IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v77y2012i4p693-709.html
   My bibliography  Save this article

Fitting and Testing Conditional Multinormal Partial Credit Models

Author

Listed:
  • David Hessen

Abstract

A multinormal partial credit model for factor analysis of polytomously scored items with ordered response categories is derived using an extension of the Dutch Identity (Holland in Psychometrika 55:5–18, 1990 ). In the model, latent variables are assumed to have a multivariate normal distribution conditional on unweighted sums of item scores, which are sufficient statistics. Attention is paid to maximum likelihood estimation of item parameters, multivariate moments of latent variables, and person parameters. It is shown that the maximum likelihood estimates can be found without the use of numerical integration techniques. More general models are discussed which can be used for testing the model, and it is shown how models with different numbers of latent variables can be tested against each other. In addition, multi-group extensions are proposed, which can be used for testing both measurement invariance and latent population differences. Models and procedures discussed are demonstrated in an empirical data example. Copyright The Psychometric Society 2012

Suggested Citation

  • David Hessen, 2012. "Fitting and Testing Conditional Multinormal Partial Credit Models," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 693-709, October.
    • Handle: RePEc:spr:psycho:v:77:y:2012:i:4:p:693-709
    DOI: 10.1007/s11336-012-9277-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11336-012-9277-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11336-012-9277-1?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. Henk Kelderman & Carl Rijkes, 1994. "Loglinear multidimensional IRT models for polytomously scored items," Psychometrika, Springer;The Psychometric Society, vol. 59(2), pages 149-176, June.
    2. 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.
    3. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    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. 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.
    6. David Andrich, 1978. "A rating formulation for ordered response categories," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 561-573, December.
    7. Stephen Schilling & R. Bock, 2005. "High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature," Psychometrika, Springer;The Psychometric Society, vol. 70(3), pages 533-555, September.
    8. William Meredith, 1993. "Measurement invariance, factor analysis and factorial invariance," Psychometrika, Springer;The Psychometric Society, vol. 58(4), pages 525-543, December.
    9. Henk Kelderman, 1992. "Computing maximum likelihood estimates of loglinear models from marginal sums with special attention to loglinear item response theory," Psychometrika, Springer;The Psychometric Society, vol. 57(3), pages 437-450, September.
    10. William Meredith & Roger Millsap, 1992. "On the misuse of manifest variables in the detection of measurement bias," Psychometrika, Springer;The Psychometric Society, vol. 57(2), pages 289-311, June.
    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. 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.
    2. 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.
    3. 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.
    4. 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.

    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. Dylan Molenaar, 2015. "Heteroscedastic Latent Trait Models for Dichotomous Data," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 625-644, September.
    2. Javier Revuelta, 2008. "The generalized Logit-Linear Item Response Model for Binary-Designed Items," Psychometrika, Springer;The Psychometric Society, vol. 73(3), pages 385-405, September.
    3. Karl Christensen & Jakob Bjorner & Svend Kreiner & Jørgen Petersen, 2002. "Testing unidimensionality in polytomous Rasch models," Psychometrika, Springer;The Psychometric Society, vol. 67(4), pages 563-574, December.
    4. Paul Holland, 1990. "On the sampling theory roundations of item response theory models," Psychometrika, Springer;The Psychometric Society, vol. 55(4), pages 577-601, December.
    5. Anders Skrondal & Sophia Rabe-Hesketh, 2022. "The Role of Conditional Likelihoods in Latent Variable Modeling," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 799-834, September.
    6. Bartolucci, Francesco & Bacci, Silvia & Gnaldi, Michela, 2014. "MultiLCIRT: An R package for multidimensional latent class item response models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 971-985.
    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. Clem Brooks, 1994. "The Selectively Political Citizen?," Sociological Methods & Research, , vol. 22(4), pages 419-459, May.
    9. Henk Kelderman & Carl Rijkes, 1994. "Loglinear multidimensional IRT models for polytomously scored items," Psychometrika, Springer;The Psychometric Society, vol. 59(2), pages 149-176, June.
    10. Silvana Bortolotti & Rafael Tezza & Dalton Andrade & Antonio Bornia & Afonso Sousa Júnior, 2013. "Relevance and advantages of using the item response theory," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(4), pages 2341-2360, June.
    11. Chengyu Cui & Chun Wang & Gongjun Xu, 2024. "Variational Estimation for Multidimensional Generalized Partial Credit Model," Psychometrika, Springer;The Psychometric Society, vol. 89(3), pages 929-957, September.
    12. Bas Hemker & L. Andries van der Ark & Klaas Sijtsma, 2001. "On measurement properties of continuation ratio models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 487-506, December.
    13. Alan Agresti, 1995. "Logit Models and Related Quasi-Symmetric Log-Linear Models for Comparing Responses to Similar Items in a Survey," Sociological Methods & Research, , vol. 24(1), pages 68-95, August.
    14. 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.
    15. Yang Liu & Ji Seung Yang & Alberto Maydeu-Olivares, 2019. "Restricted Recalibration of Item Response Theory Models," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 529-553, June.
    16. Shelby Haberman & Sandip Sinharay & Kyong Chon, 2013. "Assessing Item Fit for Unidimensional Item Response Theory Models Using Residuals from Estimated Item Response Functions," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 417-440, July.
    17. P. A. Ferrari & S. Salini, 2008. "Measuring Service Quality: The Opinion of Europeans about Utilities," Working Papers 2008.36, Fondazione Eni Enrico Mattei.
    18. 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.
    19. 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.
    20. 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.

    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:77:y:2012:i:4:p:693-709. 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.