Chris Muris, Cavit Pakel, Qichen Zhang
arXiv 22 Jul 2025 · Econometrics
arXiv:2507.16689 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Muris, Chris (2017) Estimation in the Fixed-Effects Ordered Logit Model self | 1.000 | 5 | 3 | 100% |
| 2 | Jochmans, Koen (2018) Semiparametric Analysis of Network Formation | 0.885 | 13 | 6 | 69% |
| 3 | Charbonneau, Karyne B (2017) Multiple Fixed Effects in Binary Response Panel Data Models | 0.843 | 3 | 3 | 100% |
| 4 | Baetschmann, Gregori (2012) Identification and Estimation of Thresholds in the Fixed Effects Ordered Logit Model | 0.737 | 3 | 2 | 100% |
| 5 | Botosaru, Irene, Muris, Chris, Pendakur, Krishna (2023) Identification of Time-Varying Transformation Models with Fixed Effects, with an Application to Unobserved Heterogeneity in Reso… self | 0.737 | 3 | 2 | 100% |
| 6 | Van Duijn, Marijtje A.J., Gile, Krista J., Handcock, Mark S (2009) A Framework for the Comparison of Maximum Pseudo-Likelihood and Maximum Likelihood Estimation of Exponential Family Random Graph… | 0.737 | 3 | 2 | 100% |
| 7 | Baetschmann, Gregori, Staub, Kevin E., Winkelmann, Rainer (2015) Consistent Estimation of the Fixed Effects Ordered Logit Model | 0.644 | 2 | 2 | 100% |
| 8 | Das, Marcel (1999) A Panel Data Model for Subjective Information on Household Income Growth | 0.644 | 2 | 2 | 100% |
| 9 | Graham, Bryan S (2017) An Econometric Model of Network Formation with Degree Heterogeneity | 0.644 | 2 | 2 | 100% |
| 10 | Johnson, Edward (2004) Panel Data Models with Discrete Dependent Variables | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 15 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Triadic Network Formation | 0.405 | 1 | 1 |