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What Can We Learn from a Semiparametric Factor Analysis of Item Responses and Response Time? An Illustration with the PISA 2015 Data

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  • Yang Liu

    (University of Maryland)

  • Weimeng Wang

    (University of Maryland)

Abstract

It is widely believed that a joint factor analysis of item responses and response time (RT) may yield more precise ability scores that are conventionally predicted from responses only. For this purpose, a simple-structure factor model is often preferred as it only requires specifying an additional measurement model for item-level RT while leaving the original item response theory (IRT) model for responses intact. The added speed factor indicated by item-level RT correlates with the ability factor in the IRT model, allowing RT data to carry additional information about respondents’ ability. However, parametric simple-structure factor models are often restrictive and fit poorly to empirical data, which prompts under-confidence in the suitablity of a simple factor structure. In the present paper, we analyze the 2015 Programme for International Student Assessment mathematics data using a semiparametric simple-structure model. We conclude that a simple factor structure attains a decent fit after further parametric assumptions in the measurement model are sufficiently relaxed. Furthermore, our semiparametric model implies that the association between latent ability and speed/slowness is strong in the population, but the form of association is nonlinear. It follows that scoring based on the fitted model can substantially improve the precision of ability scores.

Suggested Citation

  • Yang Liu & Weimeng Wang, 2024. "What Can We Learn from a Semiparametric Factor Analysis of Item Responses and Response Time? An Illustration with the PISA 2015 Data," Psychometrika, Springer;The Psychometric Society, vol. 89(2), pages 386-410, June.
    • Handle: RePEc:spr:psycho:v:89:y:2024:i:2:d:10.1007_s11336-023-09936-3
    DOI: 10.1007/s11336-023-09936-3
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    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. Jochen Ranger & Jorg-Tobias Kuhn, 2012. "A flexible latent trait model for response times in tests," Psychometrika, Springer;The Psychometric Society, vol. 77(1), pages 31-47, January.
    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. 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.
    5. Inhan Kang & Dylan Molenaar & Roger Ratcliff, 2023. "Erratum to: A Modeling Framework to Examine Psychological Processes Underlying Ordinal Responses and Response Times of Psychometric Data," Psychometrika, Springer;The Psychometric Society, vol. 88(4), pages 1592-1592, December.
    6. 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.
    7. Göran Kauermann & Christian Schellhase & David Ruppert, 2013. "Flexible Copula Density Estimation with Penalized Hierarchical B-splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 685-705, December.
    8. Gery Geenens & Pierre Lafaye de Micheaux, 2022. "The Hellinger Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(538), pages 639-653, April.
    9. 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.
    10. Yuchen Chen & Yuhong Yang, 2021. "The One Standard Error Rule for Model Selection: Does It Work?," Stats, MDPI, vol. 4(4), pages 1-25, November.
    11. 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.
    12. Matthias von Davier & Lale Khorramdel & Qiwei He & Hyo Jeong Shin & Haiwen Chen, 2019. "Developments in Psychometric Population Models for Technology-Based Large-Scale Assessments: An Overview of Challenges and Opportunities," Journal of Educational and Behavioral Statistics, , vol. 44(6), pages 671-705, December.
    13. L. Thurstone, 1937. "Ability, motivation, and speed," Psychometrika, Springer;The Psychometric Society, vol. 2(4), pages 249-254, December.
    14. Yang Liu & Ji Seung Yang, 2018. "Bootstrap-Calibrated Interval Estimates for Latent Variable Scores in Item Response Theory," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 333-354, June.
    15. 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.
    16. 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.
    17. 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.
    18. Mordant, Gilles & Segers, Johan, 2022. "Measuring dependence between random vectors via optimal transport," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    19. 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.
    20. Li Cai, 2010. "Metropolis-Hastings Robbins-Monro Algorithm for Confirmatory Item Factor Analysis," Journal of Educational and Behavioral Statistics, , vol. 35(3), pages 307-335, June.
    21. 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.
    22. Michal Abrahamowicz & James Ramsay, 1992. "Multicategorical spline model for item response theory," Psychometrika, Springer;The Psychometric Society, vol. 57(1), pages 5-27, March.
    23. 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.
    24. Xiaoling Dou & Satoshi Kuriki & Gwo Dong Lin & Donald Richards, 2021. "Dependence Properties of B-Spline Copulas," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 283-311, February.
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