model averaging

[fanny]

Good morning,
if I obtain 3 bests models from the list of models, with:
model 1 delta QAICc=0
model 2 delta QAICc=1.831
model 3 delta QAICc=2.201

Now model 1 and 2 seem plausibles. If I do the model averaging, do I use just the model 1 and 2 or model 3 too?
Because the distinction between model 2 and 3 is not clear.

[Eleni Papadatou]

Hi Fanny,

check Markbook, chapter 4 (comparing models), page 23!

Cheers,
Eleni

[cooch]

Hi Fanny,

check Markbook, chapter 4 (comparing models), page 23!

Cheers,
Eleni

Actually, it gets introduced more formally in Chapter 6 (starting ~ p. 13). Then, revistied in Chapter 8, as applied to 'age' and cohort models. And again in Chapter 12, when considering individual covariates.

[Renata]

I'm sorry, but I had the same question and after having read througout the book (we're talking about the book online, "MARK - A gentle introduction", right?), I still couldn't figure out the answer. I imagine that only equally-supported models are to be included in the averaging. The way to do it would be to run again only that set that was selected, and then proceed with the averaging?

[abreton]

The answer to your question is: Model average across ALL of the models in your set. Those that have only marginal weights, ~<0.01, will contribute VERY LITTLE to the final "model averaged" estimates.

I'll demonstrate using equation 4.1 on page 150 in Burnham and Anderson (2002). To keep it simple, say you only have two models in your set, one (model A) has an Akaike weight of 0.995 and the other (model B) has a weight of 0.005. Clearly, only the first model is plausible and the second is not. Now we need to model average a parameter, say phi1 (a survival estimate): model A, Phi1 = 0.94; model b, phi1 = 0.91. An estimate of the model averaged phi1 = (0.995*0.94)+(0.005*0.91) = 0.9353+0.0046 = 0.9399. Okay, so what have we learned? Models that acquire a lot of the Akaike weight contribute the most to the model averaged estimate (0.9399). Models that acquire only marginal Akaike weights contribute VERY little (0.0046). Take home message is even though I model averaged across all of hte models in this set, the final estimate came almost exclusively from the "plausible" (to use your adjective) model A.

Two other reasons to model average across the full set: (1) it's much easier to do this (using MARK) then it is to add/delete models; (2) it is the most honest way to account for model selection uncertainty, even when that uncertainty is very low - such as in my simple example. Good luck, andre