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Corrected Rasch asymptotic standard errors for person ability estimates

R M Smith

    Journal of Outcome Measurement
    |November 6, 1998
    PubMed
    Summary
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    Standard errors for Rasch model person measures are often underestimated. This study found targeting and data misfit impact standard errors, but underestimation can be corrected. Results may not apply to other Rasch models.

    Area of Science:

    • Psychometrics
    • Educational Measurement
    • Statistical Modeling

    Background:

    • Rasch model calibration programs typically report asymptotic standard errors for person and item estimates.
    • These standard errors, while theoretically sound, can be affected by estimation constraints, instrument targeting, and data misfit.
    • The impact of these factors on person measure standard errors has not been previously investigated.

    Purpose of the Study:

    • To examine how estimation constraints, instrument targeting, and data misfit influence asymptotic standard errors for person measures.
    • To assess the accuracy of reported standard errors in the context of these factors using simulated data.

    Main Methods:

    • Utilized simulated dichotomous data to model Rasch psychometric analyses.
    • Manipulated factors including instrument targeting (offset between item difficulty and person ability) and data misfit.

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  • Calculated and compared asymptotic standard errors with observed standard deviations of person ability estimates.

    • Main Results:

    • Asymptotic standard errors systematically underestimated the observed standard deviation of person ability in the simulated data.
    • The degree of underestimation was generally small for well-targeted instruments with adequate sample sizes.
    • A simple linear function was identified as a potential method to correct for this underestimation.

    Conclusions:

    • The study highlights that standard errors reported from Rasch model calibrations may not fully capture the variability in person measures under certain conditions.
    • Instrument targeting and data quality are crucial considerations when interpreting person measure standard errors.
    • While the findings are specific to dichotomous data, they suggest a need for caution and potential adjustments when using standard errors from Rasch models.