Table 2.

Bias using maximum likelihood (ML), biweight (BI, B = 4), and Huber (HU, H = 1) estimation of the latent trait when there is back random responding in the data at a severity of 30%. (Nonconvergence rates higher than 30% displayed in parentheses)

			$\theta$
	K	J	−2	−1.5	−1	−0.5	0	0.5	1	1.5	2
ML	3	10	(58.2%)	(30.2%)	0.62	0.50	0.29	0.01	−0.26	(48.0%)	(65.7%)
		30	0.95	0.71	0.44	0.22	0.01	−0.19	−0.36	−0.55	−0.71
		50	0.82	0.57	0.35	0.16	−0.01	−0.21	−0.41	−0.58	−0.74
		70	0.71	0.50	0.30	0.12	−0.08	−0.29	−0.49	−0.66	−0.78
	5	10	(38.3%)	0.35	0.07	−0.13	−0.25	−0.37	−0.47	−0.70	(33.8%)
		30	0.72	0.53	0.33	0.13	−0.07	−0.23	−0.41	−0.55	−0.74
		50	0.63	0.45	0.26	0.10	−0.05	−0.18	−0.34	−0.52	−0.75
		70	0.62	0.48	0.34	0.24	0.11	−0.06	−0.21	−0.36	−0.58
	7	10	0.94	0.70	0.56	0.43	0.31	0.15	0.00	−0.30	−0.63
		30	0.60	0.37	0.21	0.10	−0.05	−0.19	−0.36	−0.50	−0.65
		50	0.58	0.44	0.31	0.17	0.02	−0.12	−0.26	−0.43	−0.60
		70	0.59	0.44	0.32	0.18	0.02	−0.12	−0.25	−0.39	−0.57
HU	3	10	−0.08	−0.07	0.16	0.25	0.19	0.14	0.11	−0.09	−0.36
		30	0.01	0.09	0.18	0.13	−0.01	−0.10	−0.12	−0.14	−0.07
		50	0.12	0.09	0.10	0.05	0.03	−0.03	−0.14	−0.19	−0.11
		70	0.06	0.07	0.04	0.07	0.01	−0.09	−0.15	−0.15	−0.09
	5	10	0.12	−0.01	−0.11	−0.14	−0.15	−0.12	−0.04	−0.13	−0.20
		30	0.20	0.25	0.18	0.05	−0.08	−0.16	−0.15	−0.05	−0.03
		50	0.13	0.14	0.08	0.01	−0.02	−0.04	−0.10	−0.16	−0.19
		70	0.09	0.11	0.09	0.09	0.09	0.00	−0.07	−0.11	−0.18
	7	10	0.08	0.13	0.20	0.19	0.20	0.15	0.05	−0.10	−0.28
		30	0.14	0.12	0.07	0.05	−0.01	−0.08	−0.15	−0.17	−0.13
		50	0.14	0.16	0.13	0.09	0.00	−0.05	−0.08	−0.16	−0.18
		70	0.15	0.16	0.14	0.06	−0.01	−0.06	−0.08	−0.14	−0.17
BI	3	10	−0.41	−0.18	0.14	0.25	0.17	0.15	0.15	−0.02	−0.26
		30	−0.14	−0.12	0.04	0.08	−0.03	−0.10	−0.05	−0.02	0.00
		50	−0.05	−0.05	0.01	0.00	0.03	0.01	−0.07	−0.06	0.01
		70	−0.08	−0.07	−0.05	0.04	0.02	−0.06	−0.04	−0.01	0.03
	5	10	0.00	−0.06	−0.15	−0.15	−0.13	−0.08	0.02	−0.09	−0.19
		30	0.04	0.11	0.11	0.03	−0.07	−0.11	−0.07	0.06	0.07
		50	0.00	0.01	0.01	0.00	−0.02	0.00	−0.03	−0.06	−0.04
		70	−0.04	−0.02	0.02	0.05	0.06	0.02	−0.02	−0.01	−0.02
	7	10	−0.11	−0.02	0.08	0.11	0.16	0.14	0.04	−0.07	−0.23
		30	0.03	0.03	0.02	0.02	0.00	−0.02	−0.06	−0.06	−0.01
		50	0.03	0.06	0.05	0.05	−0.01	−0.01	−0.01	−0.06	−0.05
		70	0.02	0.04	0.06	0.03	−0.02	−0.02	−0.03	−0.05	−0.05