What I'd like to calculate: I'm using glmer (lme4) with a poisson distribution to estimate a bird's total population across a large region (i.e. sum predictions). I'd like to obtain confidence intervals for the total population estimate...or some metric that represents uncertainty.
Question: Would it be inappropriate to apply the model to the region using the low and high beta estimates of the fixed effects from confint(model), then sum the low and high predictions and present that as a metric for population estimate uncertainty?
Lengthy Background Info: My data set includes multiple years of survey data, where bird abundance is recorded at stops along a route. There are multiple years of data, many routes, multiple observers, and some observers run multiple routes and sometimes observers change for a route. I've structured the random effect as (1|Route/Observer)+(1|Year). My survey region is large (multiple states). My predictor variables include land cover, climatic, topographic, and survey related variables (i.e. wind speed, time of day, day of year). Land cover, climatic, and topographic data were derived from 30 m resolution rasters in a GIS.
I've been applying each model in pythonwin using arcpy. I don't have enough memory to predict in R...each raster is ~ 12GB. Since you can't really spatially apply the random effects (i.e. observer) across a region, these are left out of the formula. Therefore the new data set I'm applying the model to are the raster covariates (and I maximize the effect of survey related variables such as wind speed). I then run zonal statistics to get the sum predicted abundance of a bird across the entire region after scaling the prediction to the birds estimated detection distance.
I'd like to get some estimate of uncertainty for the population estimate. As far as I understand, it's hard to do with mixed-models: from predict.merMod “There is no option for computing standard errors of predictions because it is difficult to define an efficient method that incorporates uncertainty in the variance parameters”. But some methods have been presented. Here they are estimating the CI & PI for the marginal effect of one covariate, and here are some ideas/functions..confint(model) now works for lme4.