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!