# Intraclass correlation used to assess variability of lower-order relationships across higher-order processes/units. A function and vignettes for computing the intraclass correlation described in Aguinis & Culpepper (2015). iccbeta quantifies the share of variance in an outcome variable that is attributed to heterogeneity in slopes due to higher-order processes/units. ```r icc_beta(x, ...) ## S3 method for class 'lmerMod' icc_beta(x, ...) ## Default S3 method: icc_beta(x, l2id, T, vy, ...) ``` ## Arguments - `x`: A `lmer` model object or a design matrix with no missing values. - `...`: Additional parameters... - `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. ## Returns A `list` with: * `J` * `means` * `XcpXc` * `Nj` * `rho_beta` ## Examples ```r ## Not run: if(requireNamespace("lme4") && requireNamespace("RLRsim")){ ## Example 1: Simulated Data Example from Aguinis & Culpepper (2015) ---- 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) ## iccbeta calculation on `lmer` object icc_beta(lmm1) ## Manual specification of iccbeta # Extract components from model. X <- model.matrix(lmm1) p <- ncol(X) T1 <- VarCorr(lmm1)$l2id[1:p,1:p] # Note: vy was computed under "icca" # Computing iccb # Notice '+1' because icc_beta assumes l2ids are from 1 to 30. icc_beta(X, simICCdata2$l2id + 1, T1, vy)$rho_beta ## Example 2: Hofmann et al. (2000) ---- data(Hofmann) library("lme4") # Random-Intercepts Model lmmHofmann0 = lmer(helping ~ (1|id), data = Hofmann) vy_Hofmann = var(Hofmann[,'helping']) # Computing icca VarCorr(lmmHofmann0)$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) ## Automatic calculation of iccbeta using the lmer model amod = icc_beta(lmmHofmann1) ## Manual calculation of iccbeta X_Hofmann <- model.matrix(lmmHofmann1) P <- ncol(X_Hofmann) T1_Hofmann <- VarCorr(lmmHofmann1)$id[1:P,1:P] # Computing iccb bmod = icc_beta(X_Hofmann, Hofmann[,'id'], T1_Hofmann, vy_Hofmann)$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.") } ## End(Not run) ``` ## 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://hermanaguinis.com/pubs.html](http://hermanaguinis.com/pubs.html) ## See Also `lme4::lmer()`, `model.matrix()`, `lme4::VarCorr()`, `RLRsim::LRTSim()`, iccbeta::Hofmann , and iccbeta::simICCdata ## Author(s) Steven Andrew Culpepper

icc_beta function