IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v88y2023i3d10.1007_s11336-023-09922-9.html
   My bibliography  Save this article

Fitting and Testing Log-Linear Subpopulation Models with Known Support

Author

Listed:
  • David J. Hessen

    (Utrecht University)

Abstract

In this paper, the support of the joint probability distribution of categorical variables in the total population is treated as unknown. From a general total population model with unknown support, a general subpopulation model with its support equal to the set of all observed score patterns is derived. In maximum likelihood estimation of the parameters of any such subpopulation model, the evaluation of the log-likelihood function only requires the summation over a number of terms equal to at most the sample size. It is made clear that the parameters of a hypothesized total population model are consistently and asymptotically efficiently estimated by the values that maximize the log-likelihood function of the corresponding subpopulation model. Next, new likelihood ratio goodness-of-fit tests are proposed as alternatives to the Pearson chi-square goodness-of-fit test and the likelihood ratio test against the saturated model. In a simulation study, the asymptotic bias and efficiency of maximum likelihood estimators and the asymptotic performance of the goodness-of-fit tests are investigated.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:psycho:v:88:y:2023:i:3:d:10.1007_s11336-023-09922-9
    DOI: 10.1007/s11336-023-09922-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-023-09922-9
    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/s11336-023-09922-9?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. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    2. Carolyn Anderson, 2013. "Multidimensional Item Response Theory Models with Collateral Information as Poisson Regression Models," Journal of Classification, Springer;The Classification Society, vol. 30(2), pages 276-303, July.
    3. 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.
    4. Dean Follmann, 1988. "Consistent estimation in the rasch model based on nonparametric margins," Psychometrika, Springer;The Psychometric Society, vol. 53(4), pages 553-562, December.
    5. 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.
    6. David Hessen, 2012. "Fitting and Testing Conditional Multinormal Partial Credit Models," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 693-709, October.
    7. Erling Andersen, 1973. "A goodness of fit test for the rasch model," Psychometrika, Springer;The Psychometric Society, vol. 38(1), pages 123-140, 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. 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.
    2. 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.
    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. C. Glas & Anna Dagohoy, 2007. "A Person Fit Test For Irt Models For Polytomous Items," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 159-180, June.
    5. 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.
    6. Timo Bechger & Gunter Maris, 2015. "A Statistical Test for Differential Item Pair Functioning," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 317-340, June.
    7. Gerhard Tutz & Gunther Schauberger, 2015. "A Penalty Approach to Differential Item Functioning in Rasch Models," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 21-43, March.
    8. Georg Gittler & Gerhard Fischer, 2011. "IRT-Based Measurement of Short-Term Changes of Ability, With an Application to Assessing the “Mozart Effectâ€," Journal of Educational and Behavioral Statistics, , vol. 36(1), pages 33-75, February.
    9. Robert Zwitser & Gunter Maris, 2015. "Conditional Statistical Inference with Multistage Testing Designs," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 65-84, March.
    10. Clemens Draxler, 2010. "Sample Size Determination for Rasch Model Tests," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 708-724, December.
    11. Clem Brooks, 1994. "The Selectively Political Citizen?," Sociological Methods & Research, , vol. 22(4), pages 419-459, May.
    12. David J. Hessen, 2010. "Likelihood Ratio Tests for Special Rasch Models," Journal of Educational and Behavioral Statistics, , vol. 35(6), pages 611-628, December.
    13. Wenjia Wang & Mickaël Guedj & Viviane Bertrand & Julie Foucquier & Elisabeth Jouve & Daniel Commenges & Cécile Proust-Lima & Niall P Murphy & Olivier Blin & Laurent Magy & Daniel Cohen & Shahram Attar, 2017. "A Rasch Analysis of the Charcot-Marie-Tooth Neuropathy Score (CMTNS) in a Cohort of Charcot-Marie-Tooth Type 1A Patients," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-14, January.
    14. Clemens Draxler & Andreas Kurz & Can Gürer & Jan Philipp Nolte, 2024. "An Improved Inferential Procedure to Evaluate Item Discriminations in a Conditional Maximum Likelihood Framework," Journal of Educational and Behavioral Statistics, , vol. 49(3), pages 403-430, June.
    15. Clemens Draxler & Rainer Alexandrowicz, 2015. "Sample Size Determination Within the Scope of Conditional Maximum Likelihood Estimation with Special Focus on Testing the Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 897-919, December.
    16. 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.
    17. Jürgen M. Pelikan & Thomas Link & Christa Straßmayr & Karin Waldherr & Tobias Alfers & Henrik Bøggild & Robert Griebler & Maria Lopatina & Dominika Mikšová & Marie Germund Nielsen & Sandra Peer & Mitj, 2022. "Measuring Comprehensive, General Health Literacy in the General Adult Population: The Development and Validation of the HLS 19 -Q12 Instrument in Seventeen Countries," IJERPH, MDPI, vol. 19(21), pages 1-31, October.
    18. Karl Klauer, 1991. "An exact and optimal standardized person test for assessing consistency with the rasch model," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 213-228, June.
    19. 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.
    20. David Hessen, 2012. "Fitting and Testing Conditional Multinormal Partial Credit Models," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 693-709, October.

    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:88:y:2023:i:3:d:10.1007_s11336-023-09922-9. 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.