A semi-parametric within-subject mixture approach to the analyses of responses and response times

Dylan Molenaar*, Maria Bolsinova, Jeroen K. Vermunt

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

In item response theory, modelling the item response times in addition to the item responses may improve the detection of possible between- and within-subject differences in the process that resulted in the responses. For instance, if respondents rely on rapid guessing on some items but not on all, the joint distribution of the responses and response times will be a multivariate within-subject mixture distribution. Suitable parametric methods to detect these within-subject differences have been proposed. In these approaches, a distribution needs to be assumed for the within-class response times. In this paper, it is demonstrated that these parametric within-subject approaches may produce false positives and biased parameter estimates if the assumption concerning the response time distribution is violated. A semi-parametric approach is proposed which resorts to categorized response times. This approach is shown to hardly produce false positives and parameter bias. In addition, the semi-parametric approach results in approximately the same power as the parametric approach.

Original languageEnglish
Pages (from-to)205-228
JournalBritish Journal of Mathematical and Statistical Psychology
Volume71
Issue number2
DOIs
Publication statusPublished - 2018

Keywords

  • item response theory
  • response times
  • mixture modelling
  • PROPORTIONAL HAZARDS MODEL
  • HIERARCHICAL FRAMEWORK
  • SLOW INTELLIGENCE
  • ACCURACY
  • SPEED
  • TESTS
  • DICHOTOMIZATION
  • INFORMATION
  • PERSONALITY
  • SPEEDEDNESS

Cite this

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title = "A semi-parametric within-subject mixture approach to the analyses of responses and response times",
abstract = "In item response theory, modelling the item response times in addition to the item responses may improve the detection of possible between- and within-subject differences in the process that resulted in the responses. For instance, if respondents rely on rapid guessing on some items but not on all, the joint distribution of the responses and response times will be a multivariate within-subject mixture distribution. Suitable parametric methods to detect these within-subject differences have been proposed. In these approaches, a distribution needs to be assumed for the within-class response times. In this paper, it is demonstrated that these parametric within-subject approaches may produce false positives and biased parameter estimates if the assumption concerning the response time distribution is violated. A semi-parametric approach is proposed which resorts to categorized response times. This approach is shown to hardly produce false positives and parameter bias. In addition, the semi-parametric approach results in approximately the same power as the parametric approach.",
keywords = "item response theory, response times, mixture modelling, PROPORTIONAL HAZARDS MODEL, HIERARCHICAL FRAMEWORK, SLOW INTELLIGENCE, ACCURACY, SPEED, TESTS, DICHOTOMIZATION, INFORMATION, PERSONALITY, SPEEDEDNESS",
author = "Dylan Molenaar and Maria Bolsinova and Vermunt, {Jeroen K.}",
year = "2018",
doi = "10.1111/bmsp.12117",
language = "English",
volume = "71",
pages = "205--228",
journal = "British Journal of Mathematical and Statistical Psychology",
issn = "0007-1102",
publisher = "Wiley",
number = "2",

}

A semi-parametric within-subject mixture approach to the analyses of responses and response times. / Molenaar, Dylan; Bolsinova, Maria; Vermunt, Jeroen K.

In: British Journal of Mathematical and Statistical Psychology, Vol. 71, No. 2, 2018, p. 205-228.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - A semi-parametric within-subject mixture approach to the analyses of responses and response times

AU - Molenaar, Dylan

AU - Bolsinova, Maria

AU - Vermunt, Jeroen K.

PY - 2018

Y1 - 2018

N2 - In item response theory, modelling the item response times in addition to the item responses may improve the detection of possible between- and within-subject differences in the process that resulted in the responses. For instance, if respondents rely on rapid guessing on some items but not on all, the joint distribution of the responses and response times will be a multivariate within-subject mixture distribution. Suitable parametric methods to detect these within-subject differences have been proposed. In these approaches, a distribution needs to be assumed for the within-class response times. In this paper, it is demonstrated that these parametric within-subject approaches may produce false positives and biased parameter estimates if the assumption concerning the response time distribution is violated. A semi-parametric approach is proposed which resorts to categorized response times. This approach is shown to hardly produce false positives and parameter bias. In addition, the semi-parametric approach results in approximately the same power as the parametric approach.

AB - In item response theory, modelling the item response times in addition to the item responses may improve the detection of possible between- and within-subject differences in the process that resulted in the responses. For instance, if respondents rely on rapid guessing on some items but not on all, the joint distribution of the responses and response times will be a multivariate within-subject mixture distribution. Suitable parametric methods to detect these within-subject differences have been proposed. In these approaches, a distribution needs to be assumed for the within-class response times. In this paper, it is demonstrated that these parametric within-subject approaches may produce false positives and biased parameter estimates if the assumption concerning the response time distribution is violated. A semi-parametric approach is proposed which resorts to categorized response times. This approach is shown to hardly produce false positives and parameter bias. In addition, the semi-parametric approach results in approximately the same power as the parametric approach.

KW - item response theory

KW - response times

KW - mixture modelling

KW - PROPORTIONAL HAZARDS MODEL

KW - HIERARCHICAL FRAMEWORK

KW - SLOW INTELLIGENCE

KW - ACCURACY

KW - SPEED

KW - TESTS

KW - DICHOTOMIZATION

KW - INFORMATION

KW - PERSONALITY

KW - SPEEDEDNESS

U2 - 10.1111/bmsp.12117

DO - 10.1111/bmsp.12117

M3 - Article

VL - 71

SP - 205

EP - 228

JO - British Journal of Mathematical and Statistical Psychology

JF - British Journal of Mathematical and Statistical Psychology

SN - 0007-1102

IS - 2

ER -