Title of Document: RANDOMIZATION-BASED INFERENCE ABOUT LATENT VARIABLES FROM COMPLEX SAMPLES: THE CASE OF TWO-STAGE SAMPLING

In large-scale assessments, such as the National Assessment of Educational Progress (NAEP), plausible values based on Multiple Imputations (MI) have been used to estimate population characteristics for latent constructs under complex sample designs. Mislevy (1991) derived a closed-form analytic solution for a fixed-effect model in creating plausible values assuming a classical test theory model and a stratified student sample and proposed an analogous solution for a random-effects model to be applied with a two-stage student sample design. The research reported here extends the discussion of this random-effects model under the classical test theory framework. Under the simplified assumption of known population parameters, analytical solutions are provided for multiple imputations in the case of the classical test theory measurement model and two-stage sampling and their properties are verified in reconstructing population properties for the unobservable latent variables. With the more practical assumptions of unknown population and cluster means, this study empirically examines the reconstruction of population attributes. Next, properties of sample statistics are examined. Specifically, this research explores th