Article1992

Bayesian Estimation of Normal Ogive Item Response Curves Using Gibbs Sampling

419 citations0/0 files storedJournal of Educational Statistics

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Psychometric Methodologies and Testing Statistical Distribution Estimation and Applications Statistical Methods and Bayesian Inference

Abstract

The problem of estimating item parameters from a two-parameter normal ogive model is considered. Gibbs sampling (Gelfand & Smith, 1990) is used to simulate draws from the joint posterior distribution of the ability and item parameters. This method gives marginal posterior density estimates for any parameter of interest; these density estimates can be used to judge the accuracy of normal approximations based on maximum likelihood estimates. This simulation technique is illustrated using data from a mathematics placement exam.

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References

1969Statistical Theories of Mental Test Scores 1981Marginal Maximum Likelihood Estimation of Item Parameters: Application of an EM Algorithm 1987Stochastic Simulation 1984Item Response Theory: Principles and Applications 1985Item Response Theory 1989Latent Variable Models and Factor Analysis 1970Fitting a Response Model for n Dichotomously Scored Items 1952A theory of test scores.

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