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. Author manuscript; available in PMC: 2010 Apr 20.
Published in final edited form as: Multivariate Behav Res. 2009 Nov 1;44(6):711–740. doi: 10.1080/00273170903333574

TABLE 1.

Simulation Demonstration: Effects of Disproportionate Selection in a Multilevel Model

Before Selection
After Disproportionate Selection at Cluster-Level Only
After Disproportionate Selection at Individual-Level Only
After Disproportionate Selection at Both Levels
Infinite Population Parameters Select on zj rwj,zj = .50 Select on zj rwj,zj = .00 Select on zj ; xij zj rwj,zj = .00 Select on zj ; wj zj rwj,zj = .00 Select on wj Select on xij Select on yij At Stage 1, Select on zj At Stage 2, Select on zij rwj,zj = rzij,xij = .50
Fixed effects
  γ 00 2 6.98 7.59 7.60 7.59 2.00 2.00 3.43 12.41
  γ 10 3 3.00 3.00 8.60 3.00 3.00 3.00 2.59 3.43
  γ 01 3 3.44 3.00 3.00 8.60 3.00 3.00 2.40 3.43
Variance comp.
  τ 00 1 2.29 2.45 2.46 8.27 1.00 1.00 .71 2.29
  τ 01 0 .00 .00 1.45 .01 .00 .00 −.09 .01
  τ 11 1 .99 1.00 2.45 1.00 1.00 1.00 1.03 1.01

Note. xij is a Level 1 independent variable from Equation (6). wj is a Level 2 independent variable from Equation (6). zj is an omitted Level 2 selection variable; γzj = 2. xijzj is an omitted interaction term between a Level 1 independent variable and Level 2 selection variable; γxijzj = 2. wjzj is an omitted interaction term between a Level 2 independent variable and Level 2 selection variable; γwjzj = 2. zij is an omitted Level 1 selection variable; γzij = 2. Note that selection always occurred at the mean of the designated selection variable. Variance comp. = variance components.