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Identifying and Classifying Aberrant Response Patterns Through Functional Data Analysis

Author

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  • Eduardo Doval

    (16719Universitat Autònoma de Barcelona)

  • Pedro Delicado

    (16767Universitat Politècnica de Catalunya)

Abstract

We propose new methods for identifying and classifying aberrant response patterns (ARPs) by means of functional data analysis. These methods take the person response function (PRF) of an individual and compare it with the pattern that would correspond to a generic individual of the same ability according to the item-person response surface. ARPs correspond to atypical difference functions. The ARP classification is done with functional data clustering applied to the PRFs identified as ARP. We apply these methods to two sets of simulated data (the first is used to illustrate the ARP identification methods and the second demonstrates classification of the response patterns flagged as ARP) and a real data set (a Grade 12 science assessment test, SAT, with 32 items answered by 600 examinees). For comparative purposes, ARPs are also identified with three nonparametric person-fit indices (Ht, Modified Caution Index, and ZU3). Our results indicate that the ARP detection ability of one of our proposed methods is comparable to that of person-fit indices. Moreover, the proposed classification methods enable ARP associated with either spuriously low or spuriously high scores to be distinguished.

Suggested Citation

  • Eduardo Doval & Pedro Delicado, 2020. "Identifying and Classifying Aberrant Response Patterns Through Functional Data Analysis," Journal of Educational and Behavioral Statistics, , vol. 45(6), pages 719-749, December.
    • Handle: RePEc:sae:jedbes:v:45:y:2020:i:6:p:719-749
    DOI: 10.3102/1076998620911941
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    References listed on IDEAS

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    2. Febrero-Bande, Manuel & de la Fuente, Manuel Oviedo, 2012. "Statistical Computing in Functional Data Analysis: The R Package fda.usc," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i04).
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    5. Chalmers, R. Philip, 2012. "mirt: A Multidimensional Item Response Theory Package for the R Environment," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i06).
    6. Tendeiro, Jorge N. & Meijer, Rob R. & Niessen, A. Susan M., 2016. "PerFit: An R Package for Person-Fit Analysis in IRT," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 74(i05).
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