IDEAS home Printed from https://ideas.repec.org/a/spr/jclass/v30y2013i2p276-303.html
   My bibliography  Save this article

Multidimensional Item Response Theory Models with Collateral Information as Poisson Regression Models

Author

Listed:
  • Carolyn Anderson

Abstract

Multiple choice items on tests and Likert items on surveys are ubiquitous in educational, social and behavioral science research; however, methods for analyzing of such data can be problematic. Multidimensional item response theory models are proposed that yield structured Poisson regression models for the joint distribution of responses to items. The methodology presented here extends the approach described in Anderson, Verkuilen, and Peyton (2010) that used fully conditionally specified multinomial logistic regression models as item response functions. In this paper, covariates are added as predictors of the latent variables along with covariates as predictors of location parameters. Furthermore, the models presented here incorporate ordinal information of the response options thus allowing an empirical examination of assumptions regarding the ordering and the estimation of optimal scoring of the response options. To illustrate the methodology and flexibility of the models, data from a study on aggression in middle school (Espelage, Holt, and Henkel 2004) is analyzed. The models are fit to data using SAS. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jclass:v:30:y:2013:i:2:p:276-303
    DOI: 10.1007/s00357-013-9131-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00357-013-9131-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00357-013-9131-x?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. Joe, Harry & Liu, Ying, 1996. "A model for a multivariate binary response with covariates based on compatible conditionally specified logistic regressions," Statistics & Probability Letters, Elsevier, vol. 31(2), pages 113-120, December.
    2. Francisca Galindo-Garre & Jeroen Vermunt, 2004. "The order-restricted association model: Two estimation algorithms and issues in testing," Psychometrika, Springer;The Psychometric Society, vol. 69(4), pages 641-654, December.
    3. 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.
    4. Neal Thomas, 2002. "The role of secondary covariates when estimating latent trait population distributions," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 33-48, March.
    5. Bartolucci F. & Forcina A., 2002. "Extended RC Association Models Allowing for Order Restrictions and Marginal Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1192-1199, December.
    6. Francisca Galindo‐Garre & Jeroen K. Vermunt, 2005. "Testing log‐linear models with inequality constraints: a comparison of asymptotic, bootstrap, and posterior predictive p‐values," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(1), pages 82-94, February.
    7. 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).
    8. Iliopoulos, G. & Kateri, M. & Ntzoufras, I., 2007. "Bayesian estimation of unrestricted and order-restricted association models for a two-way contingency table," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4643-4655, May.
    9. Yee, Thomas W., 2010. "The VGAM Package for Categorical Data Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i10).
    10. 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.
    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. 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.

    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. Oh, Man-Suk, 2014. "Bayesian test on equality of score parameters in the order restricted RC association model," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 147-157.
    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. repec:jss:jstsof:20:i06 is not listed on IDEAS
    4. Demirhan, Haydar, 2013. "Bayesian estimation of order-restricted and unrestricted association models," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 109-126.
    5. 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.
    6. G. Iliopoulos & M. Kateri & I. Ntzoufras, 2009. "Bayesian Model Comparison for the Order Restricted RC Association Model," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 561-587, December.
    7. repec:jss:jstsof:39:i12 is not listed on IDEAS
    8. Siliang Zhang & Yunxiao Chen, 2024. "A Note on Ising Network Analysis with Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 89(4), pages 1186-1202, December.
    9. 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.
    10. Zhang, Siliang & Chen, Yunxiao, 2024. "A note on Ising network analysis with missing data," LSE Research Online Documents on Economics 123984, London School of Economics and Political Science, LSE Library.
    11. 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.
    12. 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.
    13. 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.
    14. Chen, Yunxiao & Li, Xiaoou & Liu, Jingchen & Ying, Zhiliang, 2018. "Robust measurement via a fused latent and graphical item response theory model," LSE Research Online Documents on Economics 103181, London School of Economics and Political Science, LSE Library.
    15. D'Alberto, R. & Targetti, S. & Schaller, L. & Bartolini, F. & Eichhorn, T. & Haltia, E. & Harmanny, K. & Le Gloux, F. & Nikolov, D. & Runge, T. & Vergamini, D. & Viaggi, D., 2024. "A European perspective on acceptability of innovative agri-environment-climate contract solutions," Land Use Policy, Elsevier, vol. 141(C).
    16. Jiang, Xianfeng & Packer, Frank, 2019. "Credit ratings of Chinese firms by domestic and global agencies: Assessing the determinants and impact," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 178-193.
    17. Xi Liu & Yiqiao Jin & Yifan Yang & Xiaoqing Pan, 2023. "Properties and Estimations of a Multivariate Folded Normal Distribution," Mathematics, MDPI, vol. 11(23), pages 1-15, December.
    18. Yiwei Fan & Jiaqi Gu & Guosheng Yin, 2023. "Sparse concordance‐based ordinal classification," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 934-961, September.
    19. Michail Tsagris & Christina Beneki & Hossein Hassani, 2014. "On the Folded Normal Distribution," Mathematics, MDPI, vol. 2(1), pages 1-17, February.
    20. Shuai Shao & Göran Kauermann, 2020. "Understanding price elasticity for airline ancillary services," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 19(1), pages 74-82, February.
    21. Shin Ji-Hyung & Infante-Rivard Claire & McNeney Brad & Graham Jinko, 2014. "A data-smoothing approach to explore and test gene-environment interaction in case-parent trios," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(2), pages 159-171, April.
    22. Thomas Yee & Alfian Hadi, 2014. "Row–column interaction models, with an R implementation," Computational Statistics, Springer, vol. 29(6), pages 1427-1445, December.

    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:jclass:v:30:y:2013:i:2:p:276-303. 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.