Efficient standard error formulas of ability estimators with dichotomous item response models.(English)Zbl 1342.62189

Summary: 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.

MSC:

 62P15 Applications of statistics to psychology 62F10 Point estimation 62F15 Bayesian inference 62F35 Robustness and adaptive procedures (parametric inference)

Software:

catR; ConQuest; R; sandwich; PP; irtoys; catIrt
Full Text:

References:

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