Modified-likelihood estimation of the b-model
Sciences Po Economics Discussion Papers
JOCHMANS Koen - Département d'économie (Auteur)
Sciences Po Economics Discussion Papers : 2016-01
asymptotic bias, b-model, Bradley-Terry model, fixed effects, modified profile likelihood, paired comparisons, matching, network formation, undirected random graph
We consider point estimation and inference based on modifications of the profile likelihood in models for dyadic interactions between agents featuring n agent-specific parameters. This setup covers the b-model of network formation and generalizations thereof. The maximum-likelihood estimator of such models has bias and standard deviation of O(n−1) and so is asymptotically biased. Estimation based on modified likelihoods leads to estimators that are asymptotically unbiased and likelihood-ratio tests that exhibit correct size. We apply the modifications to versions of the b-model for network formation and of the Bradley-Terry model for paired comparisons.