Logistic Multidimensional Data Analysis for Ordinal Response Variables Using a Cumulative Link Function

Area of Science:

• Statistics
• Data Analysis
• Multivariate Statistics

Background:

• Ordinal response variables are common in many fields but challenging to analyze.
• Existing methods may not adequately capture the underlying continuous nature of ordinal data.
• A unified framework for analyzing different types of ordinal variables is needed.

Purpose of the Study:

• To present a novel multidimensional data analysis framework for ordinal response variables.
• To incorporate unsupervised and supervised learning methods within a single framework.
• To provide a robust estimation algorithm for the proposed models.

Main Methods:

• The framework assumes an underlying continuous latent variable for ordinal data, employing cumulative logit models.
• It distinguishes between dominance variables (inner product models) and proximity variables (distance models).
• An expectation-majorization-minimization algorithm is developed for parameter estimation.

Main Results:

• The proposed framework successfully analyzes multidimensional ordinal data.
• Empirical data sets demonstrate the framework's advantages.
• A simulation study validates the performance of the estimation algorithm.

Conclusions:

• The presented framework offers a versatile and powerful approach for analyzing ordinal response variables.
• The inclusion of both unsupervised and supervised methods enhances its applicability.
• The developed algorithm provides reliable parameter estimates for the proposed models.