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Residual Maximum Likelihood (REML) Estimation of a Neighbour Model for Field Experiments

Alan C. Gleeson, B. R. Cullis

Open publisher page 201 citations

Abstract

A spatial analysis of field experiments is proposed which takes account of association between neighbouring plots. The residual maximum likelihood (REML) method of Patterson and Thompson (1971, Biometrika 58, 545-554) is used to estimate parameters of a general neighbour model, which can be expressed as an autoregressive moving average (ARMA) model. Three data sets are analysed to (i) highlight the need for a model selection procedure, (ii) illustrate the differing results between incomplete block and neighbour analysis and the effect of including treated border plots in the design, and (iii) illustrate the environmental variation within an experiment using prediction of trend.

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What this paper is about

A spatial analysis of field experiments is proposed which takes account of association between neighbouring plots. The residual maximum likelihood (REML) method of Patterson and Thompson (1971, Biometrika 58, 545-554) is used to estimate parameters of a general neighbour model, which can be expressed as an autoregressive moving average (ARMA) model. Three data sets are analysed to (i) highlight the need for a model selection procedure, (ii) illustrate the differing results between incomplete block and neighbour analysis and the effect of including treated border plots in the design, and (iii) illustrate the environmental variation within an experiment using prediction of trend.

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OpenAlex reports 201 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

A spatial analysis of field experiments is proposed which takes account of association between neighbouring plots. The residual maximum likelihood (REML) method of Patterson and Thompson (1971, Biometrika 58, 545-554) is used to estimate parameters of a general neighbour model, which can be expressed as an autoregressive moving average (ARMA) model. Three data sets are analysed to (i) highlight the need for a model selection procedure, (ii) illustrate the differing results between incomplete block and neighbour analysis and the effect of including treated border plots in the design, and (iii) illustrate the environmental variation within an experiment using prediction of trend.

Key concepts: Restricted maximum likelihood, Residual, Autoregressive model, Maximum likelihood, Statistics, Mathematics, Information Criteria, Model selection

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