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Asymptotically Corrected Person Fit Statistics for Multidimensional Constructs with Simple Structure and Mixed Item Types

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  • Maxwell Hong

    (University of Notre Dame)

  • Lizhen Lin

    (University of Notre Dame)

  • Ying Cheng

    (University of Notre Dame)

Abstract

Person fit statistics are frequently used to detect aberrant behavior when assuming an item response model generated the data. A common statistic, $$l_z$$ l z , has been shown in previous studies to perform well under a myriad of conditions. However, it is well-known that $$l_z$$ l z does not follow a standard normal distribution when using an estimated latent trait. As a result, corrections of $$l_z$$ l z , called $$l_z^*$$ l z ∗ , have been proposed in the literature for specific item response models. We propose a more general correction that is applicable to many types of data, namely survey or tests with multiple item types and underlying latent constructs, which subsumes previous work done by others. In addition, we provide corrections for multiple estimators of $$\theta $$ θ , the latent trait, including MLE, MAP and WLE. We provide analytical derivations that justifies our proposed correction, as well as simulation studies to examine the performance of the proposed correction with finite test lengths. An applied example is also provided to demonstrate proof of concept. We conclude with recommendations for practitioners when the asymptotic correction works well under different conditions and also future directions.

Suggested Citation

  • Maxwell Hong & Lizhen Lin & Ying Cheng, 2021. "Asymptotically Corrected Person Fit Statistics for Multidimensional Constructs with Simple Structure and Mixed Item Types," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 464-488, June.
  • Handle: RePEc:spr:psycho:v:86:y:2021:i:2:d:10.1007_s11336-021-09756-3
    DOI: 10.1007/s11336-021-09756-3
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    References listed on IDEAS

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