iccbeta: Multilevel Model Intraclass Correlation for Slope Heterogeneity

A function and vignettes for computing an intraclass correlation described in Aguinis & Culpepper (2015) <doi:10.1177/1094428114563618>. This package quantifies the share of variance in a dependent variable that is attributed to group heterogeneity in slopes.

References

Aguinis, H., & Culpepper, S.A. (2015). An expanded decision making procedure for examining cross-level interaction effects with multilevel modeling. Organizational Research Methods. Available at: http://www.hermanaguinis.com/pubs.html

See also

Useful links:

• https://tmsalab.github.io/iccbeta

• https://github.com/tmsalab/iccbeta

• Report bugs at https://github.com/tmsalab/iccbeta/issues

Examples

if (FALSE) {

if(requireNamespace("lme4") && requireNamespace("RLRsim")){
# Simulated Data Example
data(simICCdata)
library('lme4')

# computing icca
vy <- var(simICCdata$Y)
lmm0 <- lmer(Y ~ (1|l2id), data = simICCdata, REML = FALSE)
VarCorr(lmm0)$l2id[1,1]/vy

# Create simICCdata2
grp_means = aggregate(simICCdata[c('X1','X2')], simICCdata['l2id'],mean)
colnames(grp_means)[2:3] = c('m_X1','m_X2')
simICCdata2 = merge(simICCdata,grp_means,by='l2id')

# Estimating random slopes model
lmm1  <- lmer(Y ~ I(X1-m_X1) + I(X2-m_X2) + (I(X1-m_X1) + I(X2-m_X2) | l2id),
              data = simICCdata2, REML = FALSE)
X <- model.matrix(lmm1)
p <- ncol(X)
T1 <- VarCorr(lmm1)$l2id[1:p, 1:p]

# computing iccb
# Notice '+1' because icc_beta assumes l2ids are from 1 to 30.
icc_beta(X, simICCdata2$l2id + 1, T1, vy)$rho_beta

# Hofmann 2000 Example
data(Hofmann)
library('lme4')

# Random-Intercepts Model
lmmHofmann0 <- lmer(helping ~ (1|id), data = Hofmann)
vy_Hofmann <- var(Hofmann[,'helping'])
# computing icca
VarCorr(lmmHofmann0)$id[1,1]/vy_Hofmann

# Estimating Group-Mean Centered Random Slopes Model, no level 2 variables
lmmHofmann1  <- lmer(helping ~ mood_grp_cent + (mood_grp_cent | id),
                     data = Hofmann, REML = FALSE)
X_Hofmann <- model.matrix(lmmHofmann1)
P <- ncol(X_Hofmann)
T1_Hofmann <- VarCorr(lmmHofmann1)$id[1:P, 1:P]
# computing iccb
icc_beta(X_Hofmann, Hofmann[,'id'], T1_Hofmann, vy_Hofmann)$rho_beta

# Performing LR test
library('RLRsim')
lmmHofmann1a  <- lmer(helping ~ mood_grp_cent + (1 |id),
                      data = Hofmann, REML = FALSE)
obs.LRT <- 2*(logLik(lmmHofmann1) - logLik(lmmHofmann1a))[1]
X <- getME(lmmHofmann1,"X")
Z <- t(as.matrix(getME(lmmHofmann1,"Zt")))
sim.LRT <- LRTSim(X, Z, 0, diag(ncol(Z)))
(pval <- mean(sim.LRT > obs.LRT))
} else {
 stop("Please install packages `RLRsim` and `lme4` to run the above example.")
}
}