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An algorithm for searching optimal variance component estimators in linear mixed models. J Stat Plan Inference 2023. [DOI: 10.1016/j.jspi.2023.03.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/17/2023]
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Repeated-Measures Analysis in the Context of Heteroscedastic Error Terms with Factors Having Both Fixed and Random Levels. STATS 2022. [DOI: 10.3390/stats5020027] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
The design and analysis of experiments which involve factors each consisting of both fixed and random levels fit into linear mixed models. The assumed linear mixed-model design matrix takes either a full-rank or less-than-full-rank form. The complexity of the data structures of such experiments falls in the model-selection and parameter-estimation process. The fundamental consideration in the estimation process of linear models is the special case in which elements of the error vector are assumed equal and uncorrelated. However, different assumptions on the structure of the variance–covariance matrix of error vector in the estimation of parameters of a linear mixed model may be considered. We conceptualise a repeated-measures design with multiple between-subjects factors, in which each of these factors has both fixed and random levels. We focus on the construction of linear mixed-effects models, the estimation of variance components, and hypothesis testing in which the default covariance structure of homoscedastic error terms is not appropriate. We illustrate the proposed approach using longitudinal data fitted to a three-factor linear mixed-effects model. The novelty of this approach lies in the exploration of the fixed and random levels of the same factor and in the subsequent interaction effects of the fixed levels. In addition, we assess the differences between levels of the same factor and determine the proportion of the total variation accounted for by the random levels of the same factor.
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Hickey J, Hill WG, Blasco A, Cameron N, Cullis B, McGuirk B, Mäntysaari E, Ruane J, Simm G, Veerkamp R, Visscher PM, Wray NR. Students', colleagues' and research partners' experience about work and accomplishments from collaborating with Robin Thompson. J Anim Breed Genet 2019; 136:301-309. [PMID: 31247683 DOI: 10.1111/jbg.12418] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- John Hickey
- The Roslin Institute, University of Edinburgh, Midlothian, UK
| | - William G Hill
- Institute of Evolutionary Biology, School of Biological Sciences, University of Edinburgh, Edinburgh, UK
| | - Agustin Blasco
- Institute for Animal Science and Technology, Universitat Politècnica de València, Valencia, Spain
| | | | - Brian Cullis
- Faculty of Engineering and Information Sciences, National Institute for Applied Statistics Research Australia, University of Wollongong, Wollongong, New South Wales, Australia
| | | | - Esa Mäntysaari
- Natural Resources Institute Finland (Luke), Production Systems, Animal Genetics, Jokioinen, Finland
| | - John Ruane
- FAO, Viale delle Terme di Caracalla, Rome, Italy
| | - Geoff Simm
- Global Academy of Agriculture and Food Security, The Royal (Dick) School of Veterinary Studies and The Roslin Institute, University of Edinburgh, Midlothian, UK
| | - Roel Veerkamp
- Animal Breeding and Genomics, Wageningen University and Research, Wageningen, The Netherlands
| | - Peter M Visscher
- Institute for Molecular Bioscience, The University of Queensland, Brisbane, Queensland, Australia.,Queensland Brain Institute, The University of Queensland, Brisbane, Queensland, Australia
| | - Naomi R Wray
- Institute for Molecular Bioscience, The University of Queensland, Brisbane, Queensland, Australia.,Queensland Brain Institute, The University of Queensland, Brisbane, Queensland, Australia
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Ghosh S, Guo L, Peng L. Variance component estimators OPE, NOPE and AOPE in linear mixed effects models. AUST NZ J STAT 2018. [DOI: 10.1111/anzs.12248] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Subir Ghosh
- Department of Statistics University of California Riverside CA92521‐0138USA
| | - Li Guo
- Department of Statistics University of California Riverside CA92521‐0138USA
| | - Luyao Peng
- Department of Statistics University of California Riverside CA92521‐0138USA
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