Accounting for item calibration error in computerized adaptive testing.

Abstract

In computerized adaptive testing (CAT), item parameter estimates derived from calibration studies are considered to be known and are used as fixed values for adaptive item selection and ability estimation. This is not completely accurate because these item parameter estimates contain a certain degree of error. If this error is random, the typical CAT procedure leads to standard errors of the final ability estimates that are too small. If the calibration error is large, it has been shown that the accuracy of the ability estimates is negatively affected due to the capitalization on chance problem, especially for extreme ability levels. In order to find a solution for this fundamental problem of CAT, we conducted a Monte Carlo simulation study to examine three approaches that can be used to consider the uncertainty of item parameter estimates in CAT. The first two approaches used a measurement error modeling approach in which item parameters were treated as covariates that contained errors. The third approach was fully Bayesian. Each of the approaches was compared with regard to the quality of the resulting ability estimates. The results indicate that each of the three approaches is capable of reducing bias and the mean squared error (MSE) of the ability estimates, especially for high item calibration errors. The Bayesian approach clearly outperformed the other approaches. We recommend the Bayesian approach, especially for application areas in which the recruitment of a large calibration sample is infeasible.