Employing a Monte Carlo algorithm in Newton-type methods for restricted maximum likelihood estimation of genetic parameters.

Estimation of variance components by Monte Carlo (MC) expectation maximization (EM) restricted maximum likelihood (REML) is computationally efficient for large data sets and complex linear mixed effects models. However, efficiency may be lost due to the need for a large number of iterations of the E...

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Autores principales:	Kaarina Matilainen, Esa A Mäntysaari, Martin H Lidauer, Ismo Strandén, Robin Thompson
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2013
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/0a35311431c4489c8c1ec8fd9d18e80c
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spelling	oai:doaj.org-article:0a35311431c4489c8c1ec8fd9d18e80c2021-11-18T08:42:46ZEmploying a Monte Carlo algorithm in Newton-type methods for restricted maximum likelihood estimation of genetic parameters.1932-620310.1371/journal.pone.0080821https://doaj.org/article/0a35311431c4489c8c1ec8fd9d18e80c2013-01-01T00:00:00Zhttps://www.ncbi.nlm.nih.gov/pmc/articles/pmid/24339886/?tool=EBIhttps://doaj.org/toc/1932-6203Estimation of variance components by Monte Carlo (MC) expectation maximization (EM) restricted maximum likelihood (REML) is computationally efficient for large data sets and complex linear mixed effects models. However, efficiency may be lost due to the need for a large number of iterations of the EM algorithm. To decrease the computing time we explored the use of faster converging Newton-type algorithms within MC REML implementations. The implemented algorithms were: MC Newton-Raphson (NR), where the information matrix was generated via sampling; MC average information(AI), where the information was computed as an average of observed and expected information; and MC Broyden's method, where the zero of the gradient was searched using a quasi-Newton-type algorithm. Performance of these algorithms was evaluated using simulated data. The final estimates were in good agreement with corresponding analytical ones. MC NR REML and MC AI REML enhanced convergence compared to MC EM REML and gave standard errors for the estimates as a by-product. MC NR REML required a larger number of MC samples, while each MC AI REML iteration demanded extra solving of mixed model equations by the number of parameters to be estimated. MC Broyden's method required the largest number of MC samples with our small data and did not give standard errors for the parameters directly. We studied the performance of three different convergence criteria for the MC AI REML algorithm. Our results indicate the importance of defining a suitable convergence criterion and critical value in order to obtain an efficient Newton-type method utilizing a MC algorithm. Overall, use of a MC algorithm with Newton-type methods proved feasible and the results encourage testing of these methods with different kinds of large-scale problem settings.Kaarina MatilainenEsa A MäntysaariMartin H LidauerIsmo StrandénRobin ThompsonPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 8, Iss 12, p e80821 (2013)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Kaarina Matilainen Esa A Mäntysaari Martin H Lidauer Ismo Strandén Robin Thompson Employing a Monte Carlo algorithm in Newton-type methods for restricted maximum likelihood estimation of genetic parameters.
description	Estimation of variance components by Monte Carlo (MC) expectation maximization (EM) restricted maximum likelihood (REML) is computationally efficient for large data sets and complex linear mixed effects models. However, efficiency may be lost due to the need for a large number of iterations of the EM algorithm. To decrease the computing time we explored the use of faster converging Newton-type algorithms within MC REML implementations. The implemented algorithms were: MC Newton-Raphson (NR), where the information matrix was generated via sampling; MC average information(AI), where the information was computed as an average of observed and expected information; and MC Broyden's method, where the zero of the gradient was searched using a quasi-Newton-type algorithm. Performance of these algorithms was evaluated using simulated data. The final estimates were in good agreement with corresponding analytical ones. MC NR REML and MC AI REML enhanced convergence compared to MC EM REML and gave standard errors for the estimates as a by-product. MC NR REML required a larger number of MC samples, while each MC AI REML iteration demanded extra solving of mixed model equations by the number of parameters to be estimated. MC Broyden's method required the largest number of MC samples with our small data and did not give standard errors for the parameters directly. We studied the performance of three different convergence criteria for the MC AI REML algorithm. Our results indicate the importance of defining a suitable convergence criterion and critical value in order to obtain an efficient Newton-type method utilizing a MC algorithm. Overall, use of a MC algorithm with Newton-type methods proved feasible and the results encourage testing of these methods with different kinds of large-scale problem settings.
format	article
author	Kaarina Matilainen Esa A Mäntysaari Martin H Lidauer Ismo Strandén Robin Thompson
author_facet	Kaarina Matilainen Esa A Mäntysaari Martin H Lidauer Ismo Strandén Robin Thompson
author_sort	Kaarina Matilainen
title	Employing a Monte Carlo algorithm in Newton-type methods for restricted maximum likelihood estimation of genetic parameters.
title_short	Employing a Monte Carlo algorithm in Newton-type methods for restricted maximum likelihood estimation of genetic parameters.
title_full	Employing a Monte Carlo algorithm in Newton-type methods for restricted maximum likelihood estimation of genetic parameters.
title_fullStr	Employing a Monte Carlo algorithm in Newton-type methods for restricted maximum likelihood estimation of genetic parameters.
title_full_unstemmed	Employing a Monte Carlo algorithm in Newton-type methods for restricted maximum likelihood estimation of genetic parameters.
title_sort	employing a monte carlo algorithm in newton-type methods for restricted maximum likelihood estimation of genetic parameters.
publisher	Public Library of Science (PLoS)
publishDate	2013
url	https://doaj.org/article/0a35311431c4489c8c1ec8fd9d18e80c
work_keys_str_mv	AT kaarinamatilainen employingamontecarloalgorithminnewtontypemethodsforrestrictedmaximumlikelihoodestimationofgeneticparameters AT esaamantysaari employingamontecarloalgorithminnewtontypemethodsforrestrictedmaximumlikelihoodestimationofgeneticparameters AT martinhlidauer employingamontecarloalgorithminnewtontypemethodsforrestrictedmaximumlikelihoodestimationofgeneticparameters AT ismostranden employingamontecarloalgorithminnewtontypemethodsforrestrictedmaximumlikelihoodestimationofgeneticparameters AT robinthompson employingamontecarloalgorithminnewtontypemethodsforrestrictedmaximumlikelihoodestimationofgeneticparameters
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Employing a Monte Carlo algorithm in Newton-type methods for restricted maximum likelihood estimation of genetic parameters.

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