Participants in achievement tests or psychometric scales can be naturally divided into various sub-groups such as gender, race, social economic status, school district, etc. In order to make meaningful comparison between groups, each item in the test/scale should measure the same underlying construct for participants came from different groups.…

This dissertation is composed of projects on three aspects of gathering and learning from data in the social sciences: drawing representative samples, taking valid measurement, and making warranted inductive inferences. Chapter one studies the challenge of drawing representative human samples. It is well documented that most samples used by…

Compressed sensing (CS) is an emerging signal acquisition framework that goes against the traditional Nyquist sampling paradigm. CS demonstrates that a sparse, or compressible, signal can be acquired using a low rate acquisition process. Since noise is always present in practical data acquisition systems, sensing and reconstruction methods are…

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…