c-hat and underdispersion

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c-hat and underdispersion

Postby steven k » Thu Oct 13, 2016 5:12 pm

I estimated apparent survival (ϕ) and capture (ρ) probabilities, population growth rate (λ) and seniority (γ), and population size for adult Wood Turtles using Cormack-Jolly-Seber and other models. Over the course of 9 years 59 turtles were captured 125 times; these captures were compiled using year as the sampling period in analyses. RELEASE tests indicated my capture data were underdispersed (i.e., less variation than expected by chance). Estimates of ĉ derived from χ2 /df calculations were less than 1; the goodness of fit results by group (TEST 2 + TEST 3) yielded a chi-square value of 10.87 with 25 df. The MARK book (Cooch and White 2013, pg. 5 - 6) states “there is lack of unanimity on how to handle ĉ < 1 . . . set ĉ =1, and ‘hold your nose’”. Due to this ambiguity, the model ranking selection processes for my CJS, Pradel, and POPAN routines were also run with the c-hat adjusted to a diminished value of 0.75, as well as with c-hat = 1.0. The best supported models (based on AICc, ∆AICc, AICc weight) changed depending on the value of c-hat used.
So my question is: which sets of models (those with c-hat = 0.75 or those with c-hat = 1.0) should I accept and report?
Thank you for your help,
Steven
steven k
 
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Re: c-hat and underdispersion

Postby cooch » Thu Oct 13, 2016 5:30 pm

steven k wrote:I estimated apparent survival (ϕ) and capture (ρ) probabilities, population growth rate (λ) and seniority (γ), and population size for adult Wood Turtles using Cormack-Jolly-Seber and other models. Over the course of 9 years 59 turtles were captured 125 times; these captures were compiled using year as the sampling period in analyses. RELEASE tests indicated my capture data were underdispersed (i.e., less variation than expected by chance). Estimates of ĉ derived from χ2 /df calculations were less than 1; the goodness of fit results by group (TEST 2 + TEST 3) yielded a chi-square value of 10.87 with 25 df. The MARK book (Cooch and White 2013, pg. 5 - 6) states “there is lack of unanimity on how to handle ĉ < 1 . . . set ĉ =1, and ‘hold your nose’”. Due to this ambiguity, the model ranking selection processes for my CJS, Pradel, and POPAN routines were also run with the c-hat adjusted to a diminished value of 0.75, as well as with c-hat = 1.0. The best supported models (based on AICc, ∆AICc, AICc weight) changed depending on the value of c-hat used.
So my question is: which sets of models (those with c-hat = 0.75 or those with c-hat = 1.0) should I accept and report?
Thank you for your help,
Steven


Simple -- \hat{c}<1 implies under dispersion -- meaning probability of catching an individual reduces the probability of catching another. While I could concoct a story to support such a possibility, it is likely to be a bit of a stretch for most species. In contrast, \hat{c}>1 indicates lack of independence, and is far more likely to be 'biologically plausible'.

Thus, if \hat{c}<1, that simply might reflect the uncertainty in the estimation, rather than anything biologcal. At which point, set c=1.

Also, estimated \hat{c} for a CJS model doesn't necessarily apply to POPAN or Pradel models. For those models, your best bet might be Fletcher's \hat{c}, although this has only been formally vetted for CJS models to date.
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