Item Analysis by the Hierarchical Generalized Linear Model

Abstract

The hierarchical generalized linear model (HGLM) is presented as an explicit, two‐level formulation of a multilevel item response model. In this paper, it is shown that the HGLM is equivalent to the Rasch model and that, characteristic of the HGLM, person ability can be expressed in the form of random effects rather than parameters. The two‐level item analysis model is presented as a latent regression model with person‐characteristic variables. Furthermore, it is shown that the two‐level HGLM model can be extended to a three‐level latent regression model that permits investigation of the variation of students' performance across groups, such as is found in classrooms and schools, and of the interactive effect of person‐and group‐characteristic variables.