IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v87y2022i2d10.1007_s11336-021-09832-8.html
   My bibliography  Save this article

Semiparametric Factor Analysis for Item-Level Response Time Data

Author

Listed:
  • Yang Liu

    (University of Maryland)

  • Weimeng Wang

    (University of Maryland)

Abstract

Item-level response time (RT) data can be conveniently collected from computer-based test/survey delivery platforms and have been demonstrated to bear a close relation to a miscellany of cognitive processes and test-taking behaviors. Individual differences in general processing speed can be inferred from item-level RT data using factor analysis. Conventional linear normal factor models make strong parametric assumptions, which sacrifices modeling flexibility for interpretability, and thus are not ideal for describing complex associations between observed RT and the latent speed. In this paper, we propose a semiparametric factor model with minimal parametric assumptions. Specifically, we adopt a functional analysis of variance representation for the log conditional densities of the manifest variables, in which the main effect and interaction functions are approximated by cubic splines. Penalized maximum likelihood estimation of the spline coefficients can be performed by an Expectation-Maximization algorithm, and the penalty weight can be empirically determined by cross-validation. In a simulation study, we compare the semiparametric model with incorrectly and correctly specified parametric factor models with regard to the recovery of data generating mechanism. A real data example is also presented to demonstrate the advantages of the proposed method.

Suggested Citation

  • Yang Liu & Weimeng Wang, 2022. "Semiparametric Factor Analysis for Item-Level Response Time Data," Psychometrika, Springer;The Psychometric Society, vol. 87(2), pages 666-692, June.
  • Handle: RePEc:spr:psycho:v:87:y:2022:i:2:d:10.1007_s11336-021-09832-8
    DOI: 10.1007/s11336-021-09832-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-021-09832-8
    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/s11336-021-09832-8?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. I. D. Currie & M. Durban & P. H. C. Eilers, 2006. "Generalized linear array models with applications to multidimensional smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 259-280, April.
    2. Murray Aitkin, 1999. "A General Maximum Likelihood Analysis of Variance Components in Generalized Linear Models," Biometrics, The International Biometric Society, vol. 55(1), pages 117-128, March.
    3. David Thissen & Lynne Steinberg, 1986. "A taxonomy of item response models," Psychometrika, Springer;The Psychometric Society, vol. 51(4), pages 567-577, December.
    4. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    5. Simon N. Wood, 2004. "Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 673-686, January.
    6. R. Darrell Bock, 1972. "Estimating item parameters and latent ability when responses are scored in two or more nominal categories," Psychometrika, Springer;The Psychometric Society, vol. 37(1), pages 29-51, March.
    7. 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.
    8. J. Ramsay & S. Winsberg, 1991. "Maximum marginal likelihood estimation for semiparametric item analysis," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 365-379, September.
    9. Li Cai, 2010. "High-dimensional Exploratory Item Factor Analysis by A Metropolis–Hastings Robbins–Monro Algorithm," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 33-57, March.
    10. Alberto Maydeu-Olivares, 2017. "Assessing the Size of Model Misfit in Structural Equation Models," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 533-558, September.
    11. J. Ramsay, 1991. "Kernel smoothing approaches to nonparametric item characteristic curve estimation," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 611-630, December.
    12. Daowen Zhang & Marie Davidian, 2001. "Linear Mixed Models with Flexible Distributions of Random Effects for Longitudinal Data," Biometrics, The International Biometric Society, vol. 57(3), pages 795-802, September.
    13. Jeff Douglas, 1997. "Joint consistency of nonparametric item characteristic curve and ability estimation," Psychometrika, Springer;The Psychometric Society, vol. 62(1), pages 7-28, March.
    14. Wim Linden & Fanmin Guo, 2008. "Bayesian Procedures for Identifying Aberrant Response-Time Patterns in Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 73(3), pages 365-384, September.
    15. Lawrence Brown & Noah Gans & Avishai Mandelbaum & Anat Sakov & Haipeng Shen & Sergey Zeltyn & Linda Zhao, 2005. "Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 36-50, March.
    16. Sik-Yum Lee & Ye-Mao Xia, 2008. "A Robust Bayesian Approach for Structural Equation Models with Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 73(3), pages 343-364, September.
    Full references (including those not matched with items on IDEAS)

