Development of New Robust Optimal Score Function for the Weibull Distributed Error Term in Multilevel Models

Table 1

Bias and MSE of using Weibull, Wilcoxon, and REML methods when  = 3..

		REML		Weibull		Wilcoxon		Precision
N2	N1	Bias	MSE	Bias	MSE	Bias	MSE	Weib/REML	Weib/Wil	Wil/REML
5	5	2.416	4.867	2.093	3.866	2.207	4.622	0.794	0.836	0.95
	10	2.406	5.857	2.059	4.355	2.156	5.064	0.744	0.86	0.865
	20	2.422	9.241	2.03	6.884	2.129	7.78	0.745	0.885	0.842
	40	2.37	15.418	1.978	11.318	2.071	12.617	0.734	0.897	0.818
10	5	2.541	3.316	2.179	2.519	2.238	2.858	0.76	0.882	0.862
	10	2.517	3.953	2.163	3.018	2.221	3.318	0.763	0.91	0.839
	20	2.552	5.817	2.199	4.487	2.252	4.75	0.771	0.945	0.817
	40	2.57	9.88	2.209	7.672	2.258	8.038	0.777	0.954	0.814
20	5	2.623	2.681	2.286	2.075	2.321	2.236	0.774	0.928	0.834
	10	2.565	2.899	2.211	2.274	2.253	2.366	0.785	0.961	0.816
	20	2.597	3.975	2.258	3.13	2.283	3.233	0.787	0.968	0.813
	40	2.601	5.847	2.261	4.578	2.283	4.699	0.783	0.974	0.804
40	5	2.607	2.263	2.267	1.769	2.291	1.839	0.782	0.962	0.813
	10	2.687	2.65	2.358	2.096	2.372	2.15	0.791	0.975	0.811
	20	2.594	2.906	2.265	2.287	2.28	2.327	0.787	0.983	0.801
	40	2.644	4.034	2.313	3.211	2.33	3.241	0.796	0.991	0.804