Corrected Rasch asymptotic standard errors for person ability estimates.

Abstract

Most calibration programs designed for the family of Rasch psychometric models report the asymptotic standard errors for person and item measure estimates resulting from the calibration process. Although these estimates are theoretically correct, they may be influenced by any number of factors, e.g., restrictions due to the loss of degrees of freedom in estimation, targeting of the instrument, i.e., the degree of offset between mean item difficulty and mean person ability, and the presence of misfit in the data. The effect of these factors on the standard errors reported for the person has not been previously reported. The purpose of this study was to investigate the effects of these three factors on the asymptotic standard errors for person measures using simulated data. The results indicate that asymptotic errors systematically underestimate the observed standard deviation of ability in simulated data, though this underestimation is usually small for targeted instruments with reasonable sample size. However, the underestimation can easily be corrected with a simple linear function. These simulations use only dichotomous data and the results may not generalize to the rating scale and partial credit models.