Standard Errors of IRT Linking Coefficients in Test Equating for Mixed-Format Tests

Methods for estimating IRT linking coefficients in single-format test equating have been extended to mixed-format tests, yet little research has examined the standard errors of these coefficients. This study demonstrates the application of the bootstrap and multiple imputation methods, and reformulates the delta method, to estimate the standard errors of linking coefficients in test equating for mixed-format tests. Using simulated and real data, we evaluated the performance of the three approaches and examined the impact of common-item format on the estimates of standard errors. Results indicated that all three methods produced standard errors that were extremely close to the criterion empirical standard errors. The standard errors that were estimated based on the common items composed solely polytomous items were generally smaller than those derived based on the common items with only dichotomous item or mixed dichotomous and polytomout items, which was especially pronounced salient when using the moment equating methods.