Table 3.

Study 1 Monte Carlo slopes-as-outcomes multilevel models and “Huber–White” OLS results of parameter estimates for Y${}_2$, 5000 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
${\mathit{\beta }}_0$ for constant (=${\mathit{\gamma }}_{00})$	1	E	40.000	40.006	.256	40.006	.256	40.012	.277	40.002	.263
Standard error for ${\mathit{\beta }}_0$				.257	.004	.257	.004	.254	.004	.263	.013
${\mathit{\beta }}_{1j}$ for X${}_1$(=${\mathit{\gamma }}_{01})$	2	C	.400	.358	.091	.358	.091	.364	.113	.357	.102
Standard error for ${\mathit{\beta }}_1$				.094	.005	.093	.005	.997	.085	.108	.013
${\mathit{\gamma }}_{11}$ for Z${}_1$	2	A	.200	.275	.153	.275	.153	.263	.187	.284	.168
Standard error for ${\mathit{\beta }}_1$				.155	.009	.154	.009	1.707	.143	.168	.019
${\mathit{\beta }}_2$ for X${}_2$(=${\mathit{\gamma }}_{02})$	1	F	.500	.500	.005	.500	.005	.500	.005	.500	.005
Standard error for ${\mathit{\beta }}_2$				.005	.00008	.005	.00008	.005	.00008	.005	.00024