A Nonlinear Mixed-Model Approach to Item Response Theory Models

• Activity Number: 8
• Type: Invited
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Consulting
• Author(s): Ling Sam He and Peter M. Bentler*+ and Eric J. C. Wu and Patrick Mair
• Companies: Multivariate Software, Inc. and University of California at Los Angeles and Multivariate Software, Inc. and Vienna University of Economics & Business Administration
• Keywords: generalized nonlinear mixed models, item response theory

Abstract

Item Response Theory (IRT) has become the standard methodology for developing scales and measurement instruments in national testing programs. Conventional IRT is limited in its ability to model covariates of item and person characteristics. De Boeck and Wilson (2004) proposed a number of ways to mitigate this shortcoming. Their approach does not address a general class of IRT models. We propose a new IRT modeling framework using a Generalized Nonlinear Mixed Models approach. This framework allows item covariates and subject covariates and possibly their interactions to be added to a variety of standard IRT models. In addition, the proposed nonlinear mixed model methodology can be extended to more complex nested IRT models, such as multilevel IRT.