A Note on the Conversion of Item Parameters Standard Errors

Abstract

The relations among alternative parameterizations of the binary factor analysis (FA) model and two-parameter logistic (2PL) item response theory (IRT) model have been thoroughly discussed in literature. However, the conversion formulas widely available are mainly for transforming parameter estimates from one parameterization to another. There is a lack of discussion about the standard error (SE) conversion among different parameterizations, when SEs of IRT model parameters are often of immediate interest to practitioners. This article provides general formulas for computing the SEs of transformed parameter values, when these parameters are transformed from FA to IRT models. These formulas are suitable for unidimensional 2PL, multidimensional 2PL, and bi-factor 2PL models. A simulation study is conducted to verify the formula by providing empirical evidence. A real data example is given in the end for an illustration.