non-estimable parameters

[Andrea]

When I run a time dependent model with my capture-recapture data, 3 out of 68 parameters are non estimable. In this case they are not identifiable because of problems with the data as those 3 parameters pertain to years of prolonged drought when the number of captures was really low. So, what should I do then? Should I adjust manually the number of parameters to reflect the missing parameters as it is suggested in page 7.23 of the Gentle Introduction? Or should I not include them in the total for that model as it is suggested in page 4.20 of the book? Will it be better to fix the associated Phi parameters to an average value of the other occasions with similar drought conditions for which I did get reasonable parameter estimates, instead of leaving those impossible estimates there?
Thanks for any advice or comment,
Andrea

[cooch]

When I run a time dependent model with my capture-recapture data, 3 out of 68 parameters are non estimable. In this case they are not identifiable because of problems with the data as those 3 parameters pertain to years of prolonged drought when the number of captures was really low. So, what should I do then? Should I adjust manually the number of parameters to reflect the missing parameters as it is suggested in page 7.23 of the Gentle Introduction? Or should I not include them in the total for that model as it is suggested in page 4.20 of the book? Will it be better to fix the associated Phi parameters to an average value of the other occasions with similar drought conditions for which I did get reasonable parameter estimates, instead of leaving those impossible estimates there?
Thanks for any advice or comment,
Andrea

The latter (as suggested on p. 7-23). The text on p. 4-20 is not correct as written. Bonus points for reading the text carefully enough to spot a discrepancy in text separated by a fair number of pages.

As for fixing parameter values, rarely a good idea. But, more likely the solution will be in deriving estimates based on a constrained model. Typically, non-identifiability because of data sparseness rears its head when tryingg to fit a time-dependent model. What you're probably really after is 'drought' versus 'non-drought' - analogous to the 'flood' versus 'non-flood' models for the European dipper. The main utility of time-dependent models is their use as a 'general model' in the candidate model set - used in turn for estimation of c-hat. But - if the fully time-dependent model can't be fit to the data (because of data sparseness), then using it for GOF testing makes little sense either - the model you use in the model set for estimating c-hat needs to be sufficiently parameterized to adequately fit the data, while containing the main effect(s) of interest. Often this is a time-dependent model, but it doesn't have to be.

It is also worth noting that time-dependence of some parameter is in and of itself not particularly interesting (for most purposes). Comparing a time-dependent model versus (say) a dot model is analogous to testing the null hypothesis in ANOVA - 'is there evidence for heterogeneity in group means?' Well, the mere presence of heterogeneity is often not of interest, but 'which means differ from which other means, and why?', often is. So, in the present context, the real question of interest may not be "does" the parameter vary over time, but, instead, "why" does the parameter vary over time? In your case, it might be a climate covariate, or something else.