Applications of the Analytically Derived Asymptotic Standard Errors of Item Response Theory Item Parameter Estimates

Abstract

The analytically derived asymptotic standard errors (SEs) of maximum likelihood (ML) item estimates can be approximated by a mathematical function without examinees’ responses to test items, and the empirically determined SEs of marginal maximum likelihood estimation (MMLE)/Bayesian item estimates can be obtained when the same set of items is repeatedly estimated from the simulation (or resampling) test data. The latter method will result in rather stable and accurate SE estimates as the number of replications increases, but requires cumbersome and time‐consuming calculations. Instead of using the empirically determined method, the adequacy of using the analytical‐based method in predicting the SEs for item parameter estimates was examined by comparing results produced from both approaches. The results indicated that the SEs yielded from both approaches were, in most cases, very similar, especially when they were applied to a generalized partial credit model. This finding encourages test practitioners and researchers to apply the analytically asymptotic SEs of item estimates to the context of item‐linking studies, as well as to the method of quantifying the SEs of equating scores for the item response theory (IRT) true‐score method. Three‐dimensional graphical presentation for the analytical SEs of item estimates as the bivariate function of item difficulty together with item discrimination was also provided for a better understanding of several frequently used IRT models.