Improving Use of the 3-Parameter Logistic (3-Pl) Model in Item Response Theory Applications

• Activity Number: 529
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Social Statistics Section
• Author(s): Jerry L. Gorham*+
• Companies: Pearson, Inc.
• Keywords: logistic ; IRT ; likelihood ; item response theory ; exponential ; estimation

Abstract

In this paper I show that the 3-PL item response theory model, unlike the 1-PL or 2-PL models, is not an exponential family model because of the presence of the non-zero lower asymptote or "pseudo-guessing" parameter. It is known that under some conditions the likelihood function may be problematic for latent ability estimation. Traditionally, the issue has been cast in terms of the potential for multiple or non-definite maxima in the likelihood function and methods to ensure that the function will produce a unique estimate. This paper suggests that multiple or non-definite maxima are symptomatic of a more fundamental property of the model - the tendency for misfitting response vectors to distort the likelihood function, especially near the lower end of the scale. This model property can be considered an advantage, in some respects, over the 1-PL or 2-PL models, which remain convex regardless of the vector patterns.