Reducing Calibration Bias for Person Fit Assessment by Mixture Model Expansion

Measurement appropriateness concerns the question of whether the test or survey scale under consideration can provide a valid measure for a specific individual. An aberrant item response pattern would provide internal counterevidence against using the test/scale for this person, whereas a more typical item response pattern would imply a fit of the measure to the person. Traditional approaches, including the popular Lz person fit statistic, are hampered by their two-stage estimation procedure and the fact that the fit for the person is determined based on the model calibrated on data that include the misfitting persons. This calibration bias creates suboptimal conditions for person fit assessment. Solutions have been sought through the derivation of approximating bias-correction formulas and/or iterative purification procedures. Yet, here we discuss an alternative one-stage solution that involves calibrating a model expansion of the measurement model that includes a mixture component for target aberrant response patterns. A simulation study evaluates the approach under the most unfavorable and least-studied conditions for person fit indices, short polytomous survey scales, similar to those found in large-scale educational assessments such as the Program for International Student Assessment or Trends in Mathematics and Science Study.