Tensor Cubic Smoothing Splines in Designed Experiments Requiring Residual Modelling

A P Verbyla; J De Faveri; J D Wilkie; Tom Lewis

doi:10.1007/s13253-018-0334-9

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Tensor Cubic Smoothing Splines in Designed Experiments Requiring Residual Modelling

Journal article

Peer reviewed

Tensor Cubic Smoothing Splines in Designed Experiments Requiring Residual Modelling

A P Verbyla, J De Faveri, J D Wilkie and Tom Lewis

Journal of Agricultural, Biological, and Environmental Statistics, Vol.23(4), pp.478-508

2018

DOI: https://doi.org/10.1007/s13253-018-0334-9

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Abstract

asreml

cubic smoothing spline

mixed models

spatial variation

temporal variation

tensor spline

Modelling response surfaces using tensor cubic smoothing splines is presented for three designed experiments. The aim is to show how the analyses can be carried out using the asreml software in the R environment, and details of the analyses including the code to do so are presented in a tutorial style. The experiments were all run over time and involve an explanatory quantitative treatment variable; one experiment is a field trial which has a spatial component and involves an additional treatment. Thus, in addition to the response surface for the time by explanatory variable, modelling of temporal and, for the third experiment, of temporal and spatial effects at the residual level is required. A linear mixed model is used for analysis, and a mixed model representation of the tensor cubic smoothing spline is described and seamlessly incorporated in the full linear mixed model. The analyses show the flexibility and capacity of asreml for complex modelling. Supplementary materials accompanying this paper appear online.

Details

Title: Tensor Cubic Smoothing Splines in Designed Experiments Requiring Residual Modelling
Authors: A P Verbyla (Author) - CSIRO
J De Faveri (Author) - Queensland Department of Agriculture and Fisheries
J D Wilkie (Author) - Queensland Department of Agriculture and Fisheries
Tom Lewis (Author) - University of the Sunshine Coast - Faculty of Science, Health, Education and Engineering
Publication details: Journal of Agricultural, Biological, and Environmental Statistics, Vol.23(4), pp.478-508
Publisher: Springer New York LLC
Date published: 2018
DOI: 10.1007/s13253-018-0334-9
ISSN: 1085-7117
Organisation Unit: University of the Sunshine Coast, Queensland; Forest Research Institute
Language: English
Record Identifier: 99450854702621
Output Type: Journal article

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Web Of Science research areas: Biology; Mathematical & Computational Biology; Statistics & Probability

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