sim.mlcor: Simulate a multilevel correlation

Description

In multilevel or hierarchical nested data, correlations at the within and between levels often differ in magnitude and/or sign. For instance, Bliese and Halverson (1996) showed that the within correlation between individual reports of work hours and individual well-being was -.11. When these same data were mean-aggregated to the group-level, the between correlation based on group means was -.71. A necessary, but not sufficient, condition for differences across levels is a non-zero ICC1 value for both variables (Bliese, 2000). This simulation creates a dataset with a group ID and an X and Y variable for any combination of group size, number of groups, within and between correlations, ICC1 values and reliability (alpha).

Usage

sim.mlcor(gsize,ngrp,gcor,wcor,icc1x,icc1y,alphax=1,alphay=1)

Arguments

gsize

The simulated group size.

ngrp

The simulated number of groups.

gcor

The simulated between group correlation.

wcor

The simulated within group correlation.

icc1x

The simulated ICC1 value for X.

icc1y

The simulated ICC1 value for Y.

alphax

The reliability (alpha) of X.

alphay

The reliability (alpha) of Y.

Value

GRP

The grouping designator.

The simulated X value.

The simulated Y value.

References

Bliese, P. D. (2000). Within-group agreement, non-independence, and reliability: Implications for data aggregation and analysis. In K. J. Klein & S. W. Kozlowski (Eds.), Multilevel Theory, Research, and Methods in Organizations (pp. 349-381). San Francisco, CA: Jossey-Bass, Inc.

Bliese, P. D. & Halverson, R. R. (1996). Individual and nomothetic models of job stress: An examination of work hours, cohesion, and well-being. Journal of Applied Social Psychology, 26, 1171-1189.

Bliese, P. D., Maltarich, M. A., Hendricks, J. L., Hofmann, D. A., & Adler, A. B. (2019). Improving the measurement of group-level constructs by optimizing between-group differentiation. Journal of Applied Psychology, 104, 293-302.

Examples

Run this code

# NOT RUN {
#
# Examine the multilevel properties of work hours and well-being
# in the bh1996 data
#
data(bh1996)
with(bh1996,waba(HRS,WBEING,GRP))
mult.icc(bh1996[,c("HRS","WBEING")],bh1996$GRP)
#
#Estimate true group-mean correlation by adding ICC2 adjusted incremental
#correlation back to within correlation. For value of -.8256
#
-0.110703+(-0.7121729--0.110703)/(sqrt(0.9171286*0.771756))
#
# Simulate data with same properties assuming no measurement error
#
set.seed(578323)
SIM.ML.COR<-sim.mlcor(gsize=75,ngrp=99,gcor=-.8256,wcor=-.1107,
                 icc1x=0.04338,icc1y=0.12924,alphax=1,alphay=1)
#
# Compare Simulated results to results (above) from bh1996
#
with(SIM.ML.COR,waba(X,Y,GRP))
mult.icc(SIM.ML.COR[,c("X","Y")],SIM.ML.COR$GRP)
# }