Multilevel Item Response Theory Models

Abstract

The item response data structure is hierarchical since item responses are nested within respondents. Often respondents are also grouped into larger units and variables are available that characterize the respondents and the higher-level units. An item response modeling framework is discussed that includes a multilevel population model for the respondents and takes such a hierarchical data structure into account. An important application area is in education, where response observations are grouped in students and students grouped in schools. Several school effectiveness research studies are discussed. The hierarchical item response model is extended in several directions to handle latent explanatory variables, model latent individual growth, and identify clusters of respondents. 6.1 Introduction: School Effectiveness Research School effectiveness research is concerned with exploring differences within and between schools. The objective is to investigate the relationship between explanatory and outcome factors. This involves choosing an outcome variable, such as student's ability, and studying differences among schools after adjusting for relevant background variables. Interest is focused on the relative size of school differences and the factors that explain these differences and influence student learning. Typically, in school effectiveness research, students are nested in class-generally acceptable statistical model in the assessment of school effectiveness therefore requires the deployment of multilevel analysis techniques. A multilevel model takes the hierarchical structure into account, and variance components are modeled at each sampling level. As a result, homogeneity of results of individual pupils in the same school is accounted for since pupils in the same school share common experiences. Specifically, a multilevel model © 141 and Behavioral Sciences, DOI 10.1007/978-1-4419-0742-4_6, J.-P. Fox, Bayesian Item Response Modeling: Theory and Applications, Statistics for Social Springer Science+Business Media, LLC 2010 rooms, classrooms in schools, schools within school systems, and so on. A