A residual-based weighted robust item parameter estimation method for aberrant responses

doi:10.3724/SP.J.1041.2026.2139

Abstract

Cite this article

GAO Xuliang, LI Tingting, WANG Fang. (2026). A residual-based weighted robust item parameter estimation method for aberrant responses. Acta Psychologica Sinica, 58(10), 2139-2152.

share this article

/ / Recommend

Add to citation manager EndNote|Ris|BibTeX

URL: https://journal.psych.ac.cn/acps/EN/10.3724/SP.J.1041.2026.2139

https://journal.psych.ac.cn/acps/EN/Y2026/V58/I10/2139

Figures/Tables 2

Table 1 Comparison of estimation accuracy across methods under careless responding conditions

J	Aberrant respondents	Aberrant items	Estimation method	Bias		RMSE
J	Aberrant respondents	Aberrant items	Estimation method	Bias a	Bias b	RMSE a	RMSE b
30	0%	0%	Traditional estimation	0.007	-0.012	0.094	0.137
	20%	20%	Traditional estimation	0.278	-0.249	0.363	0.404
			${l}_{z}^{*}$ weighted estimation	0.223	-0.259	0.303	0.409
			RRW weighted estimation	-0.011	-0.251	0.139	0.335
	20%	30%	Traditional estimation	0.313	-0.402	0.426	0.497
			${l}_{z}^{*}$ weighted estimation	0.263	-0.395	0.373	0.508
			RRW weighted estimation	0.000	-0.338	0.144	0.396
	30%	20%	Traditional estimation	0.404	-0.465	0.507	0.766
			${l}_{z}^{*}$ weighted estimation	0.375	-0.495	0.472	0.804
			RRW weighted estimation	0.154	-0.481	0.250	0.615
	30%	30%	Traditional estimation	0.477	-0.737	0.614	0.953
			${l}_{z}^{*}$ weighted estimation	0.467	-0.761	0.607	1.009
			RRW weighted estimation	0.237	-0.686	0.341	0.799
50	20%	20%	Traditional estimation	0.262	-0.269	0.345	0.412
			${l}_{z}^{*}$ weighted estimation	0.211	-0.271	0.287	0.408
			RRW weighted estimation	-0.003	-0.242	0.129	0.325
	20%	30%	Traditional estimation	0.310	-0.407	0.422	0.509
			${l}_{z}^{*}$ weighted estimation	0.267	-0.393	0.375	0.505
			RRW weighted estimation	0.033	-0.333	0.145	0.391
	30%	20%	Traditional estimation	0.379	-0.44	0.475	0.672
			${l}_{z}^{*}$ weighted estimation	0.355	-0.456	0.446	0.683
			RRW weighted estimation	0.157	-0.444	0.235	0.549
	30%	30%	Traditional estimation	0.486	-0.720	0.613	0.918
			${l}_{z}^{*}$ weighted estimation	0.470	-0.732	0.601	0.953
			RRW weighted estimation	0.254	-0.652	0.349	0.749

Table 1 Comparison of estimation accuracy across methods under careless responding conditions

J	Aberrant respondents	Aberrant items	Estimation method	Bias		RMSE
J	Aberrant respondents	Aberrant items	Estimation method	Bias a	Bias b	RMSE a	RMSE b
30	0%	0%	Traditional estimation	0.007	-0.012	0.094	0.137
	20%	20%	Traditional estimation	0.278	-0.249	0.363	0.404
			${l}_{z}^{*}$ weighted estimation	0.223	-0.259	0.303	0.409
			RRW weighted estimation	-0.011	-0.251	0.139	0.335
	20%	30%	Traditional estimation	0.313	-0.402	0.426	0.497
			${l}_{z}^{*}$ weighted estimation	0.263	-0.395	0.373	0.508
			RRW weighted estimation	0.000	-0.338	0.144	0.396
	30%	20%	Traditional estimation	0.404	-0.465	0.507	0.766
			${l}_{z}^{*}$ weighted estimation	0.375	-0.495	0.472	0.804
			RRW weighted estimation	0.154	-0.481	0.250	0.615
	30%	30%	Traditional estimation	0.477	-0.737	0.614	0.953
			${l}_{z}^{*}$ weighted estimation	0.467	-0.761	0.607	1.009
			RRW weighted estimation	0.237	-0.686	0.341	0.799
50	20%	20%	Traditional estimation	0.262	-0.269	0.345	0.412
			${l}_{z}^{*}$ weighted estimation	0.211	-0.271	0.287	0.408
			RRW weighted estimation	-0.003	-0.242	0.129	0.325
	20%	30%	Traditional estimation	0.310	-0.407	0.422	0.509
			${l}_{z}^{*}$ weighted estimation	0.267	-0.393	0.375	0.505
			RRW weighted estimation	0.033	-0.333	0.145	0.391
	30%	20%	Traditional estimation	0.379	-0.44	0.475	0.672
			${l}_{z}^{*}$ weighted estimation	0.355	-0.456	0.446	0.683
			RRW weighted estimation	0.157	-0.444	0.235	0.549
	30%	30%	Traditional estimation	0.486	-0.720	0.613	0.918
			${l}_{z}^{*}$ weighted estimation	0.470	-0.732	0.601	0.953
			RRW weighted estimation	0.254	-0.652	0.349	0.749

