Trimmed Constrained Mixed Effects Models: Formulations and Algorithms. Issue 3 (16th September 2021)

• Record Type: Journal Article
• Authors: Zheng, Peng; Barber, Ryan; Sorensen, Reed J. D.; Murray, Christopher J. L.; Aravkin, Aleksandr Y.
• Is Part Of: Journal of computational and graphical statistics. Volume 30:Issue 3(2021)
• Page Start: 544
• Page End: 556
• Publication Date: 2021-09-16
• Subjects: Meta-analysis -- Mixed effects models -- Nonsmooth nonconvex optimization -- Trimming; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2020.1868303
• Languages: English
• ISSNs: 1061-8600

Abstract

Abstract: Mixed effects (ME) models inform a vast array of problems in the physical and social sciences, and are pervasive in meta-analysis. We consider ME models where the random effects component is linear. We then develop an efficient approach for a broad problem class that allows nonlinear measurements, priors, and constraints, and finds robust estimates in all of these cases using trimming in the associated marginal likelihood. The software accompanying this article is disseminated as an open-source Python package called LimeTr. LimeTr is able to recover results more accurately in the presence of outliers compared to available packages for both standard longitudinal analysis and meta-analysis, and is also more computationally efficient than competing robust alternatives. Supplementary materials that reproduce the simulations, as well as run LimeTr and third party code are available online. We also present analyses of global health data, where we use advanced functionality of LimeTr, including constraints to impose monotonicity and concavity for dose–response relationships. Nonlinear observation models allow new analyses in place of classic approximations, such as log-linear models. Robust extensions in all analyses ensure that spurious data points do not drive our understanding of either mean relationships or between-study heterogeneity.