Modified-likelihood estimation of the β-model

Koen Jochmans (1)

1 ECON - Département d'économie (Sciences Po)

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.

Keywords: Paired comparisons; Modified profile likelihood; fixed effects; Bradley-Terry model; β-model; Asymptotic bias; Matching; Network formation; Undirected random graph

Domains: Humanities and Social Sciences; Economics and Finance

Koen Jochmans. Modified-likelihood estimation of the β-model. 2016. ⟨hal-03393203⟩