Online two‐way estimation and inference via linear mixed‐effects models. (19th August 2022)

• Record Type: Journal Article
• Authors: Luo, Lan; Li, Lexin
• Is Part Of: Statistics in medicine. Volume 41:Number 25(2022)
• Page Start: 5113
• Page End: 5133
• Publication Date: 2022-08-19
• Subjects: collaborative inference -- divide‐and‐conquer -- linear mixed‐effects models -- meta‐analysis -- online learning; Medical statistics -- Periodicals; Statistique médicale -- Périodiques; Statistiques médicales -- Périodiques; 610.727
• DOI: 10.1002/sim.9557
• Languages: English
• ISSNs: 0277-6715

Abstract

Abstract : In this article, we tackle the estimation and inference problem of analyzing distributed streaming data that is collected continuously over multiple data sites. We propose an online two‐way approach via linear mixed‐effects models. We explicitly model the site‐specific effects as random‐effect terms, and tackle both between‐site heterogeneity and within‐site correlation. We develop an online updating procedure that does not need to re‐access the previous data and can efficiently update the parameter estimate, when either new data sites, or new streams of sample observations of the existing data sites, become available. We derive the non‐asymptotic error bound for our proposed online estimator, and show that it is asymptotically equivalent to the offline counterpart based on all the raw data. We compare with some key alternative solutions both analytically and numerically, and demonstrate the advantages of our proposal. We further illustrate our method with two data applications.