Table 1.

Parameter Recovery from the Correctly Specified 1-Factor Multilevel Structural Equation Model

Approach	Variable	Within Loading			Between Loading			Mean			Residual Variance
		Sim.	E(X)	SD(X)	Sim.	E(X)	SD(X)	Sim.	E(X)	SD(X)	Sim.	E(X)	SD(X)
MSEM	1	0.80	0.80	0.004	0.70	0.70	0.04	2	2.00	0.07	0.1	0.10	< 0.01
	2	0.70	0.70	0.003	0.80	0.80	0.04	3	3.00	0.08	0.1	0.10	< 0.01
	3	0.85	0.85	0.004	0.75	0.75	0.04	1	1.00	0.08	0.1	0.10	< 0.01
	4	0.75	0.75	0.003	0.65	0.65	0.03	2	2.00	0.07	0.1	0.10	< 0.01
	5	0.88	0.88	0.004	0.88	0.88	0.04	4	4.00	0.09	0.1	0.10	< 0.01
	6	0.82	0.82	0.004	0.72	0.72	0.04	2	2.00	0.07	0.1	0.10	< 0.01
	7	0.84	0.84	0.004	0.71	0.71	0.04	5	5.00	0.07	0.1	0.10	< 0.01
	8	0.67	0.67	0.003	0.68	0.68	0.03	3	3.00	0.07	0.1	0.10	< 0.01
ML-SEM	1	0.80	0.80	0.01	0.70	0.70	0.04	2	2.01	0.05	0.1	0.10	< 0.01
	2	0.70	0.70	0.01	0.80	0.80	0.04	3	3.01	0.06	0.1	0.10	< 0.01
	3	0.85	0.85	0.01	0.75	0.75	0.04	1	1.01	0.06	0.1	0.10	< 0.01
	4	0.75	0.75	0.01	0.65	0.65	0.04	2	2.00	0.05	0.1	0.10	< 0.01
	5	0.88	0.88	0.01	0.88	0.88	0.05	4	4.01	0.07	0.1	0.10	< 0.01
	6	0.82	0.82	0.01	0.72	0.72	0.04	2	2.01	0.05	0.1	0.10	< 0.01
	7	0.84	0.84	0.01	0.71	0.71	0.04	5	5.00	0.05	0.1	0.10	< 0.01
	8	0.67	0.67	0.01	0.68	0.68	0.04	3	3.00	0.05	0.1	0.10	< 0.01

Note. Sim. refers to simulated values; E(X) indicates the expected parameter mean, SD (X) indicates the expected parameter standard deviation over 500 samples. MSEM indicates multilevel structural equation modeling (e.g., Goldstein & McDonald, 1988; Muthén, 1990, 1994); ML-SEM indicates multilevel structural equation modeling (Mehta & Neale, 2005). Because of suspiciously high outlier χ² values, 4 samples from the MSEM approach and 1 sample from the ML-SEM approach were removed.