Modeling the dependence between response and response time: A bifactor model approach

doi:10.3724/SP.J.1041.2024.00352

ISSN 0439-755X
CN 11-1911/B

Acta Psychologica Sinica ›› 2024, Vol. 56 ›› Issue (3): 352-362.doi: 10.3724/SP.J.1041.2024.00352

• Reports of Empirical Studies • Previous Articles Next Articles

Modeling the dependence between response and response time: A bifactor model approach

GUO Xiaojun¹, BAI Xiaoyun¹, LUO Zhaosheng²()

¹School of Education Science / Center for Education and Economic Research, Gannan Normal University, Ganzhou 341000, China
²School of psychology, Jiangxi Normal University, Nanchang 330022, China

Published:2024-03-25 Online:2023-12-13
Contact: LUO Zhaosheng E-mail:luozs@126.com

Abstract

GUO Xiaojun, BAI Xiaoyun, LUO Zhaosheng. (2024). Modeling the dependence between response and response time: A bifactor model approach. Acta Psychologica Sinica, 56(3), 352-362.

Item Parameters	Model		ρ_bβ		N = 500								N = 1000
					m = 30				m = 60				m = 30				m = 60
					MSE		Bias		MSE		Bias		MSE		Bias		MSE		Bias
a	HM		0		0.108		0.031		0.099		0.029		0.103		0.035		0.083		0.026
			0.4		0.123		0.021		0.106		0.041		0.091		0.023		0.085		0.034
			0.8		0.101		0.035		0.102		0.026		0.091		0.045		0.096		0.046
a		Bi-HM		0		0.028		?0.012		0.024		?0.016		0.013		?0.012		0.011		?0.013
				0.4		0.028		?0.015		0.024		?0.004		0.012		?0.013		0.011		?0.009
				0.8		0.026		0		0.025		?0.015		0.012		?0.004		0.011		0.002
d		HM		0		0.028		0.002		0.027		0.002		0.02		?0.003		0.018		0.003
				0.4		0.026		0.007		0.025		0.003		0.018		0.008		0.018		?0.003
				0.8		0.027		0.009		0.026		0.013		0.019		0		0.018		?0.002
		Bi-HM		0		0.02		?0.003		0.02		0.005		0.01		0		0.009		0.003
				0.4		0.021		0.012		0.019		0.002		0.01		0.009		0.009		?0.004
				0.8		0.02		0.005		0.021		0.013		0.01		0		0.009		0
β		HM		0		0.006		?0.001		0.006		0		0.003		?0.01		0.003		0.012
				0.4		0.007		0.009		0.006		0.002		0.002		?0.002		0.003		0.003
				0.8		0.006		?0.001		0.006		0.01		0.003		?0.001		0.003		0.003
		Bi-HM		0		0.006		?0.001		0.006		0		0.003		?0.009		0.003		0.012
				0.4		0.007		0.009		0.006		0.002		0.003		?0.002		0.003		0.003
				0.8		0.006		?0.001		0.006		0.01		0.003		?0.001		0.003		0.003
α		HM		0		0.094		0.189		0.089		0.18		0.087		0.182		0.094		0.192
				0.4		0.085		0.175		0.088		0.182		0.089		0.182		0.099		0.196
				0.8		0.096		0.187		0.092		0.188		0.09		0.185		0.093		0.189
		Bi-HM		0		0.001		?0.003		0.001		?0.004		0.001		?0.004		0.001		?0.002
				0.4		0.002		?0.004		0.001		?0.004		0.001		?0.002		0.001		?0.003
				0.8		0.002		?0.005		0.001		?0.004		0.001		?0.002		0.001		?0.002
λ₁		Bi-HM		0		0.02		0.003		0.019		?0.008		0.009		?0.008		0.01		?0.006
				0.4		0.021		?0.012		0.02		?0.004		0.01		0.001		0.01		?0.008
				0.8		0.019		0.003		0.021		?0.008		0.01		0.007		0.009		?0.002
λ₂		Bi-HM		0		0.006		0.001		0.005		0.007		0.003		0.005		0.002		?0.001
				0.4		0.006		?0.002		0.005		0.004		0.003		?0.006		0.003		0.005
				0.8		0.006		?0.001		0.005		0.003		0.003		?0.003		0.003		?0.005

