Colloquium Series: Art Owen

Our upcoming event for the Statistics Colloquium Series is scheduled for Monday, March 23 from 12:00 – 1:00pm (ET) and will be an in-person presentation at Maxwell-Dworkin 134A/B. Lunch will be provided to guests following the talk. This week's speaker will be Art Owen of Stanford Department of Statistics.

Title: Composite likelihood for a very large scale binary regression with crossed random effects

 Abstract: Sparsely sampled crossed random effects models arise in review data, with effects for reviewers crossed with effects for items. 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.  Ongoing work extends this from probit to other GLMMs.

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