Table 2 Comparison of estimation accuracy across methods under cheating conditions

J	Aberrant respondents	Aberrant items	Estimation method	Bias		RMSE
J	Aberrant respondents	Aberrant items	Estimation method	Bias a	Bias b	RMSE a	RMSE b
30	0%	0%	Traditional estimation	0.007	0.012	0.094	0.137
	20%	20%	Traditional estimation	0.269	0.252	0.357	0.400
			${l}_{z}^{*}$ weighted estimation	0.205	0.250	0.284	0.399
			RRW weighted estimation	-0.014	0.255	0.141	0.342
	20%	30%	Traditional estimation	0.290	0.408	0.391	0.502
			${l}_{z}^{*}$ weighted estimation	0.245	0.397	0.346	0.509
			RRW weighted estimation	-0.007	0.341	0.154	0.400
	30%	20%	Traditional estimation	0.404	0.474	0.503	0.751
			${l}_{z}^{*}$ weighted estimation	0.373	0.493	0.465	0.765
			RRW weighted estimation	0.169	0.498	0.264	0.640
	30%	30%	Traditional estimation	0.433	0.710	0.553	0.863
			${l}_{z}^{*}$ weighted estimation	0.423	0.713	0.548	0.899
			RRW weighted estimation	0.206	0.667	0.302	0.745
50	20%	20%	Traditional estimation	0.275	0.254	0.360	0.426
			${l}_{z}^{*}$ weighted estimation	0.209	0.251	0.284	0.415
			RRW weighted estimation	0.027	0.229	0.146	0.325
	20%	30%	Traditional estimation	0.298	0.406	0.417	0.504
			${l}_{z}^{*}$ weighted estimation	0.253	0.389	0.366	0.500
			RRW weighted estimation	0.032	0.320	0.151	0.382
	30%	20%	Traditional estimation	0.396	0.470	0.492	0.765
			${l}_{z}^{*}$ weighted estimation	0.366	0.485	0.457	0.798
			RRW weighted estimation	0.178	0.488	0.269	0.649
	30%	30%	Traditional estimation	0.461	0.732	0.591	0.950
			${l}_{z}^{*}$ weighted estimation	0.440	0.724	0.572	0.944
			RRW weighted estimation	0.240	0.651	0.341	0.773

Table 2 Comparison of estimation accuracy across methods under cheating conditions

J	Aberrant respondents	Aberrant items	Estimation method	Bias		RMSE
J	Aberrant respondents	Aberrant items	Estimation method	Bias a	Bias b	RMSE a	RMSE b
30	0%	0%	Traditional estimation	0.007	0.012	0.094	0.137
	20%	20%	Traditional estimation	0.269	0.252	0.357	0.400
			${l}_{z}^{*}$ weighted estimation	0.205	0.250	0.284	0.399
			RRW weighted estimation	-0.014	0.255	0.141	0.342
	20%	30%	Traditional estimation	0.290	0.408	0.391	0.502
			${l}_{z}^{*}$ weighted estimation	0.245	0.397	0.346	0.509
			RRW weighted estimation	-0.007	0.341	0.154	0.400
	30%	20%	Traditional estimation	0.404	0.474	0.503	0.751
			${l}_{z}^{*}$ weighted estimation	0.373	0.493	0.465	0.765
			RRW weighted estimation	0.169	0.498	0.264	0.640
	30%	30%	Traditional estimation	0.433	0.710	0.553	0.863
			${l}_{z}^{*}$ weighted estimation	0.423	0.713	0.548	0.899
			RRW weighted estimation	0.206	0.667	0.302	0.745
50	20%	20%	Traditional estimation	0.275	0.254	0.360	0.426
			${l}_{z}^{*}$ weighted estimation	0.209	0.251	0.284	0.415
			RRW weighted estimation	0.027	0.229	0.146	0.325
	20%	30%	Traditional estimation	0.298	0.406	0.417	0.504
			${l}_{z}^{*}$ weighted estimation	0.253	0.389	0.366	0.500
			RRW weighted estimation	0.032	0.320	0.151	0.382
	30%	20%	Traditional estimation	0.396	0.470	0.492	0.765
			${l}_{z}^{*}$ weighted estimation	0.366	0.485	0.457	0.798
			RRW weighted estimation	0.178	0.488	0.269	0.649
	30%	30%	Traditional estimation	0.461	0.732	0.591	0.950
			${l}_{z}^{*}$ weighted estimation	0.440	0.724	0.572	0.944
			RRW weighted estimation	0.240	0.651	0.341	0.773

References

Metrics

Viewed

Full text

Abstract

Comments

Abstract
Figures/Tables
References
Related Articles
Recommended Articles
Metrics
Comments

TOP