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Generalized Residuals for General Models for Contingency Tables With Application to Item Response Theory

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  • Shelby J. Haberman
  • Sandip Sinharay

Abstract

Generalized residuals are a tool employed in the analysis of contingency tables to examine possible sources of model error. They have typically been applied to log-linear models and to latent-class models. A general approach to generalized residuals is developed for a very general class of models for contingency tables. To illustrate their use, generalized residuals are applied to models based on item response theory (IRT) models. Such models are commonly applied to analysis of standardized achievement or aptitude tests. To obtain a realistic perspective on application of generalized residuals, actual testing data are employed.

Suggested Citation

  • Shelby J. Haberman & Sandip Sinharay, 2013. "Generalized Residuals for General Models for Contingency Tables With Application to Item Response Theory," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1435-1444, December.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:504:p:1435-1444
    DOI: 10.1080/01621459.2013.835660
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    Cited by:

    1. 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.
    2. Scott Monroe, 2021. "Testing Latent Variable Distribution Fit in IRT Using Posterior Residuals," Journal of Educational and Behavioral Statistics, , vol. 46(3), pages 374-398, June.
    3. Felix Zimmer & Clemens Draxler & Rudolf Debelak, 2023. "Power Analysis for the Wald, LR, Score, and Gradient Tests in a Marginal Maximum Likelihood Framework: Applications in IRT," Psychometrika, Springer;The Psychometric Society, vol. 88(4), pages 1249-1298, December.
    4. Jochen Ranger & Kay Brauer, 2022. "On the Generalized S − X 2 –Test of Item Fit: Some Variants, Residuals, and a Graphical Visualization," Journal of Educational and Behavioral Statistics, , vol. 47(2), pages 202-230, April.
    5. Peter W. Rijn & Usama S. Ali, 2018. "A Generalized Speed–Accuracy Response Model for Dichotomous Items," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 109-131, March.

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