ON THE ESTIMATION OF HIERARCHICAL LATENT LINEAR MODELS FOR LARGE SCALE ASSESSMENTS

Abstract

A hierarchical latent regression model is suggested to estimate nested and nonnested relationships in complex samples such as found in the National Assessment of Educational Progress (NAEP). The proposed model aims at improving both parameters and variance estimates via a two-level hierarchical linear model. This model falls naturally within the set of models used in most large scale surveys, in that all of them are special cases of the hierarchical latent regression model. The model parameter estimates are obtained via the expectation-maximization (EM) algorithm. An example with NAEP data is presented and results of parameter estimation and standard errors are compared with results from operational procedures of NAEP.