Fast and Accurate Binary Response Mixed Model Analysis via Expectation Propagation

Expectation propagation is a general prescription for approximation of integrals in statistical inference problems. Its literature is mainly concerned with Bayesian inference scenarios. However, expectation propagation can also be used to approximate integrals arising in frequentist statistical inference. We focus on likelihood-based inference for binary response mixed models and show that fast and accurate quadrature-free inference can be realized for the probit link case with multivariate random effects and higher levels of nesting. The approach is supported by asymptotic theory in which expectation propagation is seen to provide consistent estimation of the exact likelihood surface. Numerical studies reveal the availability of fast, highly accurate and scalable methodology for binary mixed model analysis.