IDEAS home Printed from https://ideas.repec.org/a/jss/jstsof/v020i06.html
   My bibliography  Save this article

Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables

Author

Listed:
  • Anderson, Carolyn J.
  • Li, Zhushan
  • Vermunt, Jeroen K.

Abstract

The Rasch family of models considered in this paper includes models for polytomous items and multiple correlated latent traits, as well as for dichotomous items and a single latent variable. An R package is described that computes estimates of parameters and robust standard errors of a class of log-linear-by-linear association (LLLA) models, which are derived from a Rasch family of models. The LLLA models are special cases of log-linear models with bivariate interactions. Maximum likelihood estimation of LLLA models in this form is limited to relatively small problems; however, pseudo-likelihood estimation overcomes this limitation. Maximizing the pseudo-likelihood function is achieved by maximizing the likelihood of a single conditional multinomial logistic regression model. The parameter estimates are asymptotically normal and consistent. Based on our simulation studies, the pseudo-likelihood and maximum likelihood estimates of the parameters of LLLA models are nearly identical and the loss of efficiency is negligible. Recovery of parameters of Rasch models fit to simulated data is excellent.

Suggested Citation

  • Anderson, Carolyn J. & Li, Zhushan & Vermunt, Jeroen K., 2007. "Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i06).
    • Handle: RePEc:jss:jstsof:v:020:i06
    DOI: http://hdl.handle.net/10.18637/jss.v020.i06
    as

