Alternative estimating procedures for multiple membership logit models with mixed effects: indirect inference and data cloning

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