MULTILEVEL ITEM RESPONSE MODELS - AN APPROACH TO ERRORS-IN-VARIABLES REGRESSION

In this article we show how certain analytic problems that arise when one attempts to use latent variables as outcomes in regression analyse s can be addressed by taking a multilevel perspective on item response modeling. Under a multilevel, or hierarchical, perspective we cast th e item response model as a within-student model and the student popula tion distribution as a between-student model. Taking this perspective leads naturally to an extension of the student population model to inc lude a range of student level variables, and it invites the possibilit y of further extending the models to additional levels so that multile vel models can be applied with latent outcome variables. In the two-le vel case, he model that we employ is formally equivalent to the plausi ble value procedures that are used as part of the National Assessment of Educational Progress (NAEP), but we present the method for a differ ent class of measurement models, and we use a simultaneous estimation method rather than two-step estimation. In our application of the mode ls to the appropriate treatment of measurement error in the dependent variable of a between-student regression, we also illustrate the adequ acy of some approximate procedures that are used in NAEP.