Title: Composite Likelihood for a Very Large Scale Binary Regression with Crossed Random Effects

Summary:

Sparsely sampled crossed random effects models arise in product review data, with effects for customers crossed with effects for products. The settings have no balance and the least squares algebra grows as N^(3/2) or worse. For generalized linear mixed models (GLMMs) there is the further difficulty of a very high dimensional integral. For instance we consider a likelihood with an integral over D~700,000 random effects, using only N~5,000,000 observations. The usual Laplace approximation method evaluates the D dimensional integral using just one integration point, and there is uncertainty about whether that is reliable. The MLE is infeasible in this problem and has only recently been shown to be consistent (Jiang, 2013). For a probit model, we develop a composite likelihood approach based on computing D one dimensional integrals. It is very scalable and we prove consistency which might not hold for the Laplace based method.

This is based on joint work with Ruggero Bellio and Swarnadip Ghosh and Cristiano Varin.

Bio:

Art Owen is the Max H. Stein Professor of Statistics at Stanford University. He is best known for inventing the empirical likelihood and for developing and studying randomized quasi-Monte Carlo methods. His research interests are centered on ways to measure uncertainty and ways to sample. He is a fellow of the American Statistical Association and the Institute of Mathematical Statistics. He received the 2020 Senior Noether Prize in nonparametric statistics from the ASA and the 2021 Gold Medal from the Statistical Society of Canada and became a SIAM Fellow in 2024.