IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v84y2019i3d10.1007_s11336-019-09668-3.html
   My bibliography  Save this article

Characterizing the Manifest Probability Distributions of Three Latent Trait Models for Accuracy and Response Time

Author

Listed:
  • M. Marsman

    (University of Amsterdam)

  • H. Sigurdardóttir

    (Tilburg University)

  • M. Bolsinova

    (ACTNext)

  • G. Maris

    (University of Amsterdam
    ACTNext)

Abstract

In this paper we study the statistical relations between three latent trait models for accuracies and response times: the hierarchical model (HM) of van der Linden (Psychometrika 72(3):287–308, 2007), the signed residual time model (SM) proposed by Maris and van der Maas (Psychometrika 77(4):615–633, 2012), and the drift diffusion model (DM) as proposed by Tuerlinckx and De Boeck (Psychometrika 70(4):629–650, 2005). One important distinction between these models is that the HM and the DM either assume or imply that accuracies and response times are independent given the latent trait variables, while the SM does not. In this paper we investigate the impact of this conditional independence property—or a lack thereof—on the manifest probability distribution for accuracies and response times. We will find that the manifest distributions of the latent trait models share several important features, such as the dependency between accuracy and response time, but we also find important differences, such as in what function of response time is being modeled. Our method for characterizing the manifest probability distributions is related to the Dutch identity (Holland in Psychometrika 55(6):5–18, 1990).

