Dissertations, Theses, and Capstone Projects

Date of Degree

6-2026

Document Type

Doctoral Dissertation

Degree Name

Doctor of Philosophy

Program

Educational Psychology

Advisor

Keith Markus

Committee Members

David Rindskopf

Wei Wang

Tammy Trierweiler

Howard Everson

Subject Categories

Educational Psychology | Quantitative Psychology

Keywords

ordinal, longitudinal, simulation, cross-classified

Abstract

This is a simulation study that compares four models for analyzing three-level longitudinal cross-classified data with an ordinal outcome, treatment effect and a category-specific effect. The models include the cumulative model, the sequential model, the adjacent category model, and a metric model. Data were generated for each of the first three models with 27,000 generated datasets each, totaling 81,000. The datasets vary along three continuous variables: the number of level-3 units, the ratio of treatment groups to control groups, and the treatment effect size. The outcome has four ordinal response categories. Each model had two predictor variables: treatment and time. Each of the models (cumulative, sequential, adjacent category and metric) were run on each generated dataset. The main research question is how each model fared in terms of the bias, relative bias, and the empirical standard error of each response category, the root mean square (RMS) bias, a weighted kappa score, power of the treatment effect size as well as each category-specific effect for the time variable, Type I error of the treatment effect, model fit using the leave-one out information criterion, coverage of the treatment effect size (to illustrate how this is not an appropriate metric to use for comparison of ordinal models), and mean run time for a model. This study contributes to filling a gap in the literature on three-level, longitudinal ordinal models with cross-classification rather than the typical two-level nested model.

Download

Share

COinS