# Calculating 95% confidence intervals for GLMM additive coefficient - count data estimates

I am running a GLMM on some data where the response is count data, using the glmmADMD package in R. I would like to plot the results giving estimates for the response variable with certain explanatory variables.

model <- glmmadmb(response ~ var1 + var2 + var3 - 1 + (1|rvar1),
data = data1, family = 'nbinom', zeroInflation = FALSE)


When I get my results from the summary() function,

summary(model)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
var1D      -0.744      0.177   -4.21  2.5e-05 ***
var1J      -0.455      0.170   -2.68  0.00745 **
var2PI      0.620      0.115    5.41  6.4e-08 ***
var2SO      0.228      0.111    2.05  0.04026 *
var32016   -0.624      0.169   -3.68  0.00023 ***
var32017   -0.988      0.312   -3.17  0.00153 **
var32018   -0.767      0.191   -4.02  5.9e-05 ***
---


I know that I can get a count estimate by reverse transforming my coefficients,

 exp(0.620) #for var2PI


and that I can get a 95% confidence interval by exponentiating two standard deviations in either direction,

exp(0.620 +/- 2*(0.115)) #for var2PI


such that I now have an estimate and a 95% confidence interval with respect to that single variable. To look at multiple coefficients, I know I can simply add the coefficients together to get a count estimate,

exp(0.620 + (-0.624)) #for var2PI and var32016


My question is - how do I achieve a 95% confidence interval for this estimate that of the multiple added coefficients? Do I take an average of the two standard errors? Any help, or a text that explains this would be of great help! I've tried the R book, a few GLMM books (Littell et al 2006, McCulloch et al 2008) to no avail. A citation of where this information could be found officially would be awesome!

• look for contrasts() in the car or emmeans package ... – Ben Bolker Dec 21 '18 at 20:37

You will also need to account for the covariance between the two coefficients. You can get the expected along with a 95% confidence interval using the effectPlotData() function of the GLMMadaptive package that can fit the same model.