IDEAS home Printed from https://ideas.repec.org/a/sae/jedbes/v37y2012i2p231-255.html
   My bibliography  Save this article

The Generalized Multilevel Facets Model for Longitudinal Data

Author

Listed:
  • Lai-Fa Hung

    (Chang Jung Christian University, Taiwan)

  • Wen-Chung Wang

    (The Hong Kong Institute of Education)

Abstract

In the human sciences, ability tests or psychological inventories are often repeatedly conducted to measure growth. Standard item response models do not take into account possible autocorrelation in longitudinal data. In this study, the authors propose an item response model to account for autocorrelation. The proposed three-level model consists of multiple facets (e.g., person, item, and rater facets) and slope parameters. Level 1 is an item response (within-occasion) model; Level 2 is a between-occasion and within-person model; and Level 3 is a between-person model. Parameters can be estimated using the computer software WinBUGS, which uses Markov Chain Monte Carlo (MCMC) algorithms. Through a series of simulations, it was found that the parameters in the proposed model can be recovered fairly well. Real data of job performance judged by raters at various time points were analyzed to illustrate the implications and application of the proposed model.

Suggested Citation

  • Lai-Fa Hung & Wen-Chung Wang, 2012. "The Generalized Multilevel Facets Model for Longitudinal Data," Journal of Educational and Behavioral Statistics, , vol. 37(2), pages 231-255, April.
    • Handle: RePEc:sae:jedbes:v:37:y:2012:i:2:p:231-255
    DOI: 10.3102/1076998611402503
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.3102/1076998611402503
    Download Restriction: no
    File URL: https://libkey.io/10.3102/1076998611402503?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
    ---><---

    References listed on IDEAS

    as
    1. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    2. Aeilko Zwinderman, 1991. "A generalized rasch model for manifest predictors," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 589-600, December.
    3. Jean-Paul Fox & Cees Glas, 2001. "Bayesian estimation of a multilevel IRT model using gibbs sampling," Psychometrika, Springer;The Psychometric Society, vol. 66(2), pages 271-288, June.
    4. A. Béguin & C. Glas, 2001. "MCMC estimation and some model-fit analysis of multidimensional IRT models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 541-561, December.
    5. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    6. Sik-Yum Lee, 1981. "A bayesian approach to confirmatory factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 46(2), pages 153-160, June.
    7. David Andrich, 1978. "A rating formulation for ordered response categories," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 561-573, December.
    8. Richard Scheines & Herbert Hoijtink & Anne Boomsma, 1999. "Bayesian estimation and testing of structural equation models," Psychometrika, Springer;The Psychometric Society, vol. 64(1), pages 37-52, March.
    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. Anders Skrondal & Sophia Rabe‐Hesketh, 2007. "Latent Variable Modelling: A Survey," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 712-745, December.
    2. Jiwei Zhang & Zhaoyuan Zhang & Jian Tao, 2021. "A Bayesian algorithm based on auxiliary variables for estimating GRM with non-ignorable missing data," Computational Statistics, Springer, vol. 36(4), pages 2643-2669, December.
    3. Hanneke Geerlings & Cees Glas & Wim Linden, 2011. "Modeling Rule-Based Item Generation," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 337-359, April.
    4. David Kaplan & Chansoon Lee, 2018. "Optimizing Prediction Using Bayesian Model Averaging: Examples Using Large-Scale Educational Assessments," Evaluation Review, , vol. 42(4), pages 423-457, August.
    5. Xiaohui Zheng & Sophia Rabe-Hesketh, 2007. "Estimating parameters of dichotomous and ordinal item response models with gllamm," Stata Journal, StataCorp LP, vol. 7(3), pages 313-333, September.
    6. Bacci, Silvia & Fabbricatore, Rosa & Iannario, Maria, 2023. "Multilevel IRT models for the analysis of satisfaction for distance learning during the Covid-19 pandemic," Socio-Economic Planning Sciences, Elsevier, vol. 86(C).
    7. Fox, Jean-Paul, 2007. "Multilevel IRT Modeling in Practice with the Package mlirt," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i05).
    8. Azevedo, Caio L.N. & Bolfarine, Heleno & Andrade, Dalton F., 2011. "Bayesian inference for a skew-normal IRT model under the centred parameterization," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 353-365, January.
    9. Gonçalves, F.B. & Gamerman, D. & Soares, T.M., 2013. "Simultaneous multifactor DIF analysis and detection in Item Response Theory," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 144-160.
    10. 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.
    11. repec:jss:jstsof:20:i05 is not listed on IDEAS
    12. Mariagiulia Matteucci & Bernard Veldkamp, 2013. "On the use of MCMC computerized adaptive testing with empirical prior information to improve efficiency," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(2), pages 243-267, June.
    13. R. Klein Entink & J.-P. Fox & W. Linden, 2009. "A Multivariate Multilevel Approach to the Modeling of Accuracy and Speed of Test Takers," Psychometrika, Springer;The Psychometric Society, vol. 74(1), pages 21-48, March.
    14. Padilla, Juan L. & Azevedo, Caio L.N. & Lachos, Victor H., 2018. "Multidimensional multiple group IRT models with skew normal latent trait distributions," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 250-268.
    15. P. A. Ferrari & S. Salini, 2008. "Measuring Service Quality: The Opinion of Europeans about Utilities," Working Papers 2008.36, Fondazione Eni Enrico Mattei.
    16. Chang, Hsin-Li & Yang, Cheng-Hua, 2008. "Explore airlines’ brand niches through measuring passengers’ repurchase motivation—an application of Rasch measurement," Journal of Air Transport Management, Elsevier, vol. 14(3), pages 105-112.
    17. Leonidas A. Zampetakis & Melina Vekini & Vassilis Moustakis, 2009. "Entrepreneurial orientation, access to financial resources, and product performance in the Greek commercial TV industry," The Service Industries Journal, Taylor & Francis Journals, vol. 31(6), pages 897-910, April.
    18. Ivana Bassi & Matteo Carzedda & Enrico Gori & Luca Iseppi, 2022. "Rasch analysis of consumer attitudes towards the mountain product label," Agricultural and Food Economics, Springer;Italian Society of Agricultural Economics (SIDEA), vol. 10(1), pages 1-25, December.
    19. Antonio Caronni & Marina Ramella & Pietro Arcuri & Claudia Salatino & Lucia Pigini & Maurizio Saruggia & Chiara Folini & Stefano Scarano & Rosa Maria Converti, 2023. "The Rasch Analysis Shows Poor Construct Validity and Low Reliability of the Quebec User Evaluation of Satisfaction with Assistive Technology 2.0 (QUEST 2.0) Questionnaire," IJERPH, MDPI, vol. 20(2), pages 1-19, January.
    20. 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.
    21. Curt Hagquist & Raili Välimaa & Nina Simonsen & Sakari Suominen, 2017. "Differential Item Functioning in Trend Analyses of Adolescent Mental Health – Illustrative Examples Using HBSC-Data from Finland," Child Indicators Research, Springer;The International Society of Child Indicators (ISCI), vol. 10(3), pages 673-691, September.

    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:sae:jedbes:v:37:y:2012:i:2:p:231-255. 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: SAGE Publications (email available below). General contact details of provider: .

    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.