An efficient standard error formula for the weighted likelihood estimator of ability

The weighted likelihood estimator (WLE; Warm, 1989) has become a very popular ability estimator in item response theory. It was developed to basically cancel the estimation bias of the maximum likelihood estimator (MLE) with short tests. However, some uncertainty remains about its standard error formula. Warm (1989) established the asymptotic equivalence of the standard errors of both MLE and WLE, but there exists actually various practical formulas for the latter (Magis & Raîche, 2012; Nydick, 2013; Partchev, 2012; Warm, 2007), leading obviously to confusion.
The purpose of this talk is to briefly sketch a general approach to derive a first-order approximation of the standard error of the WLE. Based on asymptotic adjustments of the law of large numbers and central limit theorem, a simple formula is derived. The efficiency of the latter is compared to aforementioned formulas by means of a simulation study under Rasch modeling. Preliminary results indicate that the derived formula has lower bias and RMSE than any other competing formula, especially with short tests. All formulas behave similarly with longer tests, as expected.