# [R-sig-ME] ICC for the GLMM

Timothy Lau timothy.s.lau at gmail.com
Sat Jan 23 19:25:41 CET 2016

``` I've written functions to compute the ICC for most of the GLMM using
the lme4 package:

###################################################
### compute ICC in lme4
###################################################
# use
# https://stat.ethz.ch/pipermail/r-sig-mixed-models/2014q3/022538.html
# for example interpretation

# Negative Binomial ICC lme4 (numerator can also be a list of values)
# function based off of http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3916583/
ICC.NB <- function(model, numerator){
require(lme4)
mout <- data.frame(VarCorr(model)) # random intercept model variances
sigma_a2 <- sum(mout[mout\$grp %in% numerator, "vcov"]) # random
effect(s) in numerator
sigma_2 <- sum(mout["vcov"]) # sum of random effects variance in denominator
beta <- as.numeric(fixef(model)["(Intercept)"]) # fixed effect intercept
r <- getME(object = model, "glmer.nb.theta") # theta
icc <- (exp(sigma_a2) - 1) / ((exp(sigma_2) - 1) + (exp(sigma_2) /
r) + (exp(-beta) - (sigma_2 / 2)))
return(icc)
}
# example (cid = a school)
ICC.NB(model = glmer.nb(formula = awards ~ 1 + (1 | cid), data =
"http://www.ats.ucla.edu/stat/data/hsbdemo.dta")), numerator = "cid")

# Binomial ICC lme4 (numerator can also be a list of values)
# function based off of http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3426610/
ICC.BIN <- function(model, numerator){
require(lme4)
mout <- data.frame(VarCorr(model)) # random intercept model variances
level1 <- pi^2 / 3 # level 1 variance of all binomial models
sigma_a2 <- sum(mout[mout\$grp %in% numerator,"vcov"]) # random
effect(s) in numerator
sigma_2 <- sum(data.frame(VarCorr(model))[,"vcov"], level1) # sum of
random effects variance in denominator
icc <- sigma_a2 / sigma_2
return(icc)
}

# example (herd = a herd of bovine)
ICC.BIN(model = glmer(formula = cbind(incidence, size - incidence) ~ 1
+ (1 | herd), data = cbpp, family = binomial), numerator = "herd")

# Gaussian ICC lme4 (numerator can also be a list of values)
# function based off of http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1540459/
ICC.GAU <- function(model, numerator){
require(lme4)
mout <- data.frame(VarCorr(model)) # random intercept model variances
sigma_a2 <- sum(mout[mout\$grp %in% numerator, "vcov"]) # random
effect(s) in numerator
sigma_2 <- sum(mout["vcov"]) # sum of random effects variance in denominator
icc <- sigma_a2 / sigma_2
return(icc)
}
# example (Subject = an individual person)
ICC.GAU(model = lmer(formula = Reaction ~ 1 + (1 | Subject), data =
sleepstudy), numerator = "Subject")

# Poisson ICC lme4 (numerator can also be a list of values)
# function based off of p.22
http://www.ssicentral.com/supermix/Documentation/count_final.pdf
ICC.POI <- function(model, numerator){
require(lme4)
mout <- data.frame(VarCorr(model)) # random intercept model variances
sigma_a2 <- sum(mout[mout\$grp %in% numerator, "vcov"]) # random
effect(s) in numerator
sigma_2 <- sum(mout["vcov"]) # sum of random effects variance in denominator
icc <- sigma_a2 / (1 + sigma_2)
return(icc)
}
# example (cid = schools)
ICC.POI(model = glmer(formula = awards ~ 1 + (1 | cid), family =
poisson, data = foreign::read.dta(file =
"http://www.ats.ucla.edu/stat/data/hsbdemo.dta")), numerator = "cid")

###################################################

But I'm stuck on the Gamma distribution and Inverse Gaussian. If
anyone has some suggestions for how to compute the ICC for these
distributions or wants to help more directly via github I've put the
functions here:
https://github.com/timothyslau/ICC.merMod

Best,
Timothy

"The will to win means nothing without the will to prepare."
http://en.wikipedia.org/wiki/Juma_Ikangaa

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