RANDOMIZATION-BASED INFERENCE ABOUT LATENT-VARIABLES FROM COMPLEX SAMPLES

Standard procedures for drawing inferences from complex samples do not apply when the variable of interest theta cannot be observed directly, but must be inferred from the values of secondary random variables that depend on theta-stochastically. Examples are proficiency variables in item response models and class memberships in latent class models. Rubin's "multiple imputation" techniques yield approximations of sample statistics that would have been obtained, had theta been observable, and associated variance estimates that account for uncertainty due to both the sampling of respondents and the latent nature of theta. The approach is illustrated with data from the National Assessment for Educational Progress.