Real data are unlikely to be exactly normally distributed. Ignoring non-normality will cause misleading and unreliable parameter estimates, standard error estimates, and model fit statistics. For non-normal data, researchers have proposed a distributionally-weighted least squares (DLS) estimator to combines the normal theory based generalized…

Managing and analysing large qualitative datasets pose a particular challenge for researchers seeking a consistent and rigorous approach to qualitative data analysis. This paper describes and demonstrates the development and adoption of a matrix tool to guide the qualitative data analysis of a large sample (N = 122) of interview data. The paper…

The standard methodology for many large-scale assessments in education involves regressing latent variables on numerous contextual variables to estimate proficiency distributions. To reduce the number of contextual variables used in the regression and improve estimation, we propose and evaluate principal component analysis on the covariance matrix…

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 purpose of this article is to describe the analytic process of a method of data collection known as Q Methodology. This method is an alternative method in collecting data especially suited to research on "points of views" (Coogan & Herrington, 2011, p. 24). The analytic process of Q methodology involves factor analysis, a…

Collapsing categories is a commonly used data reduction technique; however, to date there do not exist principled methods to determine whether collapsing categories is appropriate in practice. With ordinal responses under the partial credit model, when collapsing categories, the true model for the collapsed data is no longer a partial credit…

The article aims to study the verbal collaborative interaction in both symmetrical and asymmetrical dyads according to specific individual cognitive competence. The interaction was analyzed in terms of cognitive and non-cognitive aspects. 19 dyads (38 fifth and sixth graders) participated. First, they individually solved a set of logical problems…