Model averaging and individual covariates

[mmcleod]

Thanks, everyone, for your clarifications. So, is model averaging for real parameters over the entire model set the equivalent of averaging betas by setting beta=0 in models without the covariate and then calculating real parameters from the betas?

As far as re-normalizing weights and calculating by hand, etc. -- can't you delete the models without the covariate from your model set and then let MARK do the dirty work?

[cooch]

Thanks, everyone, for your clarifications. So, is model averaging for real parameters over the entire model set the equivalent of averaging betas by setting beta=0 in models without the covariate and then calculating real parameters from the betas?

As far as re-normalizing weights and calculating by hand, etc. -- can't you delete the models without the covariate from your model set and then let MARK do the dirty work?

Somewhat more complicated - and really, depends on what you're after - are you interested in model averaged relationships between survival (say) and the value of the covariate, or something else? A model with a covariate provides an estimate of the parameter for a given value of the covariate. A model without the covariate provides an estimate of the parameter that would be the same for all individuals, regardless of the value of their covariate...

And, as discussed, if you go this route, you don't need to delete models without the covariate, since the beta for them is simply 0. You're model averaging the reals for each model, and you can generate a real for each model, regardless of whether or not it has the covariate. The big decision is what real to use for the model with the covariate. You could for example simply calculate the real parameter for the mean of the covariate (i.e., the mean over all individuals in your sample), take those, and model average them with estimates from the models without the covariates, using the normal AIC weights.

[darryl]

The big decision is what real to use for the model with the covariate. You could for example simply calculate the real parameter for the mean of the covariate (i.e., the mean over all individuals in your sample), take those, and model average them with estimates from the models without the covariates, using the normal AIC weights.

This is a shortcoming of MARK (sorry Gary) when you start looking at models with covariates, it only gives you 1 real value for a certain set of covariates. In some circumstances you may want to produce a plot of all the phis (say) across the range of observed covariate values. Difficult to do in MARK directly (I think), but I imagine it would be doable using RMARK.

[cooch]

The big decision is what real to use for the model with the covariate. You could for example simply calculate the real parameter for the mean of the covariate (i.e., the mean over all individuals in your sample), take those, and model average them with estimates from the models without the covariates, using the normal AIC weights.

This is a shortcoming of MARK (sorry Gary) when you start looking at models with covariates, it only gives you 1 real value for a certain set of covariates. In some circumstances you may want to produce a plot of all the phis (say) across the range of observed covariate values. Difficult to do in MARK directly (I think), but I imagine it would be doable using RMARK.

Nope - MARK now has the capability for doing the plot you described - for a given model with covariates. See section 11.5.

[darryl]

Nope - MARK now has the capability for doing the plot you described - for a given model with covariates. See section 11.5.

Ok, I stand corrected, should have RTFM. However, are you able to extract those values out of MARK (into Excel say) so you can do the model averaging by hand if necessary? I see (bottom of page 11-28) that you can do this using RMARK.

[gwhite]

Darryl:

You can extract the predictions into Excel (along with 95% CI), and thus combine estimates from multiple plots or model.

Evan has been after me since this feature went into MARK to do model averaging as well, but I've found other more pressing issues to work on! You, for one, keep publishing new models that need to be coded into MARK.

Gary

[darryl]

You, for one, keep publishing new models that need to be coded into MARK.

Gary

Sorry about that, will try to be less productive this year. Plus there's the grouse control program you're working on.

[cooch]

Darryl:

You can extract the predictions into Excel (along with 95% CI), and thus combine estimates from multiple plots or model.

Evan has been after me since this feature went into MARK to do model averaging as well, but I've found other more pressing issues to work on! You, for one, keep publishing new models that need to be coded into MARK.

Gary

There is, of course, the related issue of 'how best to do it' - I've collected a few things from B&A and it seems clear there is no completely satisfactory approach - I'm guessing the 'when in doubt, punt' choice will be to generate reals from all models with and w/o the covariate (with the later using beta=0 for covariate terms), but...we shall see.