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Adjusted Rasch person-fit statistics.

Dimiter M Dimitrov1, Richard M Smith

  • 1College of Education and Human Development, George Mason University, 4400 University Drive, MS 4B3, Fairfax, VA 22030-4444, USA. ddimitro@gmu.edu

Journal of Applied Measurement
|April 25, 2006
PubMed
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Adjusted person-fit statistics (t* and Z3*) slightly outperform original versions (t and Z3) in detecting response anomalies. However, the non-parametric HT statistic significantly outperforms all parametric methods on longer tests.

Area of Science:

  • Psychometrics
  • Educational Measurement
  • Statistical Modeling

Background:

  • Person-fit statistics assess response behavior consistency within the dichotomous Rasch model (RM).
  • Common parametric statistics include the unweighted person-fit statistic (t) and the likelihood-based statistic (Z3).
  • Aberrant response patterns can compromise test validity.

Purpose of the Study:

  • To compare the power of adjusted parametric person-fit statistics (t* and Z3*) against their original counterparts (t and Z3).
  • To evaluate the performance of these parametric statistics against a non-parametric statistic (HT).
  • To assess detection power for aberrant response patterns in short tests (10, 20, 30 items).

Main Methods:

  • Adjustment of t and Z3 statistics using symmetric functions in the dichotomous Rasch model.

Related Experiment Videos

  • Simulation of unidimensional Rasch data.
  • Comparison of detection power across different test lengths and Type I error rates (0.10 and 0.05).

    • Main Results:

    • Adjusted statistics (t* and Z3*) showed slightly superior performance over original t and Z3.
    • The non-parametric HT statistic substantially outperformed t, Z3, t*, and Z3* for 20- and 30-item tests.
    • HT did not outperform parametric statistics for very short (10-item) tests.

    Conclusions:

    • Adjusting parametric person-fit statistics offers marginal improvement in detecting aberrant responses.
    • The non-parametric HT statistic is a more powerful tool for detecting response anomalies in moderately long tests.
    • Careful consideration of test length is crucial when selecting person-fit statistics.