Francis K. C. Hui

Mitchell L. Prevett, Francis K. C. Hui, Zhi Yang Tho et al.

Linear mixed models are widely used for clustered data, but their reliance on parametric forms limits flexibility in complex and high-dimensional settings. In contrast, gradient boosting methods achieve high predictive accuracy through nonparametric estimation, but do not accommodate clustered data structures or provide uncertainty quantification. We introduce Gradient Boosted Mixed Models (GBMixed), a framework and algorithm that extends boosting to jointly estimate mean and variance components via likelihood-based gradients. In addition to nonparametric mean estimation, the method models both random effects and residual variances as potentially covariate-dependent functions using flexible base learners such as regression trees or splines, enabling nonparametric estimation while maintaining interpretability. Simulations and real-world applications demonstrate accurate recovery of variance components, calibrated prediction intervals, and improved predictive accuracy relative to standard linear mixed models and nonparametric methods. GBMixed provides heteroscedastic uncertainty quantification and introduces boosting for heterogeneous random effects. This enables covariate-dependent shrinkage for cluster-specific predictions to adapt between population and cluster-level data. Under standard causal assumptions, the framework enables estimation of heterogeneous treatment effects with reliable uncertainty quantification.

Łukasz Kidziński, Francis K. C. Hui, David I. Warton et al.

Unmeasured or latent variables are often the cause of correlations between multivariate measurements, which are studied in a variety of fields such as psychology, ecology, and medicine. For Gaussian measurements, there are classical tools such as factor analysis or principal component analysis with a well-established theory and fast algorithms. Generalized Linear Latent Variable models (GLLVMs) generalize such factor models to non-Gaussian responses. However, current algorithms for estimating model parameters in GLLVMs require intensive computation and do not scale to large datasets with thousands of observational units or responses. In this article, we propose a new approach for fitting GLLVMs to high-dimensional datasets, based on approximating the model using penalized quasi-likelihood and then using a Newton method and Fisher scoring to learn the model parameters. Computationally, our method is noticeably faster and more stable, enabling GLLVM fits to much larger matrices than previously possible. We apply our method on a dataset of 48,000 observational units with over 2,000 observed species in each unit and find that most of the variability can be explained with a handful of factors. We publish an easy-to-use implementation of our proposed fitting algorithm.