A pairwise likelihood approach to estimation in multilevel probit models

A pairwise likelihood (PL) estimation procedure is examined in multilevel models with binary responses and probit link. The PL is obtained as the product of bivariate likelihoods for within-cluster pairs of observations. The resulting estimator still enjoys desirable asymptotic properties such as consistency and asymptotic normality. Therefore, with this approach a compromise between computational burden and loss of efficiency is sought. A simulation study was conducted to compare PL with second-order penalized quasi-likelihood (PQL2) and maximum (marginal) likelihood (ML) estimation methods. The loss of efficiency of the PL estimator is found to be generally moderate. Also, PL tends to show more robustness against convergence problems than PQL2.

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