Estimating multiple-membership logit models with mixed effects: indirect inference versus data cloning

ABSTRACT

Multiple-membership logit models with random effects are models for clustered binary data, where each statistical unit can belong to more than one group. The likelihood function of these models is analytically intractable. We propose two different approaches for parameter estimation: indirect inference and data cloning (DC). The former is a non-likelihood-based method which uses an auxiliary model to select reasonable estimates. We propose an auxiliary model with the same dimension of parameter space as the target model, which is particularly convenient to reach good estimates very fast. The latter method computes maximum likelihood estimates through the posterior distribution of an adequate Bayesian model, fitted to cloned data. We implement a DC algorithm specifically for multiple-membership models. A Monte Carlo experiment compares the two methods on simulated data. For further comparison, we also report Bayesian posterior mean and Integrated Nested Laplace Approximation hybrid DC estimates. Simulations show a negligible loss of efficiency for the indirect inference estimator, compensated by a relevant computational gain. The approaches are then illustrated with two real examples on matched paired data.

KEYWORDS:

• Bradley–Terry models
• intractable likelihood
• integrated nested Laplace approximation
• non-hierarchical random effects models

SUBJECT CLASSIFICATION CODES:

• 62F12
• 62J12

Acknowledgements

The authors are grateful to Alan Agresti and David Firth for the useful discussions. We acknowledge the Associate Editor and the referee for their suggestions, which have led to major improvements of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Anna Gottard  http://orcid.org/0000-0002-8246-4962.