GOF-analysis, deviance residual plot

[feliona]

Dear MARK-Forum,
I’m struggling with the interpretation of the GOF-/ model-analysis and would very much appreciate some hints about how to proceed!
We monitored winter activity and habitat use of 400 individually tagged fish (PIT-tags) in a small, shallow stream by weekly mobile tracking (remote detection). The fish belong to three groups comprising different species and age-classes and were all tagged the same day (single release cohort).
The return rate (percentage of the totally tagged individuals that was re-encountered) varied quite considerably over the 26 tracking occasions and between the different groups (see graph on flickr: http://www.flickr.com/photos/feli2013/6685215881/) Therefore, I’d like to analyze the effects of methodological (e.g. tag size) and environmental factors (e.g. ice formation, individual characteristics) on apparent survival and recapture probability.

I run a time-dependent CJS-model {Phi(t) p(g*t)}, which resulted in a good estimability for all but 1 of the 104 parameters – what let me assume (in accordance to page 39, chap. 5) that the model structure was appropriate. However, deviance was quite pronounced (4220,94), with the deviance residuals showing a highly asymmetrical distribution (see graph on flickr: http://www.flickr.com/photos/feli2013/6685215711/). This pattern was consistent when applying other model structures, e.g. {Phi(g*t) p(g*t) PIM} or {Phi(t) p(t) PIM} or {Phi(g*ICE) p(g*ICE) }.
Based on the text on page 34/35 in Chapter 5 I interpreted the residual plot as follows:
a) I have a trend in my data (“structural problem”) as the residuals do not scatter randomly above and below the 0-line, but are to a great extent positive. (BUT: This conclusion is contradicting the one I made before where I considered model structure to be OK as the model did not have estimability problems).
b) I have some extra-binomial variation as the residuals are not close to the 0-line, but rather large (outside the dashed lines).

I used two different methods of GOF-assessment, with variable success:
1) Median c-hat (with 1300 simulations): I ran it several times and continuously narrowed the estimation range. From the simulation results exported to Excel, I could calculate c-hat to be around 1,139. However, I faced some problems with the MARK-output (see graph on flickr: http://www.flickr.com/photos/feli2013/6685229869/). The position of the 50% value is clearly visible (around 1.139), but the values given for c-hat and SE don’t correspond/ don’t make sense.
2) RELEASE: Mainly TEST 3 produced invalid results due to insufficient values in the contingency tables. In accordance to page 36 in chapter 5, I assume this is related to the sparseness and structure of my data (-> a single release cohort, not too big of a sample size (n= 400), many encounter occasions (n=27) and quite a high recapture rate in the beginning of the study).
If I adjust c-hat stepwise (as proposed on page 5-39), this does not change anything in the rankings of models I have so far.

Based on the residual plot I believe my model has a lack of fit and I would like to identify why. Is this due to data sparseness, i.e. may sparse data lead to both structural and/ or over-dispersion problems?
I have some difficulties to see my next steps. Do I just not have the adequate data to be analyzed with MARK? Does anybody with more experience have some thoughts about this?
Many thanks for a feedback! Also ideas for alternative approaches for analyzing return rates- apparent survival – recapture probabilities are very much welcome!
Best regards and have a good day, christine

[cooch]

On my way out the door, but might be worth having a look at sidebar beginning on p. 47 of Chapter 11 (the individual covariates chapter). If you didn't have individual covariates in your data when you generated the residual plots, then this might not apply.

If individual covariates themselves aren't the culprit, then generally, when points appear clustered 'above' or 'below' the line, this indicates a structural problem with the model. See examples for TSM models in Chapter 7.