title: Efficient Standard Error Formulas of Ability Estimators with Dichotomous Item Response Models.
abstract: This paper focuses on the computation of asymptotic standard errors (ASE) of ability estimators with dichotomous item response models. A general framework is considered, and ability estimators are defined from a very restricted set of assumptions and formulas. This approach encompasses most standard methods such as maximum likelihood, weighted likelihood, maximum a posteriori, and robust estimators. A general formula for the ASE is derived from the theory of M-estimation. Well-known results are found back as particular cases for the maximum and robust estimators, while new ASE proposals for the weighted likelihood and maximum a posteriori estimators are presented. These new formulas are compared to traditional ones by means of a simulation study under Rasch modeling.
authors.affiliation: Department of Education (B32), University of Liège, Boulevard du Rectorat 5, 4000,  Liège, Belgium. david.magis@ulg.ac.be.|KU Leuven, Leuven, Belgium. david.magis@ulg.ac.be.
authors.forename: David
authors.initials: D
authors.lastname: Magis
mesh_terms: D001499:Bayes Theorem; D003198:Computer Simulation; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D011594:Psychometrics
keywords: Bayesian estimation; Robust estimation; ability estimation; asymptotic standard error; item response theory; maximum likelihood; weighted likelihood