Monica
monicaarso
 
Posts: 20
Joined: Wed Feb 22, 2012 2:58 pm

Re: Which c-hat to use in age model and Test 2.CL not runnin

Postby simone77 » Fri Sep 17, 2021 9:47 am

A) I believe this is because the effect size is diluted in a larger sample size.
B) If you have a transient effect among females, I would try to "suppress (delete) the first encounter" of the female group and see if the female test3.SR is now OK - I assume nothing has changed for the males so you should get the same result there. Then, if the test3.SR is OK for the females, I'd define a global model with a TSM (or age, same thing) effect in the apparent survival of females (you have to keep that structure in all your models). I'm almost certain you won't get a significant p-value for the global model if you suppress the first female encounter, so I wouldn't touch the c-chat in MARK (or E-SURGE).
C) I believe the answer to this question is in the previous question.

Aside: it appears that you have some individuals/events with known sex and others with unknown sex. This is an ideal situation for using a multi-event approach in E-SURGE and utilizing all of your data without risking data censorship or other strategies... I say risky because you never know if you're unintentionally biasing your analysis by excluding events or individuals who aren't a random subsample of the sample.
simone77
 
Posts: 184
Joined: Mon Aug 10, 2009 2:52 pm

Re: Which c-hat to use in age model and Test 2.CL not runnin

Postby monicaarso » Thu Sep 23, 2021 8:12 am

Hi Simone,

Many thanks for your replies.

I eventually managed to fit models with TSM only on one group (instead of removing first encounter for that group as you suggest, but it should achieve the same effect of "controling" some of the heterogeneity detected, in this case in the form of transience).

I also managed to calculate the general GOF in R2ucare with separate groups, here is a summary in case anybody else is interested:

- First, run separate GOF tests for your two groups (e.g. males/females) as explained in the R2ucare userguide within R by Olivier Gimenez. This will be useful to check the overall fit for each group and any presence of transience/trap dep in the groups. If, for example, transience is only detected in females, then TSM models can be applied to the full dataset but only affecting females (see MARK book Appendix C.6 Design covariates in RMark for an example with the Dipper data)

- The results from the separate GOF tests will match what you would get in UCARE when looking at the individual tests (group 1, group 2), i.e. the R2ucare individual stat value and p-value match the Overall test Quadratic Chi2 and p-level in the direct test for groups 1 and 2.

- Summing the individual overall_CJS Chi2 statistics for the two groups in R2ucare will match the "sum over groups" Chi2 in UCARE. Here you can first exclude a component, e.g. TEST 3.SR for females, if your models are accounting for it. To calculate the p-value associated to this overall_CJS Chi2 simply use:
Code: Select all
1-pchisq(new_chat,new_df)
, where new_chat is the sum of the two overall_CJS Chi2 stat, and new_df is the sum of df. This might still show over-dispersion (c-hat) which can then be applied to modify model statistics and model selection accordingly.

Regarding E-SURGE, I have no experience using it, but I will certainly check it out.

Many thanks once again,
Monica
monicaarso
 
Posts: 20
Joined: Wed Feb 22, 2012 2:58 pm

Re: Which c-hat to use in age model and Test 2.CL not runnin

Postby simone77 » Thu Sep 23, 2021 8:59 am

Hi Monica,

It's good to see you've kept up with your analyses, and it's even better to see you've posted information that the phidot audience might find useful. I just wanted to clear up any confusion: I suggested removing the first encounter of the female groups for the U-CARE analysis, not for the CMR analyses. This will give you an idea of whether a CJS with a TSM structure for the females' group (and not for the males' group) would fit well your data...just that.
As said before, I strongly recommend giving the multi-event framework a try. You might find the examples on sex uncertainty in Olivier Gimenez's online (in preparation) book useful.
Good luck with your analysis!
simone77
 
Posts: 184
Joined: Mon Aug 10, 2009 2:52 pm


Return to analysis help

Who is online

Users browsing this forum: No registered users and 2 guests

cron