Table 4.

Simulation results: bias, coverage and efficiency of different imputation models.

				Bias (β1 = 2)		Empirical SE		Coverage
R2	CV (a2)	Imputation model		MCAR	MAR	MCAR	MAR	MCAR	MAR
0.1	0.1	Complete data		0.000		0.273		95.2
		Complete cases		0.003	− 0.172	0.366	0.352	95.1	92.6
		x	M1	− 0.005	− 0.004	0.368	0.386	93.8	94.9
		x,a1	M2	− 0.001	0.002	0.333	0.345	94.6	94.7
		x,a2	M3	− 0.009	− 0.003	0.363	0.383	94.6	94.9
		x,a1,a2	M4	− 0.005	0.005	0.330	0.342	94.7	95.0
		a1,a2	M5	− 0.017	− 0.016	0.328	0.337	94.8	95.0
		ln(a1),ln(a2)	M6	− 0.016	− 0.034	0.329	0.332	94.9	95.1
0.1	0.3	Complete data		0.006		0.267		95.3
		Complete cases		0.001	− 0.168	0.359	0.351	95.3	92.9
		x	M1	− 0.009	0.005	0.358	0.385	94.7	94.9
		x,a1	M2	− 0.007	0.014	0.348	0.372	94.9	94.9
		x,a2	M3	− 0.001	0.031	0.334	0.362	95.4	95.0
		x,a1,a2	M4	− 0.001	0.038	0.325	0.346	95.0	94.7
		a1,a2	M5	− 0.562	− 0.665	0.350	0.334	94.3	92.6
		ln(a1),ln(a2)	M6	− 0.038	− 0.064	0.313	0.318	95.8	95.4
0.3	0.1	Complete data		0.003		0.137		95.2
		Complete cases		0.001	− 0.139	0.183	0.188	95.5	88.5
		x	M1	− 0.005	0.031	0.171	0.187	95.3	94.0
		x,a1	M2	− 0.003	0.026	0.159	0.171	95.8	95.0
		x,a2	M3	− 0.007	0.029	0.170	0.188	95.2	93.8
		x,a1,a2	M4	− 0.003	0.026	0.159	0.171	95.9	94.6
		a1,a2	M5	− 0.016	0.000	0.158	0.168	96.1	95.3
		ln(a1),ln(a2)	M6	− 0.016	− 0.031	0.158	0.163	96.2	95.6
0.3	0.3	Complete data		− 0.002		0.137		95.0
		Complete cases		− 0.006	− 0.143	0.184	0.192	94.9	88.5
		x	M1	− 0.009	0.054	0.174	0.196	94.2	93.0
		x,a1	M2	− 0.012	0.057	0.172	0.193	94.8	93.3
		x,a2	M3	− 0.010	0.076	0.170	0.191	94.3	91.5
		x,a1,a2	M4	− 0.009	0.080	0.167	0.187	94.2	91.8
		a1,a2	M5	− 0.580	− 0.814	0.287	0.300	94.3	93.3
		ln(a1),ln(a2)	M6	− 0.051	− 0.070	0.162	0.164	95.1	94.6

SE, standard error; CV, coefficient of variation; MCAR, missing completely at random; MAR, missing at random.