+ 1 parameter & +1 deviance

[jclaisse]

Here are results from my basic analysis. L was a lenght individual covariate and s was site differences (3 sites).

Model_______AICc___AICdif____wi_______NumPar____Dev
phi(.)p(.)____852.2____0_______0.58_______2________848.3
phi(L)p(.)____854.0____1.73____0.24_______3________848.0
phi(s)p(.)____855.4____3.14____0.12_______4________847.3
phi(s+L)p(.)__857.1____4.81____0.052______5________847.0

It appears there isn't really any support for the 2nd model because of the +1 parameter and basically no change in deviance? If this is the case is it kosher to remove that model from the list and recalcualting the weights and doing model averaging on the reduced model set?

[abreton]

In your small set of models, all are best, i.e., all are within ~5 AIC units of the top model. This view hinges on whether or not you agree with text on pages 70-79 in Burnham and Anderson (2002), which, in my view, seems logical and straightforward. Thus, if all are best models under the Information-Theoretic approach to model selection, then none should be discarded, all should be used to make inferences from the data through model averaging.

Alternatively, if model 1 and 2 were tied for best and models 3 and 4 had no support (AIC difference >= about then I would probably present estimates from both models in the same table. I also would be certain, in this case and the former, to (1) present the estimate of the covariate slope coefficient from model 2 with its SE as the latter provides an indication of the effect size and precision of the estimate; and (2) identify, as you did below, that an increase in 1 parameter resulted in no change in the model deviance. Both 1 and 2 are evidence regarding the importance of the length covariate.

I'll be curious to see how others might proceed in this case. And note, my approach has changed over time - a few years ago I relied more heavily on differences between model deviances in the "alternative" case I suggested above.

[abreton]

One issue I failed to mention and one that may have contributed to your inquiry is model averaging when one of the models includes an individual covariate. As long as you specify the mean value of the individual covariates for model 2, then model averaging with this model in the set is intuitively reasonable. Additional helpful considerations can be found in the MARK help file by typing in Model Averaging (Index) and scrollling down to "A final trap...".

Note, smiling face with sunglasses in my previous post should be replaced with "eight)".