# Which method to use when calculating the confidence interval of GLMM Gamma Regression with the lme4 package in R

I am fitting a GLMM with family gamma using the lme4 package in R. Below is a code example to simulate the gamma GLMM fitting.

# Load packages
library(tidyverse)
library(lme4)
library(lmerTest)

# Set seed
set.seed(200)

# Create an example data frame
dat <- data_frame(X = rgamma(500, shape = 2),
Group = rep(c("A", "B", "C", "D", "E"), each = 100)) %>%
mutate(R = unlist(map(1:5, ~rnorm(100, .x)))) %>%
mutate(Y = exp(X + R))

# Fit a GLMM with Gamma and log link
fit <- glmer(Y ~ X + (1 | Group), data = dat, family = Gamma(link = "log"))


For poisson or binomial GLMM, we can use the confint function to calculate the confidence interval. But the default setting (method = "profile) is not working for gamma GLMM.

confint(fit)
Computing profile confidence intervals ...
Error in profile.merMod(object, which = parm, signames = oldNames, ...) :
can't (yet) profile GLMMs with non-fixed scale parameters


Instead, we can set the method to be Wald or boot to calculate the confidence interval.

# Calculate the confidence interval using the Wald method
confint(fit, method = "Wald")
#                2.5 %   97.5 %
# .sig01            NA       NA
# .sigma            NA       NA
# (Intercept) 2.199512 4.548215
# X           1.018495 1.131192

# Calculate the confidence interval using the boot method
confint(fit, method = "boot")
#                 2.5 %    97.5 %
# .sig01      0.4264700 1.9473079
# .sigma      0.8331289 0.9826871
# (Intercept) 2.1469817 4.5461055
# X           1.0202349 1.1340656
# Warning message:
#   In bootMer(object, FUN = FUN, nsim = nsim, ...) :
#   some bootstrap runs failed (5/500)


I am curious about which method to use and what would be the pros and cons. As far as I can tell, the Wald method is fast to compute, while the bootstrapping method takes a long time to run. But Wald method can only compute the confidence interval of the fixed-effect parameters. Any insights or suggestion would be appreciated.