Let Continuous Outcome Variables Remain Continuous

Table 3

Simulated relative mean square errors, relative intervals lengths, coverage probabilities, and absolute biases for the proposed and dichotomizing methods (using a truncated normal distribution for the explanatory variable and an extreme value distribution for the errors).

Sample size	𝜔 Cut off	.75	.9	1.1	1.2	1.3	1.4	1.5
		1.17^a	1.02	1.08	1.13	1.19	1.28	1.36
		1.11^b	1.03	1.03	1.06	1.10	1.25	1.22
	0.10	0.942^c	0.948	0.948	0.952	0.944	0.942	0.940
		0.951^d	0.951	0.950	0.952	0.949	0.951	0.951
		0.08^e	0.06	0.03	0.14	0.13	0.14	0.16
		0.10^f	0.11	0.15	0.23	0.30	0.39	0.39
		1.26	1.24	1.26	1.28	1.28	1.25	1.28
		1.24	1.13	1.13	1.14	1.14	1.15	1.17
1000	0.50	0.944	0.948	0.952	0.947	0.947	0.944	0.941
		0.948	0.951	0.949	0.949	0.947	0.950	0.949
		0.02	0.09	0.08	0.07	0.18	0.16	0.13
		0.03	0.06	0.12	0.16	0.20	0.16	0.14
		12.33	13.12	13.03	12.71	12.86	12.55	12.88
		3.62	3.59	3.61	3.62	3.64	3.68	3.71
	0.95	0.944	0.951	0.948	0.948	0.945	0.945	0.946
		0.952	0.948	0.95	0.949	0.949	0.951	0.952
		0.10	0.04	0.11	0.04	0.16	0.16	0.20
		1.26	1.05	1.56	1.36	1.43	1.80	1.94
		1.18	1.09	1.06	1.75	1.23	1.32	1.58
		1.11	1.03	1.03	1.06	1.11	1.16	1.23
	0.10	0.945	0.95	0.951	0.951	0.949	0.943	0.944
		0.953	0.953	0.953	0.950	0.949	0.951	0.950
		0.04	0.13	0.31	0.18	0.33	0.36	0.37
		0.21	0.08	0.37	0.50	0.62	0.69	0.96
		1.25	1.27	1.27	1.29	1.27	1.29	1.25
		1.14	1.13	1.13	1.14	1.15	1.16	1.17
500	0.50	0.944	0.948	0.949	0.947	0.948	0.944	0.935
		0.951	0.951	0.951	0.948	0.951	0.948	0.949
		0.13	0.22	0.35	0.37	0.35	0.30	0.44
		0.16	0.19	0.39	0.48	0.44	0.41	0.54
		13.11	14.02	14.02	13.5	13.54	13.80	14.32
		3.73	3.71	3.73	3.75	3.77	3.81	3.86
	0.95	0.944	0.95	0.951	0.950	0.947	0.944	0.944
		0.954	0.95	0.951	0.953	0.948	0.956	0.953
		0.15	0.10	0.24	0.38	0.32	0.33	0.43
		2.50	2.70	2.92	3.10	2.92	3.36	3.89
		1.28	1.11	1.12	1.19	1.33	1.54	1.76
		1.11	1.03	1.04	1.08	1.13	1.19	1.28
	0.10	0.947	0.951	0.950	0.947	0.950	0.950	0.942
		0.951	0.950	0.950	0.952	0.954	0.952	0.951
		0.40	0.34	0.37	0.64	0.69	0.58	0.81
		0.26	0.06	0.69	1.08	1.30	1.55	2.22
		1.32	1.30	1.27	1.33	1.31	1.33	1.31
		1.15	1.13	1.13	1.14	1.18	1.17	1.18
250	0.50	0.951	0.95	0.953	0.951	0.940	0.945	0.940
		0.949	0.951	0.952	0.948	0.948	0.950	0.948
		0.22	0.43	0.57	0.69	0.66	0.58	0.66
		0.38	0.53	0.64	0.89	0.91	0.82	0.91
		14.09	14.51	16.27	15.91	15.89	15.73	15.60
		3.86	3.87	3.93	3.92	3.98	4.04	4.11
	0.95	0.943	0.95	0.951	0.951	0.947	0.944	0.937
		0.953	0.95	0.953	0.956	0.953	0.956	0.952
		0.30	0.37	0.57	0.68	0.42	0.62	0.75
		4.98	5.52	6.547	5.91	6.17	6.88	7.72

a: Relative mean square errors, b: Relative intervals lengths, c: Coverage probability (proposed), d: Coverage probability (dichotomized), e: % bias (proposed), f: % bias (dichotomized).