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A Latent Space Diffusion Item Response Theory Model to Explore Conditional Dependence between Responses and Response Times

Author

Listed:
  • Inhan Kang

    (Yonsei University)

  • Minjeong Jeon

    (UNIVERSITY OF CALIFORNIA, LOS ANGELES)

  • Ivailo Partchev

    (Cito)

Abstract

Traditional measurement models assume that all item responses correlate with each other only through their underlying latent variables. This conditional independence assumption has been extended in joint models of responses and response times (RTs), implying that an item has the same item characteristics fors all respondents regardless of levels of latent ability/trait and speed. However, previous studies have shown that this assumption is violated in various types of tests and questionnaires and there are substantial interactions between respondents and items that cannot be captured by person- and item-effect parameters in psychometric models with the conditional independence assumption. To study the existence and potential cognitive sources of conditional dependence and utilize it to extract diagnostic information for respondents and items, we propose a diffusion item response theory model integrated with the latent space of variations in information processing rate of within-individual measurement processes. Respondents and items are mapped onto the latent space, and their distances represent conditional dependence and unexplained interactions. We provide three empirical applications to illustrate (1) how to use an estimated latent space to inform conditional dependence and its relation to person and item measures, (2) how to derive diagnostic feedback personalized for respondents, and (3) how to validate estimated results with an external measure. We also provide a simulation study to support that the proposed approach can accurately recover its parameters and detect conditional dependence underlying data.

Suggested Citation

  • Inhan Kang & Minjeong Jeon & Ivailo Partchev, 2023. "A Latent Space Diffusion Item Response Theory Model to Explore Conditional Dependence between Responses and Response Times," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 830-864, September.
    • Handle: RePEc:spr:psycho:v:88:y:2023:i:3:d:10.1007_s11336-023-09920-x
    DOI: 10.1007/s11336-023-09920-x
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    References listed on IDEAS

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    1. Wim van der Linden, 2007. "A Hierarchical Framework for Modeling Speed and Accuracy on Test Items," Psychometrika, Springer;The Psychometric Society, vol. 72(3), pages 287-308, September.
    2. Francis Tuerlinckx & Paul Boeck, 2005. "Two interpretations of the discrimination parameter," Psychometrika, Springer;The Psychometric Society, vol. 70(4), pages 629-650, December.
    3. Chen, Haiqin & De Boeck, Paul & Grady, Matthew & Yang, Chien-Lin & Waldschmidt, David, 2018. "Curvilinear dependency of response accuracy on response time in cognitive tests," Intelligence, Elsevier, vol. 69(C), pages 16-23.
    4. Lewandowski, Daniel & Kurowicka, Dorota & Joe, Harry, 2009. "Generating random correlation matrices based on vines and extended onion method," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1989-2001, October.
    5. Ick Hoon Jin & Minjeong Jeon, 2019. "A Doubly Latent Space Joint Model for Local Item and Person Dependence in the Analysis of Item Response Data," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 236-260, March.
    6. Maria Bolsinova & Paul Boeck & Jesper Tijmstra, 2017. "Modelling Conditional Dependence Between Response Time and Accuracy," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1126-1148, December.
    7. Molenaar, Dylan & Tuerlinckx, Francis & van der Maas, Han L. J., 2015. "Fitting Diffusion Item Response Theory Models for Responses and Response Times Using the R Package diffIRT," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 66(i04).
    8. Mark S. Handcock & Adrian E. Raftery & Jeremy M. Tantrum, 2007. "Model‐based clustering for social networks," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(2), pages 301-354, March.
    9. Minjeong Jeon & Ick Hoon Jin & Michael Schweinberger & Samuel Baugh, 2021. "Mapping Unobserved Item–Respondent Interactions: A Latent Space Item Response Model with Interaction Map," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 378-403, June.
    10. Wim Linden & Cees Glas, 2010. "Statistical Tests of Conditional Independence Between Responses and/or Response Times on Test Items," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 120-139, March.
    11. Kang, Inhan & De Boeck, Paul & Partchev, Ivailo, 2022. "A randomness perspective on intelligence processes," Intelligence, Elsevier, vol. 91(C).
    12. Chun Wang & Gongjun Xu & Zhuoran Shang, 2018. "A Two-Stage Approach to Differentiating Normal and Aberrant Behavior in Computer Based Testing," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 223-254, March.
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