Averaging occupancy estimates

[mbrooks]

I would like to average occupancy estimates across categorical treatment levels from individual site occupancy estimates. I can't include the treatment effect in the model because my sample size is small, and the treatment adds too many variables for the model to run properly. My question is, can I average the individual site occupancy estimates across treatment levels (e.g., an ANOVA)? I'm worried that averaging parameter estimates with associated standard errors is a no no because the resulting averages would not incorporate the individual parameter estimates' errors. I would end up with standard errors for the treatment-level mean estimates, but not for the parameter estimates. Is it OK to average occupancy estimates, and is there a way to incorporate the occupancy estimate errors into the errors associated with averaging?

[darryl]

You should account for the uncertainty in the estimates, but more basic question is how are those estimates varying if you can't get the covariate in the model? Recall that these estimates are not observed values (like you have with standard ANOVA) but are essentially predicted values based upon the model fit to the data. If the model doesn't allow the predicted values to be different among the different treatment levels, there's not going to be a difference there (unless you happen to have some other covariate in the model that is highly correlated with the treatment levels).

[mbrooks]

Thanks for the reply. I'm pretty sure that there are some differences in some of my treatment levels, and I also have several important continuous covariates. I think that I just have too many treatment levels for my model to handle. As for averaging occupancy estimates across treatment levels, is there a way to do this that incorporates the estimates' standard errors? I can't find any formula for this type of situation.

[darryl]

I'm sure there is a way, couldn't write it down exactly off the top of my head, but my point remains that averaging the estimated psi values across those treatment levels from a model that does not include treatment as a factor, is unlikely to give you any indication of a difference simply because the model that has been fit to the data does not allow them to be different even if they are.

If you have too many treatment levels then you should look at combining them, or think about a random effects model (have to do it in WinBUGS though at the moment)

Darryl