    Download full text from publisher

    File URL: https://www.jstatsoft.org/index.php/jss/article/view/v020i06/v20i06.pdf
    Download Restriction: no
    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v020i06/plRasch_0.1.tar.gz
    Download Restriction: no
    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v020i06/v20i06.R.zip
    Download Restriction: no
    File URL: https://libkey.io/http://hdl.handle.net/10.18637/jss.v020.i06?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. Becker, Mark P., 1989. "On the bivariate normal distribution and association models for ordinal categorical data," Statistics & Probability Letters, Elsevier, vol. 8(5), pages 435-440, October.
    2. 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.
    3. Mair, Patrick & Hatzinger, Reinhold, 2007. "Extended Rasch Modeling: The eRm Package for the Application of IRT Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i09).
    4. Huwang, Longcheen & Gene Hwang, J. T., 2002. "Prediction and confidence intervals for nonlinear measurement error models without identifiability information," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 355-362, July.
    5. Carolyn Anderson & Ulf Böckenholt, 2000. "Graphical regression models for polytomous variables," Psychometrika, Springer;The Psychometric Society, vol. 65(4), pages 497-509, December.
    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. repec:jss:jstsof:20:i09 is not listed on IDEAS
    2. repec:jss:jstsof:20:i01 is not listed on IDEAS
    3. Carolyn J. Anderson & Jay Verkuilen & Buddy L. Peyton, 2010. "Modeling Polytomous Item Responses Using Simultaneously Estimated Multinomial Logistic Regression Models," Journal of Educational and Behavioral Statistics, , vol. 35(4), pages 422-452, August.
    4. repec:jss:jstsof:39:i12 is not listed on IDEAS
    5. David Andrich, 2010. "Sufficiency and Conditional Estimation of Person Parameters in the Polytomous Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 75(2), pages 292-308, June.
    6. repec:jss:jstsof:34:i03 is not listed on IDEAS
    7. 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.
    8. Mair, Patrick & Hatzinger, Reinhold, 2007. "Extended Rasch Modeling: The eRm Package for the Application of IRT Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i09).
    9. 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.
    10. de Leeuw, Jan & Mair, Patrick, 2007. "An Introduction to the Special Volume on "Psychometrics in R"," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i01).
    11. Cheng-Hua, Yang & Hsin-Li, Chang, 2012. "Exploring the perceived competence of airport ground staff in dealing with unruly passenger behaviors," Tourism Management, Elsevier, vol. 33(3), pages 611-621.
    12. Alexander Robitzsch, 2021. "A Comprehensive Simulation Study of Estimation Methods for the Rasch Model," Stats, MDPI, vol. 4(4), pages 1-23, October.
    13. 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. repec:jss:jstsof:20:i06 is not listed on IDEAS
    2. Alexander Robitzsch, 2021. "A Comprehensive Simulation Study of Estimation Methods for the Rasch Model," Stats, MDPI, vol. 4(4), pages 1-23, October.
    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. César Merino-Soto & Gina Chávez-Ventura & Verónica López-Fernández & Guillermo M. Chans & Filiberto Toledano-Toledano, 2022. "Learning Self-Regulation Questionnaire (SRQ-L): Psychometric and Measurement Invariance Evidence in Peruvian Undergraduate Students," Sustainability, MDPI, vol. 14(18), pages 1-17, September.
    5. repec:jss:jstsof:39:i08 is not listed on IDEAS
    6. Frick, Hannah & Strobl, Carolin & Leisch, Friedrich & Zeileis, Achim, 2012. "Flexible Rasch Mixture Models with Package psychomix," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i07).
    7. 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.
    8. Cervantes, Víctor H., 2017. "DFIT: An R Package for Raju's Differential Functioning of Items and Tests Framework," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i05).
    9. repec:jss:jstsof:20:i01 is not listed on IDEAS
    10. repec:jss:jstsof:39:i12 is not listed on IDEAS
    11. Shrum, Trisha & Donovan, Christopher & Bloch, Sadie & Cripps, Emma & Boyson, Ceclia, 2024. "The REBL Score: A dynamic measure of pro-environmental behavior," OSF Preprints w92se, Center for Open Science.
    12. Piero Veronese & Eugenio Melilli, 2021. "Confidence Distribution for the Ability Parameter of the Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 131-166, March.
    13. de Leeuw, Jan & Mair, Patrick, 2007. "An Introduction to the Special Volume on "Psychometrics in R"," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i01).
    14. repec:jss:jstsof:36:c01 is not listed on IDEAS
    15. Alessandro Barbiero & Asmerilda Hitaj, 2020. "Goodman and Kruskal’s Gamma Coefficient for Ordinalized Bivariate Normal Distributions," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 905-925, December.
    16. 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.
    17. Yunxiao Chen & Xiaoou Li & Jingchen Liu & Zhiliang Ying, 2018. "Robust Measurement via A Fused Latent and Graphical Item Response Theory Model," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 538-562, September.
    18. Elizabeth Ooi, 2020. "Give mind to the gap: Measuring gender differences in financial knowledge," Journal of Consumer Affairs, Wiley Blackwell, vol. 54(3), pages 931-950, September.
    19. repec:jss:jstsof:35:i12 is not listed on IDEAS
    20. Yuchung Wang, 1997. "Multivariate normal integrals and contingency tables with ordered categories," Psychometrika, Springer;The Psychometric Society, vol. 62(2), pages 267-284, June.
    21. Maria Adam Nyangasa & Christoph Buck & Soerge Kelm & Mohammed Sheikh & Antje Hebestreit, 2019. "Exploring Food Access and Sociodemographic Correlates of Food Consumption and Food Insecurity in Zanzibari Households," IJERPH, MDPI, vol. 16(9), pages 1-15, May.
    22. Clemens Draxler & Andreas Kurz, 2021. "Conditional Inference in Small Sample Scenarios Using a Resampling Approach," Stats, MDPI, vol. 4(4), pages 1-13, October.
    23. Lapp, Krista & Molenberghs, Geert & Lesaffre, Emmanuel, 1998. "Models for the association between ordinal variables," Computational Statistics & Data Analysis, Elsevier, vol. 28(4), pages 387-411, October.
    24. Carolin Strobl & Julia Kopf & Achim Zeileis, 2011. "A new method for detecting differential item functioning in the Rasch model," Working Papers 2011-01, Faculty of Economics and Statistics, Universität Innsbruck.
    25. Chen, Xiaohong & Hu, Yingyao & Lewbel, Arthur, 2008. "A note on the closed-form identification of regression models with a mismeasured binary regressor," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1473-1479, September.
    26. Carla Sabariego & Cornelia Oberhauser & Aleksandra Posarac & Jerome Bickenbach & Nenad Kostanjsek & Somnath Chatterji & Alana Officer & Michaela Coenen & Lay Chhan & Alarcos Cieza, 2015. "Measuring Disability: Comparing the Impact of Two Data Collection Approaches on Disability Rates," IJERPH, MDPI, vol. 12(9), pages 1-23, August.

    More about this item

    Statistics

    Access and download statistics

    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:jss:jstsof:v:020:i06. 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: Christopher F. Baum (email available below). General contact details of provider: http://www.jstatsoft.org/ .

    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.