Estimating binary multilevel models through indirect inference1
Non-normal multilevel models usually lead to intractable likelihood functions, as they involve integrals without closed-form solution. A flexible approach for their estimation consists in replacing the initial model with an approximated one which is easier to handle, as the quasi-likelihood method with a linearising transformation proposed by Goldstein (1991) or the approximated likelihood developed by Longford (1988). Simulation studies of Rodriguez and Goldman (1995) have shown the occurrence of large biases when such approximated methods are applied; recent works propose second-order corrections (Goldstein and Rasbash, 1996) and iterative bootstrap bias correction (Goldstein, 1996) to improve the estimates. In order to correct for the asymptotic bias of the quasi-likelihood estimator, we propose the use of indirect inference Gourieroux et al., 1993; Gallant and Tauchen, 1994), which uses simulations performed under the initial model to correct the estimates derived from the auxiliary (approximated) model. We show asymptotic equivalence between indirect inference and iterative bootstrap Kuk, 1995) estimators in the just identified case. Some Monte Carlo experiments show the performance of the indirect inference estimator, comparing its correction with the bootstrap one.
indirect inference bias correction multilevel logit models