Item Parameters	Model		ρ_bβ		N = 500								N = 1000
					m = 30				m = 60				m = 30				m = 60
					MSE		Bias		MSE		Bias		MSE		Bias		MSE		Bias
a	HM		0		0.108		0.031		0.099		0.029		0.103		0.035		0.083		0.026
			0.4		0.123		0.021		0.106		0.041		0.091		0.023		0.085		0.034
			0.8		0.101		0.035		0.102		0.026		0.091		0.045		0.096		0.046
a		Bi-HM		0		0.028		?0.012		0.024		?0.016		0.013		?0.012		0.011		?0.013
				0.4		0.028		?0.015		0.024		?0.004		0.012		?0.013		0.011		?0.009
				0.8		0.026		0		0.025		?0.015		0.012		?0.004		0.011		0.002
d		HM		0		0.028		0.002		0.027		0.002		0.02		?0.003		0.018		0.003
				0.4		0.026		0.007		0.025		0.003		0.018		0.008		0.018		?0.003
				0.8		0.027		0.009		0.026		0.013		0.019		0		0.018		?0.002
		Bi-HM		0		0.02		?0.003		0.02		0.005		0.01		0		0.009		0.003
				0.4		0.021		0.012		0.019		0.002		0.01		0.009		0.009		?0.004
				0.8		0.02		0.005		0.021		0.013		0.01		0		0.009		0
β		HM		0		0.006		?0.001		0.006		0		0.003		?0.01		0.003		0.012
				0.4		0.007		0.009		0.006		0.002		0.002		?0.002		0.003		0.003
				0.8		0.006		?0.001		0.006		0.01		0.003		?0.001		0.003		0.003
		Bi-HM		0		0.006		?0.001		0.006		0		0.003		?0.009		0.003		0.012
				0.4		0.007		0.009		0.006		0.002		0.003		?0.002		0.003		0.003
				0.8		0.006		?0.001		0.006		0.01		0.003		?0.001		0.003		0.003
α		HM		0		0.094		0.189		0.089		0.18		0.087		0.182		0.094		0.192
				0.4		0.085		0.175		0.088		0.182		0.089		0.182		0.099		0.196
				0.8		0.096		0.187		0.092		0.188		0.09		0.185		0.093		0.189
		Bi-HM		0		0.001		?0.003		0.001		?0.004		0.001		?0.004		0.001		?0.002
				0.4		0.002		?0.004		0.001		?0.004		0.001		?0.002		0.001		?0.003
				0.8		0.002		?0.005		0.001		?0.004		0.001		?0.002		0.001		?0.002
λ₁		Bi-HM		0		0.02		0.003		0.019		?0.008		0.009		?0.008		0.01		?0.006
				0.4		0.021		?0.012		0.02		?0.004		0.01		0.001		0.01		?0.008
				0.8		0.019		0.003		0.021		?0.008		0.01		0.007		0.009		?0.002
λ₂		Bi-HM		0		0.006		0.001		0.005		0.007		0.003		0.005		0.002		?0.001
				0.4		0.006		?0.002		0.005		0.004		0.003		?0.006		0.003		0.005
				0.8		0.006		?0.001		0.005		0.003		0.003		?0.003		0.003		?0.005

Person parameters	Model	ρ_bβ	N = 500				N = 1000
			m = 30		m = 60		m = 30		m = 60
			MSE	Bias	MSE	Bias	MSE	Bias	MSE	Bias
θ	HM	0	0.252	0.001	0.2	0.001	0.26	0.001	0.194	0.006
		0.4	0.283	0.009	0.206	0.002	0.259	0.006	0.194	?0.003
		0.8	0.263	0.004	0.202	0.011	0.253	?0.001	0.204	0
	Bi-HM	0	0.148	0.001	0.09	0.002	0.151	0.001	0.086	0.005
		0.4	0.157	0.009	0.087	0.002	0.151	0.006	0.087	?0.004
		0.8	0.152	0.004	0.088	0.011	0.151	0	0.084	0
τ	HM	0	0.158	?0.001	0.141	0.001	0.157	?0.011	0.135	0.008
		0.4	0.136	0.007	0.135	0.003	0.166	0	0.144	0.004
		0.8	0.156	0.004	0.122	0.007	0.122	?0.001	0.114	0.004
	Bi-HM	0	0.035	?0.001	0.02	0.002	0.035	?0.011	0.017	0.008
		0.4	0.038	0.007	0.019	0.003	0.034	0	0.017	0.003
		0.8	0.035	0.004	0.019	0.007	0.032	?0.001	0.017	0.004
η	Bi-HM	0	0.05	0.002	0.028	0.005	0.05	?0.002	0.025	?0.009
		0.4	0.057	?0.007	0.028	?0.001	0.051	0.006	0.024	0.003
		0.8	0.051	0.004	0.026	?0.008	0.051	?0.001	0.025	?0.002

Person parameters	Model	ρ_bβ	N = 500				N = 1000
			m = 30		m = 60		m = 30		m = 60
			MSE	Bias	MSE	Bias	MSE	Bias	MSE	Bias
θ	HM	0	0.252	0.001	0.2	0.001	0.26	0.001	0.194	0.006
		0.4	0.283	0.009	0.206	0.002	0.259	0.006	0.194	?0.003
		0.8	0.263	0.004	0.202	0.011	0.253	?0.001	0.204	0
	Bi-HM	0	0.148	0.001	0.09	0.002	0.151	0.001	0.086	0.005
		0.4	0.157	0.009	0.087	0.002	0.151	0.006	0.087	?0.004
		0.8	0.152	0.004	0.088	0.011	0.151	0	0.084	0
τ	HM	0	0.158	?0.001	0.141	0.001	0.157	?0.011	0.135	0.008
		0.4	0.136	0.007	0.135	0.003	0.166	0	0.144	0.004
		0.8	0.156	0.004	0.122	0.007	0.122	?0.001	0.114	0.004
	Bi-HM	0	0.035	?0.001	0.02	0.002	0.035	?0.011	0.017	0.008
		0.4	0.038	0.007	0.019	0.003	0.034	0	0.017	0.003
		0.8	0.035	0.004	0.019	0.007	0.032	?0.001	0.017	0.004
η	Bi-HM	0	0.05	0.002	0.028	0.005	0.05	?0.002	0.025	?0.009
		0.4	0.057	?0.007	0.028	?0.001	0.051	0.006	0.024	0.003
		0.8	0.051	0.004	0.026	?0.008	0.051	?0.001	0.025	?0.002

Model	NP	LL	AIC	BIC	SABIC
HM	241	?28652.849	57787.698	58765.383	58000.598
Fix-Bi-HM	241	?28740.198	57962.396	58940.081	58175.296
Bi-HM	361	?27862.329	56446.657	57911.156	56765.566

Modeling the dependence between response and response time: A bifactor model approach

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