The Effect of Uncertainty of Item Parameter Estimation on Ability Estimates
- 1 June 1990
- journal article
- Published by Cambridge University Press (CUP) in Psychometrika
- Vol. 55 (2) , 371-390
- https://doi.org/10.1007/bf02295293
Abstract
The conventional method of measuring ability, which is based on items with assumed true parameter values obtained from a pretest, is compared to a Bayesian method that deals with the uncertainties of such items. Computational expressions are presented for approximating the posterior mean and variance of ability under the three-parameter logistic (3PL) model. A 1987 American College Testing Program (ACT) math test is used to demonstrate that the standard practice of using maximum likelihood or empirical Bayes techniques may seriously underestimate the uncertainty in estimated ability when the pretest sample is only moderately large.Keywords
This publication has 8 references indexed in Scilit:
- Approximation for Bayesian Ability EstimationJournal of Educational Statistics, 1988
- MAXIMUM LIKELIHOOD AND BAYESIAN PARAMETER ESTIMATION IN ITEM RESPONSE THEORYJournal of Educational Measurement, 1986
- Estimation of Two-Parameter Logistic Item Response CurvesJournal of Educational Statistics, 1984
- Marginal Maximum Likelihood Estimation of Item Parameters: Application of an EM AlgorithmPsychometrika, 1981
- Bayes Empirical BayesJournal of the American Statistical Association, 1981
- Approximate Bayesian methodsTrabajos de estadistica y de investigacion operativa, 1980
- Maximum Likelihood from Incomplete Data Via the EM AlgorithmJournal of the Royal Statistical Society Series B: Statistical Methodology, 1977
- Statistical theory for logistic mental test models with a prior distribution of abilityJournal of Mathematical Psychology, 1969