Beta Estimates Bounding Zero...

[Fish_Boy]

I have been analyzing a dataset using Robust Design closed captures. My 'best' models consistently have beta estimates that bound zero. Typically these are gamma estimates unless g'(.)=g"(.). The other parameters do not appear to change dramatically, if at all, compared with time varying versions with the exception of the beta estimates (and of course real estimates for confidence intervals). One of the aspects of the study is to gauge the relative proportion of the 'superpopulation' that is present in the study area during any given year, so I would prefer beta estimates for gamma parameters that provide real estimates with 'nice' confidence intervals. I recall one of the instructors mentioning at a workshop that the 'best model' may not be the most 'appropriate model' and that the final model selection may be the second or third model or the model that makes the most biological sense. Would I be justified rejecting the AIC 'best model' on the grounds that beta estimates bound zero and the model makes less biological sense than the second or third model?

So in the event that g'(.)=g"(.) are used with N(t) to extrapolate a 'superpopulation' estimate (N(t)/(1-g)), N(t) would represent only the estimate of abundance for local study area for time (t). For this particular study this aspect is important because the species has a variable interval of utilizing the local study area depending on the spawning interval. How do we extrapolate in the event that g'(t)=g"(t)? There will undoubtedly be a confounding year based on the graphical explanation of gamma parameters. Any help in the right direction would be appreciated.

[sbonner]

Hey Fish_Boy,

Can you clarify what you mean by "beta estimates that bound zero"? Do you mean that the confidence interval bounds zero? If so, then this isn't a problem. The beta estimates are on a transformed scale -- logit or sin for most parameters, including the robust design gammas, so that a beta of 0 corresponds to a probability of .5.

Hope I'm not too far off the mark (or should that be MARK?).

[Fish_Boy]

I seem to remember that if the beta estimate confidence intervals are positive for one and negative for the other e.g., -1.2 and 1.2 that this had some potential issue for generating unreliable real estimates.

[sbonner]

Not a problem, as long as you have chosen the correct link functions for your parameters (or not modified the default). If, for example, you are modelling a probability using the logit link then the 95% confidence interval you have given for the beta parameter, (-1.2, 1.2), would correspond to a 95% confidence interval of (.23,.77). If you are modelling population size using a log link, then this would correspond to a 95% confidence interval of (0.3,3.0). The only time this would be a problem would be if you'd selected an unreasonable link for one of the parameters so that values of beta on one side of zero or the other were impossible. For example, a confidence interval of (-1.2,1.2) could result but would not be sensible if you were modelling a probability using the identity link because probabilities must be between 0 and 1.

Problems do arise for certain link functions if the real parameter estimates are very close to 0 or 1. Check out the information on link functions in the gentle introduction -- like the side bar on pages 6-11 and 6-12.

Cheers...