iccbeta (version 1.0)

icc_beta: Intraclass correlation used to assess variability of lower-order relationships across higher-order processes/units.

Description

A function and vignettes for computing the intraclass correlation described in Aguinis & Culpepper (in press). iccbeta quantifies the share of variance in an outcome variable that is attributed to heterogeneity in slopes due to higher-order processes/units.

Usage

icc_beta(X, l2id, T, vy)

Arguments

X

The design matrix of fixed effects from a lmer model.

l2id

A vector that identifies group membership. The vector must be coded as a sequence of integers from 1 to J, the number of groups.

T

A matrix of the estimated variance-covariance matrix of a lmer model fit.

vy

The variance of the outcome variable.

References

Aguinis, H., & Culpepper, S.A. (in press). An expanded decision making procedure for examining cross-level interaction effects with multilevel modeling. Organizational Research Methods. Available at: http://mypage.iu.edu/~haguinis/pubs.html

See Also

lmer, model.matrix, VarCorr, LRTSim, Hofmann, simICCdata

Examples

## Not run: 
# #Simulated Data Example from Aguinis & Culpepper (in press)
# data(simICCdata)
#   require(lme4)
#   
#   #computing icca
#   vy = var(simICCdata$Y)
#   lmm0 <- lmer(Y ~ (1|l2id),data=simICCdata,REML=F)
#   VarCorr(lmm0)$l2id[1,1]/vy
#     
#   #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=F)
#   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)$rho_beta
#   
# #Hofmann et al. (2000) Example
# data(Hofmann)
#   require(lme4)
# 
#   #Random-Intercepts Model
#   lmmHofmann0 = lmer(helping ~ (1|id),data=Hofmann)
#   vy_Hofmann = var(Hofmann[,'helping'])
#   #computing icca
#   VarCorr(lmmHofmann0)$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=F)
#   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=F)
#   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))
# ## End(Not run)