Use of Bayesian Priors to Assist Ability Estimation for Nonexistent Maximum Likelihoods in 3-Parameter Logistic Models for Item Response Theory Applications

• Activity Number: 423
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Social Statistics Section
• Author(s): Jerry Gorham*+ and Huijuan Meng and Marijana Dragan
• Companies: Pearson, Inc. and Pearson, Inc. and National Council of State Boards of Nursing
• Keywords: logistic ; IRT ; likelihood ; parametric ; bayesian

Abstract

In item response theory applications to standardized tests, examinee response vectors sometimes produce maximum likelihood functions of examinee ability with non-existent maximums. In these cases, few options are available to the applied researcher in assigning a score to the examinee, particularly when the number-correct score is not extremely low but the response vector is moderately to highly aberrant. This situation is not uncommon when applying the 3-parameter logistic (3-PL) item response theory model (Gorham, 2011, JSM Proceedings). Misfitting response vectors for the 3-PL model often distort the non-convex likelihood functions near the lower end of the scale and create problems with the direct estimation of ability. We suggest that an alternative is to assist estimation using minimally informative ("barely-fitting") priors applied to the likelihoods in order to obtain maximum a posteriori estimates. Bias and RMSEs between true and estimated abilities based on simulations are compared to evaluate the effectiveness of this method under four conditions for test length.