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. x_ij is a Level 1 independent variable from Equation (6). w_j is a Level 2 independent variable from Equation (6). z_j is an omitted Level 2 selection variable; γ_zj = 2. x_ijz_j is an omitted interaction term between a Level 1 independent variable and Level 2 selection variable; γ_xijzj = 2. w_jz_j is an omitted interaction term between a Level 2 independent variable and Level 2 selection variable; γ_wjzj = 2. z_ij is an omitted Level 1 selection variable; γ_zij = 2. Note that selection always occurred at the mean of the designated selection variable. Variance comp. = variance components.