Generalized Residuals for Item Response Theory Models with an Application to the National Assessment of Educational Progress

• Activity Number: 39
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Social Statistics Section
• Author(s): Sandip Sinharay*+ and Shelby Haberman
• Companies: CTB/McGraw-Hill and Educational Testing Service
• Keywords: IRT ; two-parameter logistic model ; Rasch model ; three-parameter logistic model ; NAEP

Abstract

Generalized residuals (Haberman, 1976) are employed in the analysis of contingency tables to examine possible sources of model misfit. They have typically been applied to log-linear models and to latent-class models. A general approach to generalized residuals is developed for a very general class of models for contingency tables. To illustrate their use, generalized residuals are applied to models based on item response theory (IRT) models. IRT models are commonly applied to analysis of standardized achievement or aptitude tests (e.g., Lord, 1980; Junker, 1993). To obtain a realistic perspective on application of the proposed generalized residuals, data from operational tests are employed. One of the data sets is from the National Assessment of Educational Progress (NAEP), which is an ongoing survey of the academic achievement of school students in the US in a number of subject areas.