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Some Remarks on Applications of Tests for Detecting A Change Point to Psychometric Problems

Author

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  • Sandip Sinharay

    (Pacific Metrics Corporation
    Educational Testing Service)

Abstract

Tests for a change point (e.g., Chen and Gupta, Parametric statistical change point analysis (2nd ed.). Birkhuser, Boston, 2012; Hawkins et al., J Qual Technol 35:355–366, 2003) have recently been brought into the spotlight for their potential uses in psychometrics. They have been successfully applied to detect an unusual change in the mean score of a sequence of administrations of an international language assessment (Lee and von Davier, Psychometrika 78:557–575, 2013) and to detect speededness of examinees (Shao et al., Psychometrika, 2015). The differences in the type of data used, the test statistics, and the manner in which the critical values were obtained in these papers lead to questions such as “what type of psychometric problems can be solved by tests for a change point?” and “what test statistics should be used with tests for a change point in psychometric problems?” This note attempts to answer some of these questions by providing a general overview of tests for a change point with a focus on application to psychometric problems. A discussion is provided on the choice of an appropriate test statistic and on the computation of a corresponding critical value for tests for a change point. Then, three real data examples are provided to demonstrate how tests for a change point can be used to make important inferences in psychometric problems. The examples include some clarifications and remarks on the critical values used in Lee and von Davier (Psychometrika, 78:557–575, 2013) and Shao et al. (Psychometrika, 2015). The overview and the examples provide insight on tests for a change point above and beyond Lee and von Davier (Psychometrika, 78:557–575, 2013) and Shao et al. (Psychometrika, 2015). Thus, this note extends the research of Lee and von Davier (Psychometrika, 78:557–575, 2013) and Shao et al. (Psychometrika, 2015) on tests for a change point.

Suggested Citation

  • Sandip Sinharay, 2017. "Some Remarks on Applications of Tests for Detecting A Change Point to Psychometric Problems," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1149-1161, December.
  • Handle: RePEc:spr:psycho:v:82:y:2017:i:4:d:10.1007_s11336-016-9531-z
    DOI: 10.1007/s11336-016-9531-z
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    References listed on IDEAS

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    1. Yi-Hsuan Lee & Shelby Haberman, 2013. "Harmonic Regression and Scale Stability," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 815-829, October.
    2. Ashish Sen & S. Srivastava, 1975. "On tests for detecting change in mean when variance is unknown," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 27(1), pages 479-486, December.
    3. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    4. Arturo Estrella & Anthony P. Rodrigues, 2005. "One-sided test for an unknown breakpoint: theory, computation, and application to monetary theory," Staff Reports 232, Federal Reserve Bank of New York.
    5. Yi-Hsuan Lee & Alina Davier, 2013. "Monitoring Scale Scores over Time via Quality Control Charts, Model-Based Approaches, and Time Series Techniques," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 557-575, July.
    6. Sandip Sinharay, 2016. "Person Fit Analysis in Computerized Adaptive Testing Using Tests for a Change Point," Journal of Educational and Behavioral Statistics, , vol. 41(5), pages 521-549, October.
    7. Gombay, Edit & Horváth, Lajos, 1996. "On the Rate of Approximations for Maximum Likelihood Tests in Change-Point Models," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 120-152, January.
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