Gaussian Variational Approximation for Ordinal Data with Crossed Random Effects

We consider large scale ordinal response models with crossed random effects. We use a Gaussian variational approximation simplifying the associated optimization problem using the delta method, and other approximations to calculate both point estimates and standard errors whilst maintaining computational scalability. We apply our methodology on large scale recommender systems and are able to fit the proposed model with millions of observations within minutes on a standard laptop computer. Experiments show that estimation using this methodology scales close to linearly, and a factor better than the Penalized Quasi-Likelihood (PQL), with the number of observations, while maintaining an accuracy close to the Laplace Approximation (LA) with only slightly more underestimated variance parameters compared to LA in these large-scale settings. Our method thereby enables estimation of accurate, large scale ordinal models with crossed random effects.