Fast and Accurate Estimation of Non-Nested Binomial Hierarchical Models Using Variational Inference
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Estimating non-linear hierarchical models can be computationally burdensome in the presence of large datasets and many non-nested random effects. Popular inferential techniques may take hours to fit even relatively straightforward models. This paper provides two contributions to scalable and accurate inference. First, I propose a new mean-field algorithm for estimating logistic hierarchical models with an arbitrary number of non-nested random effects. Second, I propose "marginally augmented variational Bayes" (MAVB) that further improves the initial approximation through a post-processing step. I show that MAVB provides a guaranteed improvement in the approximation quality at low computational cost and induces dependencies that were assumed away by the initial factorization assumptions. I apply these techniques to a study of voter behavior. Existing estimation took hours whereas the algorithms proposed run in minutes. The posterior means are well-recovered even under strong factorization assumptions. Applying MAVB further improves the approximation by partially correcting the under-estimated variance. The proposed methodology is implemented in an open source software package.
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