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…

An algorithm is described for fitting the DEDICOM model (proposed by R. A. Harshman in 1978) for the analysis of asymmetric data matrices. The method modifies a procedure proposed by Y. Takane (1985) to provide guaranteed monotonic convergence. The algorithm is based on a technique known as majorization. (SLD)

ORDMET is applicable to structures obtained from additive conjoint measurement designs, unfolding theory, general Fechnerian scaling, types of multidimensional scaling, and ordinal multiple regression. A description is obtained of the space containing all possible numerical representations which can satisfy the structure, size, and shape of which…

Beginning with the results of Girschick on the asymptotic distribution of principal component loadings and those of Lawley on the distribution of unrotated maximum likelihood factor loadings, the asymptotic distributions of the corresponding analytically rotated loadings is obtained. The principal difficulty is the fact that the transformation…

Commonality analysis is an attempt to understand the relative predictive power of the regressor variables, both individually and in combination. The squared multiple correlation is broken up into elements assigned to each individual regressor and to each possible combination of regressors. The elements have the property that the appropriate sums…