Dyadic data with ordered outcome variables

2025-07-22

AI Summary

This paper addresses the severe incidental parameter problem arising in ordered logit models for directed binary network data, where sender and receiver fixed effects vary arbitrarily across outcome categories—especially under network sparsity or low-frequency ordinal categories. We propose the first identifiable, consistent, and fixed-effect–free estimator for such models. Innovatively extending quadruple-difference conditional maximum likelihood to ordered choice network settings, we develop two estimators: the equally weighted triple-logit estimator (ETLE) and the pooled triple-logit estimator (PTLE). PTLE achieves asymptotic consistency under weaker identification conditions by pooling information across ordinal categories. Monte Carlo simulations demonstrate PTLE’s superiority over existing approaches. An empirical application to Dutch university student friendship networks reveals significant positive homophily by gender, smoking behavior, and field of study; in contrast, standard fixed-effect–ignoring estimators yield counterintuitive biases.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Causal Learning
• Game Theory and Economic Paradigms: Behavioral Game Theory

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Social Networks and Social Media: Social media analysis through the lenses of networks
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We consider ordered logit models for directed network data that allow for flexible sender and receiver fixed effects that can vary arbitrarily across outcome categories. This structure poses a significant incidental parameter problem, particularly challenging under network sparsity or when some outcome categories are rare. We develop the first estimation method for this setting by extending tetrad-differencing conditional maximum likelihood (CML) techniques from binary choice network models. This approach yields conditional probabilities free of the fixed effects, enabling consistent estimation even under sparsity. Applying the CML principle to ordered data yields multiple likelihood contributions corresponding to different outcome thresholds. We propose and analyze two distinct estimators based on aggregating these contributions: an Equally-Weighted Tetrad Logit Estimator (ETLE) and a Pooled Tetrad Logit Estimator (PTLE). We prove PTLE is consistent under weaker identification conditions, requiring only sufficient information when pooling across categories, rather than sufficient information in each category. Monte Carlo simulations confirm the theoretical preference for PTLE, and an empirical application to friendship networks among Dutch university students demonstrates the method's value. Our approach reveals significant positive homophily effects for gender, smoking behavior, and academic program similarities, while standard methods without fixed effects produce counterintuitive results.

Problem

• Estimating ordered logit models for directed network data
• Addressing incidental parameter problem in sparse networks
• Developing consistent estimators for varying outcome categories

Innovation

• Extends tetrad-differencing CML to ordered data
• Proposes ETLE and PTLE for fixed effects removal
• PTLE ensures consistency under weaker conditions