abreton wrote:The model averaging procedure in MARK appears to include estimates of parameters from models whether the parameter was estimable in that model or not. For example, given three CJS type models Phi (.) p (.), Phi (t) p (.) and Phi (t) p (t), the last encounter and survival probabilities are estimable in the first two models but not the last. However, in the model averaged output, estimates from all parameters appear suggesting that the 'nonestimable' parameters are averaged with the estimable parameters.
Given the oversights I've made in the past (MANY!), I suspect I'm off here as well. But if I'm onto a real problem, then one option is to take the model averaging output, import it into excel, and go through the long process of recalculating model averaged thetas and their variances excluding models when a parameter is nonestimable...is this my only option?
Nothing really to worry about, in my opinion, if you're thinking about whats going on (and not simply clicking 'model averaging' in MARK, dumping output to a spreadsheet, and plotting a figure without thinking).
Consider the following situation. Suppose that the estimate of the final phi value (final interval) for phi(t)p(.) is 0.8. Suppose that the estimate of the function of the product of phi and p for the final interval from phi(t)p(t) is (say) 0.6. OK. Now, we know that phi and p aren't separately identifiable for phi(t)p(t).
OK, now consider 3 different model averaging scenarios, where the model set consists entirely of these two models:
1.
model phi(t)p(.) has virtually all the support in the data, and model phi(t)p(t) has virtually no support. So, the 'confounded estimate' from phi(t)p(t) has no appreciable influence on the model average estimate of phi for the final interval, since that model (phi(t)p(t)) has virtually no weight. So, 'model averaged' estimate for final interval would be ~0.8.
2.
model phi(t)p(t) has virtually all of the weight, and model phi(t)p(.) has no support (or very little). So, the model averaged value of the estimate is essentially the 'confounded' estimate from model phi(t)p(t). This is what MARK reports - something ~0.6. OK, so at this point, you're supposed to be smart enough to note that in this case the model with the most support in the data is one where the estimate for the final interval is confounded. And, thus, you don't report it, or use it. So, there is no model averaged estimate for the final interval (even though MARK reports one, you ignore it).
OK, scenario (1) and (2) are the extremes. In the former, the inclusion of the confounded estimate does not influence the model averaged value to any appreciable degree. In the second, it means you simply don't have a meaninful (interpretable) model averaged value for the final interval - meaing you ignore the value MARK reports.
Final, apparently more complicated scenario - (3)
both models have significant weight (at the extreme - assume equal AIC weights -0.5 each). MARK would report 0.7 as model averaged value ([0.8*0.5+0.6*0.5]=0.7).
Appears more complicated, but again, this effectively reduces to scenario (2) - yes, you have a non-confounded estimated of phi for the final interval from model phi(t)p(.), but based on weight of evidence, you can't differentiate that model from model phi(t)p(t), and thus, there is no reasonable model averaging to be done.
So, as long as you're really thinking about what is and is not identifiable in the models in your candidate model set, and not simply taking the value MARK gives you, then you should be able to make reasonable assessments about when model averaging is, or is not, reasonable for a given parameter.
by abreton » Wed May 17, 2006 7:06 pm 