TABLE 3.

Empirical bias and variance of our estimators in a simulation study guided by the dental data of nine-year-old children from the Iowa Fluoride Study. The number of clusters is 200; the size of each cluster is 15. Each entry is based on 100 Monte Carlo iterations. The performances of ZIP estimators are also added.

MPL
			Low intraclass correlation			High intraclass correlation
		True	Bias	SE	SE (Adj_SW)	Bias	SE	SE (Adj_SW)
Count part	Intercept	1.00	0.0645	0.2040	0.2835	0.3191	0.5564	0.5916
	AUCmhF5_9yrs	0.01	−0.0006	0.1388	0.1274	0.0462	0.3889	0.2966
	AUCSodaOz5_9yrs	−0.01	−0.0011	0.0201	0.0167	−0.0076	0.0558	0.0430
	ToothBrushingFeq.Per_DayAvg	−0.13	−0.0117	0.0920	0.0879	−0.0290	0.2439	0.2086
	HomeFluorideppm.Avg	−0.16	0.0080	0.1000	0.0999	−0.0631	0.3174	0.2453
	v	0.60	0.0427	0.1030	0.1277	0.1892	0.2052	0.2461
			Low intraclass correlation			High intraclass correlation
		True	Bias	SE	SE (Adj_SW)	Bias	SE	SE (Adj_SW)
Zero part	Intercept	2.00	0.0533	0.4238	0.4117	0.0274	0.7473	0.8477
	AUCmhF5_9yrs	0.70	0.0044	0.3068	0.3156	0.0356	0.5244	0.6381
	AUCSodaOz5_9yrs	−0.07	0.0091	0.0489	0.0433	0.0129	0.0879	0.0902
	ToothBrushingFeq.Per_DayAvg	0.56	−0.0417	0.2324	0.2235	−0.0157	0.4599	0.4592
	HomeFluorideppm.Avg	−0.30	−0.0006	0.2491	0.2317	0.0328	0.5282	0.4942
MES
			Low intraclass correlation			High intraclass correlation
		True	Bias	SE	SE (BS)	Bias	SE	SE (BS)
Count part	Intercept	1.00	−0.0045	0.0687	0.1016	−0.0068	0.1481	0.1593
	AUCmhF5_9yrs	0.01	−0.0025	0.0487	0.0820	0.0133	0.1235	0.1282
	AUCSodaOz5_9yrs	−0.01	−0.0003	0.0074	0.0099	−0.0019	0.0177	0.0182
	ToothBrushingFeq.Per_DayAvg	−0.13	−0.0006	0.0353	0.0531	−0.0033	0.0717	0.0862
	HomeFluorideppm.Avg	−0.16	0.0032	0.0359	0.0558	−0.0154	0.0934	0.0982
	v	0.60	−0.0069	0.0539	0.0686	−0.0034	0.0640	0.0430
			Low intraclass correlation			High intraclass correlation
		True	Bias	SE	SE (BS)	Bias	SE	SE (BS)
Zero part	Intercept	2.00	0.0240	0.1537	0.1623	0.0115	0.3154	0.3664
	AUCmhF5_9yrs	0.70	−0.0046	0.1061	0.1182	0.0048	0.2075	0.2734
	AUCSodaOz5_9yrs	−0.07	0.0027	0.0161	0.0158	0.0072	0.0335	0.0358
	ToothBrushingFeq.Per_DayAvg	0.56	−0.0140	0.0820	0.0816	−0.0052	0.1786	0.1913
	HomeFluorideppm.Avg	−0.30	−0.0026	0.0767	0.0877	0.0176	0.1798	0.2022
ZIP
			Low intraclass correlation			High intraclass correlation
		True	Bias	SE	SE (pscl, Adj_SW)	Bias	SE	SE (pscl, Adj_SW)
Count part	Intercept	1.00	0.7203	0.2361	0.1665, 0.2038	0.7002	0.5395	0.1922, 0.4104
	AUCmhF5_9yrs	0.01	−0.0063	0.1782	0.1374, 0.1646	0.0721	0.4532	0.1597, 0.3348
	AUCSodaOz5_9yrs	−0.01	−0.0044	0.0272	0.0182, 0.0215	−0.0102	0.0654	0.0231, 0.0484
	ToothBrushingFeq.Per_DayAvg	−0.13	−0.0566	0.1253	0.0919, 0.1123	−0.0620	0.2790	0.1067, 0.2312
	HomeFluorideppm.Avg	−0.16	−0.0418	0.1372	0.1038, 0.1265	−0.1092	0.3700	0.1249, 0.2710
			Low intraclass correlation			High intraclass correlation
		True	Bias	SE	SE (pscl, Adj_SW)	Bias	SE	SE (pscl, Adj_SW)
Zero part	Intercept	2.00	0.0596	0.4234	0.3117, 0.4086	0.0372	0.7874	0.3220, 0.8389
	AUCmhF5_9yrs	0.70	−0.0069	0.3026	0.2446, 0.3122	0.0335	0.5423	0.2532, 0.6292
	AUCSodaOz5_9yrs	−0.07	0.0114	0.0490	0.0333, 0.0429	0.0135	0.0880	0.0354, 0.0882
	ToothBrushingFeq.Per_DayAvg	0.56	−0.0258	0.2333	0.1671, 0.2219	−0.0047	0.4678	0.1733, 0.4534
	HomeFluorideppm.Avg	−0.30	0.0174	0.2469	0.1801, 0.2288	0.0388	0.5456	0.1957, 0.4911

SE: Monte Carlo; SE (BS): bootstrap estimated standard error, SE (Adj_SW): square root of adjusted sandwich variance estimate, SE (pscl): standard errors obtained from the Hessian matrix.