{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:27:51Z","timestamp":1760243271673,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,28]],"date-time":"2022-09-28T00:00:00Z","timestamp":1664323200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Variance-component models are an indispensable tool for statisticians wanting to capture both random and fixed model effects. They have applications in a wide range of scientific disciplines. While maximum likelihood estimation (MLE) is the most popular method for estimating the variance-component model parameters, it is numerically challenging for large data sets. In this article, we consider the class of coordinate descent (CD) algorithms for computing the MLE. We show that a basic implementation of coordinate descent is numerically costly to implement and does not easily satisfy the standard theoretical conditions for convergence. We instead propose two parameter-expanded versions of CD, called PX-CD and PXI-CD. These novel algorithms not only converge faster than existing competitors (MM and EM algorithms) but are also more amenable to convergence analysis. PX-CD and PXI-CD are particularly well-suited for large data sets\u2014namely, as the scale of the model increases, the performance gap between the parameter-expanded CD algorithms and the current competitor methods increases.<\/jats:p>","DOI":"10.3390\/a15100354","type":"journal-article","created":{"date-parts":[[2022,9,28]],"date-time":"2022-09-28T20:58:47Z","timestamp":1664398727000},"page":"354","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Coordinate Descent for Variance-Component Models"],"prefix":"10.3390","volume":"15","author":[{"given":"Anant","family":"Mathur","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2868-9420","authenticated-orcid":false,"given":"Sarat","family":"Moka","sequence":"additional","affiliation":[{"name":"School of Mathematical and Physical Sciences, Macquarie University, Sydney, NSW 2109, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zdravko","family":"Botev","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1038\/ng.548","article-title":"Variance component model to account for sample structure in genome-wide association studies","volume":"42","author":"Kang","year":"2010","journal-title":"Nat. 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