Empirical Study of Power for LR vs. Wald Tests Under a Coincidence Paradigm for Binary Outcomes Restricted; Files Only

Abstract

Wald-type and likelihood ratio (LR) tests are commonly applied for evaluating structural hypotheses in logistic regression, such as coincidence, parallelism, and equal intercepts across subpopulations. While logistic regression is a standard framework for modeling binary outcomes, the discriminant function approach based on multivariable linear regression (MLR) offers enhanced flexibility and analytical tractability. This study develops an exact test for parallelism along with Wald-type test statistics for testing coincidence and equal intercepts of binary outcome regressions across groups. These are developed within the MLR framework for univariate and joint hypotheses by employing a discriminant function approach and leveraging the multivariate delta method for variance approximation. Through simulation studies across various settings, we compare empirical power and type I error rates of the MLR-based exact and Wald test statistics with conventional logistic regression-based LR and Wald tests. Results indicate that when the model is correctly specified, the MLR-based tests generally maintain appropriate type I error rates and demonstrate superior power. The discriminant function approach shows promise as a powerful alternative for hypothesis testing in binary outcome analysis, particularly when the parallelism test is of interest. Potential limitations and areas for further improvement are discussed.

Table of Contents

Introduction 1

Methods 3

1. Model Framework 3

1.1 Logistic Regression Model 3

1.2 Discriminant Function (MLR) Model 3

2. Hypothesis Testing Under the Logistic Regression Model 4

2.1 Coincidence 5

2.2 Parallelism 6

2.3 Equal Intercepts 7

3. Hypothesis Testing Under Discriminant Function Framework 8

4. Wald-type Tests and Multivariate Delta Method for Variance Estimation 13

Example 17

Simulation Studies and Results 21

Discussion 27

References 30

About this Master's Thesis

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School	Rollins School of Public Health
Department	Biostatistics
Subfield / Discipline	Biostatistics - MPH & MSPH
Degree	M.S.P.H.
Submission	Master's Thesis
Language	English
Research Field	Statistics
Parola chiave	Logistic regression Hypothesis testing Discriminant function approach Simulation study Multivariate delta method
Committee Chair / Thesis Advisor	Robert Lyles, Emory University
Committee Members	Ying Guo, Emory University

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