Table 2.

Study 1 Monte Carlo means-as-outcomes multilevel models and “Huber–White” OLS results of parameter estimates for Y1, 5,000 replications

Population parameter				RML estimation		Full information maximum likelihood estimation				OLS estimation
				Multilevel		Multilevel		Quasi-weighted MLM		Huber–White
Labels	Level	Class	Value	Mean	SD	Mean	SD	Mean	SD	Mean	SD
${\mathit{\beta }}_{0j}$ for constant (=${\mathit{\lambda }}_{00})$	2	D	20.00	20.028	.220	20.028	.220	20.054	.235	20.058	.237
Standard error for ${\mathit{\beta }}_0$				.220	.004	.220	.004	.976	.053	.238	.014
${\mathit{\lambda }}_{10}$ for Z${}_1$	2	B	.200	.140	.176	.140	.176	.140	.176	.140	.181
Standard error for ${\mathit{\lambda }}_{10}$				.180	.009	.180	.009	1.640	.088	.186	.015
${\mathit{\beta }}_1$ for X${}_1$(=${\mathit{\lambda }}_{01})$	1	F	.350	.351	.027	.351	.027	.350	.029	.353	.034
Standard error for ${\mathit{\beta }}_1$				.026	.001	.026	.001	.026	.0008	.034	.003
${\mathit{\beta }}_2$ for X${}_2$(=${\mathit{\lambda }}_{02})$	1	F	.450	.450	.004	.450	.004	.450	.004	.450	.004
Standard error for ${\mathit{\beta }}_2$				.004	.00006	.004	.00001	.003	.0001	.004	.0002