Efficient Computation of High-Dimensional Penalized Generalized Linear Mixed Models by Latent Factor Modeling of the Random Effects

• Activity Number: 204 - Statistical Computing by Deep Learning and Penalization
• Type: Contributed
• Date/Time: Monday, August 8, 2022 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Hillary M. Heiling* and Naim U. Rashid and Quefeng Li and Joseph G Ibrahim
• Companies: University of North Carolina Chapel Hill and University of North Carolina Chapel Hill and University of North Carolina Chapel Hill and University of North Carolina
• Keywords: generalized linear mixed models; variable selection; factor model; high dimension

Abstract

Modern biomedical datasets are increasingly high dimensional and exhibit complex correlation structures. Generalized Linear Mixed Models (GLMMs) have long been employed to account for such dependencies. However, proper specification of the fixed and random effects in GLMMs is increasingly difficult in high dimension, and computational complexity grows with increasing dimension of the random effects. We present a novel reformulation of the GLMM using a factor model decomposition of the random effects, enabling scalable computation of GLMMs in high dimensions by reducing the latent space from a large number of random effects to a smaller set of common factors. We also extend our prior work to estimate model parameters using a modified version of the Monte Carlo Expectation Conditional Minimization algorithm, allowing us to perform variable selection on both the fixed and random effects simultaneously. We show through simulation that through this factor model decomposition, our method can fit high dimensional penalized GLMMs faster than comparable methods and more easily scale to larger dimensions not previously seen in existing approaches.