Suggested Citation

  • M. Marsman & H. Sigurdardóttir & M. Bolsinova & G. Maris, 2019. "Characterizing the Manifest Probability Distributions of Three Latent Trait Models for Accuracy and Response Time," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 870-891, September.
    • Handle: RePEc:spr:psycho:v:84:y:2019:i:3:d:10.1007_s11336-019-09668-3
    DOI: 10.1007/s11336-019-09668-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-019-09668-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11336-019-09668-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fox, Jean-Paul & Entink, Rinke Klein & van der Linden, Wilm, 2007. "Modeling of Responses and Response Times with the Package cirt," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i07).
    2. 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.
    3. Francis Tuerlinckx & Paul Boeck, 2005. "Two interpretations of the discrimination parameter," Psychometrika, Springer;The Psychometric Society, vol. 70(4), pages 629-650, December.
    4. Noel Cressie & Paul Holland, 1983. "Characterizing the manifest probabilities of latent trait models," Psychometrika, Springer;The Psychometric Society, vol. 48(1), pages 129-141, March.
    5. Edward Ip, 2002. "Locally dependent latent trait model and the dutch identity revisited," Psychometrika, Springer;The Psychometric Society, vol. 67(3), pages 367-386, September.
    6. Hua-Hua Chang, 1996. "The asymptotic posterior normality of the latent trait for polytomous IRT models," Psychometrika, Springer;The Psychometric Society, vol. 61(3), pages 445-463, September.
    7. Yunxiao Chen & Xiaoou Li & Jingchen Liu & Zhiliang Ying, 2018. "Robust Measurement via A Fused Latent and Graphical Item Response Theory Model," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 538-562, September.
    8. Hua-Hua Chang & William Stout, 1993. "The asymptotic posterior normality of the latent trait in an IRT model," Psychometrika, Springer;The Psychometric Society, vol. 58(1), pages 37-52, March.
    9. Paul Holland, 1990. "The Dutch Identity: A new tool for the study of item response models," Psychometrika, Springer;The Psychometric Society, vol. 55(1), pages 5-18, March.
    10. Sacha Epskamp & Joost Kruis & Maarten Marsman, 2017. "Estimating psychopathological networks: Be careful what you wish for," PLOS ONE, Public Library of Science, vol. 12(6), pages 1-13, June.
    11. David Hessen, 2012. "Fitting and Testing Conditional Multinormal Partial Credit Models," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 693-709, October.
    12. 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.
    13. Gunter Maris & Han Maas, 2012. "Speed-Accuracy Response Models: Scoring Rules based on Response Time and Accuracy," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 615-633, October.
    14. Chen, Yunxiao & Li, Xiaoou & Liu, Jingchen & Ying, Zhiliang, 2018. "Robust measurement via a fused latent and graphical item response theory model," LSE Research Online Documents on Economics 103181, London School of Economics and Political Science, LSE Library.
    15. Jinming Zhang & William Stout, 1997. "On Holland's Dutch identity conjecture," Psychometrika, Springer;The Psychometric Society, vol. 62(3), pages 375-392, September.
    16. Carolyn Anderson & Hsiu-Ting Yu, 2007. "Log-Multiplicative Association Models as Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 72(1), pages 5-23, March.
    17. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Udo Boehm & Maarten Marsman & Han L. J. Maas & Gunter Maris, 2021. "An Attention-Based Diffusion Model for Psychometric Analyses," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 938-972, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Inhan Kang & Paul Boeck & Roger Ratcliff, 2022. "Modeling Conditional Dependence of Response Accuracy and Response Time with the Diffusion Item Response Theory Model," Psychometrika, Springer;The Psychometric Society, vol. 87(2), pages 725-748, June.
    2. Dylan Molenaar & Paul Boeck, 2018. "Response Mixture Modeling: Accounting for Heterogeneity in Item Characteristics across Response Times," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 279-297, June.
    3. 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.
    4. Zhang, Siliang & Chen, Yunxiao, 2024. "A note on Ising network analysis with missing data," LSE Research Online Documents on Economics 123984, London School of Economics and Political Science, LSE Library.
    5. Kang, Inhan & De Boeck, Paul & Partchev, Ivailo, 2022. "A randomness perspective on intelligence processes," Intelligence, Elsevier, vol. 91(C).
    6. Mia J. K. Kornely & Maria Kateri, 2022. "Asymptotic Posterior Normality of Multivariate Latent Traits in an IRT Model," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 1146-1172, September.
    7. David J. Hessen, 2023. "Fitting and Testing Log-Linear Subpopulation Models with Known Support," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 917-939, September.
    8. Shaw, Amy & Elizondo, Fabian & Wadlington, Patrick L., 2020. "Reasoning, fast and slow: How noncognitive factors may alter the ability-speed relationship," Intelligence, Elsevier, vol. 83(C).
    9. Peter W. Rijn & Usama S. Ali, 2018. "A Generalized Speed–Accuracy Response Model for Dichotomous Items," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 109-131, March.
    10. Yunxiao Chen & Xiaoou Li & Jingchen Liu & Zhiliang Ying, 2018. "Robust Measurement via A Fused Latent and Graphical Item Response Theory Model," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 538-562, September.
    11. Sandip Sinharay & Peter W. van Rijn, 2020. "Assessing Fit of the Lognormal Model for Response Times," Journal of Educational and Behavioral Statistics, , vol. 45(5), pages 534-568, October.
    12. Jinxin Guo & Xin Xu & Zhiliang Ying & Susu Zhang, 2022. "Modeling Not-Reached Items in Timed Tests: A Response Time Censoring Approach," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 835-867, September.
    13. Minjeong Jeon & Paul Boeck & Jevan Luo & Xiangrui Li & Zhong-Lin Lu, 2021. "Modeling Within-Item Dependencies in Parallel Data on Test Responses and Brain Activation," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 239-271, March.
    14. Hua-Hua Chang, 2015. "Psychometrics Behind Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 1-20, March.
    15. Maria Bolsinova & Jesper Tijmstra, 2016. "Posterior Predictive Checks for Conditional Independence Between Response Time and Accuracy," Journal of Educational and Behavioral Statistics, , vol. 41(2), pages 123-145, April.
    16. Inhan Kang & Dylan Molenaar & Roger Ratcliff, 2023. "A Modeling Framework to Examine Psychological Processes Underlying Ordinal Responses and Response Times of Psychometric Data," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 940-974, September.
    17. Maria Bolsinova & Jesper Tijmstra, 2019. "Modeling Differences Between Response Times of Correct and Incorrect Responses," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 1018-1046, December.
    18. Hyeon-Ah Kang & Yi Zheng & Hua-Hua Chang, 2020. "Online Calibration of a Joint Model of Item Responses and Response Times in Computerized Adaptive Testing," Journal of Educational and Behavioral Statistics, , vol. 45(2), pages 175-208, April.
    19. Gunter Maris & Timo Bechger & Ernesto Martin, 2015. "A Gibbs Sampler for the (Extended) Marginal Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 859-879, December.
    20. Chen, Yunxiao & Li, Xiaoou & Liu, Jingchen & Ying, Zhiliang, 2018. "Robust measurement via a fused latent and graphical item response theory model," LSE Research Online Documents on Economics 103181, London School of Economics and Political Science, LSE Library.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:psycho:v:84:y:2019:i:3:d:10.1007_s11336-019-09668-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.