Thank you for your response everyone. I should provide more information on
the method I used.

1.) I fit the model using the glmmadmb package with a negative binomial
distribution.

2.) I created a model matrix (mm) of fixed effects with new data
(n=~150,000), and multiplied this matrix with the vcov(glmmadmb_model)
matrix, according to some excellent documentation and code examples
developed online (r-sig-wikidot-FAQ-GLMM, etc.):

predvar<-diag(mm%*%vcov(glmmadmb_object)%*%t(mm))

3.) Then I took the square root of predvar to get the SE of each prediction
point:

newdata$SE<-sqrt(predvar)

4.) I made predictions with the fixed effects of the glmmadmb model, and
transformed that response with the link (exp(prediction)).

5.) To compute the upper and lower ranges of population estimates at each
point, I used the following:

(exp transformed prediction) +/- 1.96(SE)

The result is three columns of ~150,000 observations in my new dataset:
upper CI, lower CI, and transformed prediction.

As my question states I was hoping to simply sum the columns for a
reach-wide, minimum and maximum population estimate. However, I understand
the caveats of using glmms in this way for predictions. Have I missed
something? I'm hoping to use this method for a manuscript intended for
publication, so it needs to be sound, if that is even possible with all
things considered.


On Mon, Jul 28, 2014 at 12:05 PM, Reuben Smit <smit.reuben@gmail.com> wrote:

>
>
> I am generating a river reach population estimate for a freshwater mussel
> by summing point estimates made across a gridded point network (within the
> reach) using a generalized linear mixed model framework. I have generated
> 95% confidence/prediction intervals at each of the ~150,000 point locations
> in R. I have summed all of the point estimates to derive the reach
> population estimate, but am unsure how to derive a single confidence
> interval for the population estimate using the 150,000 individual-point
> confidence intervals. My question: Is it statistically valid to simply sum
> all the lower estimates and upper estimates to obtain the absolute upper
> and lower most population confidence limits?
>

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