    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. Björn Andersson & Tao Xin, 2021. "Estimation of Latent Regression Item Response Theory Models Using a Second-Order Laplace Approximation," Journal of Educational and Behavioral Statistics, , vol. 46(2), pages 244-265, April.
    2. Javier Revuelta, 2004. "Analysis of distractor difficulty in multiple-choice items," Psychometrika, Springer;The Psychometric Society, vol. 69(2), pages 217-234, June.
    3. Albert Maydeu-Olivares & Harry Joe, 2006. "Limited Information Goodness-of-fit Testing in Multidimensional Contingency Tables," Psychometrika, Springer;The Psychometric Society, vol. 71(4), pages 713-732, December.
    4. Yang Liu & Jan Hannig, 2017. "Generalized Fiducial Inference for Logistic Graded Response Models," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1097-1125, December.
    5. 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.
    6. Dylan Molenaar, 2015. "Heteroscedastic Latent Trait Models for Dichotomous Data," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 625-644, September.
    7. Singh, Jagdip, 2004. "Tackling measurement problems with Item Response Theory: Principles, characteristics, and assessment, with an illustrative example," Journal of Business Research, Elsevier, vol. 57(2), pages 184-208, February.
    8. Longjuan Liang & Michael W. Browne, 2015. "A Quasi-Parametric Method for Fitting Flexible Item Response Functions," Journal of Educational and Behavioral Statistics, , vol. 40(1), pages 5-34, February.
    9. Vock, David & Davidian, Marie & Tsiatis, Anastasios, 2014. "SNP_NLMM: A SAS Macro to Implement a Flexible Random Effects Density for Generalized Linear and Nonlinear Mixed Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 56(c02).
    10. Xueli Xu & Jeff Douglas, 2006. "Computerized adaptive testing under nonparametric IRT models," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 121-137, March.
    11. Anne Thissen-Roe & David Thissen, 2013. "A Two-Decision Model for Responses to Likert-Type Items," Journal of Educational and Behavioral Statistics, , vol. 38(5), pages 522-547, October.
    12. Javier Revuelta, 2009. "Identifiability and Equivalence of GLLIRM Models," Psychometrika, Springer;The Psychometric Society, vol. 74(2), pages 257-272, June.
    13. Michael Peress, 2012. "Identification of a Semiparametric Item Response Model," Psychometrika, Springer;The Psychometric Society, vol. 77(2), pages 223-243, April.
    14. Javier Revuelta, 2010. "Estimating Difficulty from Polytomous Categorical Data," Psychometrika, Springer;The Psychometric Society, vol. 75(2), pages 331-350, June.
    15. Cees Glas, 1999. "Modification indices for the 2-PL and the nominal response model," Psychometrika, Springer;The Psychometric Society, vol. 64(3), pages 273-294, September.
    16. Michelle M. LaMar, 2018. "Markov Decision Process Measurement Model," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 67-88, March.
    17. Bas Hemker & Klaas Sijtsma & Ivo Molenaar & Brian Junker, 1996. "Polytomous IRT models and monotone likelihood ratio of the total score," Psychometrika, Springer;The Psychometric Society, vol. 61(4), pages 679-693, December.
    18. E. Zanini & E. Eastoe & M. J. Jones & D. Randell & P. Jonathan, 2020. "Flexible covariate representations for extremes," Environmetrics, John Wiley & Sons, Ltd., vol. 31(5), August.
    19. Yoav Bergner & Peter Halpin & Jill-Jênn Vie, 2022. "Multidimensional Item Response Theory in the Style of Collaborative Filtering," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 266-288, March.
    20. Yang Liu, 2020. "A Riemannian Optimization Algorithm for Joint Maximum Likelihood Estimation of High-Dimensional Exploratory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 439-468, June.

    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:87:y:2022:i:2:d:10.1007_s11336-021-09832-8. 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.