Categorical data become increasingly ubiquitous in the modern big data era. In this dissertation, we propose novel statistical learning and inference methods for large-scale categorical data, focusing on latent variable models and their applications to psychometrics. In psychometric assessments, the subjects' underlying aptitude often cannot be…

The problem of mapping items to skills is gaining interest with the emergence of recent techniques that can use data for both defining this mapping, and for refining mappings given by experts. We investigate the problem of refining mapping from an expert by combining the output of different techniques. The combination is based on a partition tree…

The problem of dimensionality with respect to Raven's Advanced Progressive Matrices (APM) specifically and, more generally, "g" or fluid intelligence, has been a long-standing issue. The present article reports two studies examining the dimensionality of both the original Set II of the APM (n = 506) and a short form (n = 644), using principal…

The sample assessment items in this volume are sorted according to the strands of number and operations, algebra, geometry, measurement, and data analysis and probability. Because one goal of assessment is to determine students' abilities to communicate mathematically, the writing team suggests ways to extend or modify multiple-choice and…