. Author manuscript; available in PMC: 2017 May 11.

Published in final edited form as: J Multivar Anal. 2014 Apr 5;130:176–193. doi: 10.1016/j.jmva.2014.03.012

Table 2.

Power and robustness study (Scenario I) with L = 8,K = 2000, D = 1000, (ρ₁₃ ,ρ₂₃) = (.5,.6),σ_α = 1, σ_ε = .5. Standard deviation (std.dev.) relates to variation across the randomly generated 500 covariate matrices X

Power	m = 500, EN = 1750		m = 50, EN = 175		m = 20, EN = 70
β₃ = .25	mean	std.dev.	mean	std.dev.	mean	std.dev.
Theo.Pow.	0.800	0.040	0.120	0.023	0.086	0.018
Theo.Pow.hat	0.799	0.039	0.125	0.023	0.090	0.019
Empi.Pow.n	0.799	0.037	0.111	0.022	0.063	0.017

Misspecification of the error term distribution

Empi.Pow.t₃	0.798	0.036	0.112	0.023	0.062	0.019
Empi.Pow.t₅	0.799	0.036	0.111	0.022	0.063	0.018

Misspecification of the random intercept distribution

Empi.Pow.t₃	0.817	0.033	0.132	0.027	0.076	0.021
Empi.Pow.t₅	0.799	0.036	0.116	0.023	0.067	0.018

Power	m = 500, EN = 1750		m = 50, EN = 175		m = 20, EN = 70
β₃ = .8	mean	std.dev.	mean	std.dev.	mean	std.dev.
Theo.Pow.	1	0	0.847	0.104	0.541	0.189
Theo.Pow.hat	1	0	0.821	0.096	0.512	0.151
Empi.Pow.n	1	0	0.820	0.102	0.444	0.161

Misspecification of the error term distribution

Empi.Pow.t₃	1	0	0.821	0.102	0.449	0.164
Empi.Pow.t₅	1	0	0.821	0.102	0.444	0.162

Misspecification of the random intercept distribution

Empi.Pow.t₃	1	0	0.852	0.074	0.545	0.155
Empi.Pow.t₅	1	0	0.824	0.094	0.472	0.159