Maximum Augmented Empirical Likelihood Estimation of Categorical Marginal Models for Large Sparse Contingency Tables

Area of Science:

• Statistics
• Computational Statistics
• Data Analysis

Background:

• Categorical marginal models (CMMs) are effective for dependent categorical data when dependencies are not the primary focus.
• Maximum likelihood (ML) estimation for CMMs becomes computationally infeasible with an increasing number of variables due to exponentially growing contingency tables.
• Maximum empirical likelihood (MEL) estimation offers an alternative with optimal asymptotic efficiency but struggles with large, sparse tables.

Purpose of the Study:

• To address the breakdown of maximum empirical likelihood (MEL) estimation in large, sparse contingency tables.
• To introduce a novel estimation method for categorical marginal models (CMMs) that is computationally feasible for large datasets.
• To provide a robust statistical tool for analyzing complex categorical data structures.

Main Methods:

• Development of maximum augmented empirical likelihood (MAEL) estimation.
• MAEL involves augmenting the empirical likelihood support with carefully selected cells.
• Simulation studies were conducted to evaluate the performance of MAEL.

Main Results:

• Maximum empirical likelihood (MEL) estimation was shown to be unreliable for large, sparse contingency tables.
• The proposed maximum augmented empirical likelihood (MAEL) method demonstrates good finite sample performance.
• MAEL is effective even for very large contingency tables, overcoming the limitations of previous methods.

Conclusions:

• Maximum augmented empirical likelihood (MAEL) estimation provides a viable and robust alternative to maximum likelihood (ML) and maximum empirical likelihood (MEL) for CMMs.
• MAEL is particularly well-suited for analyzing large and sparse categorical datasets where traditional methods fail.
• The proposed method enhances the applicability of CMMs in complex statistical modeling scenarios.