Cited by 570Statistical Methods and Bayesian InferenceOptimal Experimental Design MethodsAgriculture, Soil, Plant Science

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The Analysis of Designed Experiments and Longitudinal Data by Using Smoothing Splines

Verbyla, Arũnas P., Cullis, Brian R., Kenward, Michael G., Welham, Sue J.·1999·Journal of the Royal Statistical Society Series C: Applied Statistics

DOI 10.1111/1467-9876.00154

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Abstract

SUMMARY: In designed experiments and in particular longitudinal studies, the aim may be to assess the effect of a quantitative variable such as time on treatment effects. Modelling treatment effects can be complex in the presence of other sources of variation. Three examples are presented to illustrate an approach to analysis in such cases. The first example is a longitudinal experiment on the growth of cows under a factorial treatment structure where serial correlation and variance heterogeneity complicate the analysis. The second example involves the calibration of optical density and the concentration of a protein DNase in the presence of sampling variation and variance heterogeneity. The final example is a multienvironment agricultural field experiment in which a yield–seeding rate relationship is required for several varieties of lupins. Spatial variation within environments, heterogeneity between environments and variation between varieties all need to be incorporated in the analysis. In this paper, the cubic smoothing spline is used in conjunction with fixed and random effects, random coefficients and variance modelling to provide simultaneous modelling of trends and covariance structure. The key result that allows coherent and flexible empirical model building in complex situations is the linear mixed model representation of the cubic smoothing spline. An extension is proposed in which trend is partitioned into smooth and non-smooth components. Estimation and inference, the analysis of the three examples and a discussion of extensions and unresolved issues are also presented.

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Self-citation

Authors: Verbyla, A. P., Cullis, B. R., Kenward, M. G., & Welham, S. J.
Affiliations: University of Adelaide and South Australian Research and Development Institute , Glen Osmond , Australia
New South Wales Agriculture , Wagga Wagga , Australia
University of Kent (GB)
Rothamsted Research (GB)
ORCID: Cullis, Brian R.
Kenward, Michael G.
Venue: Journal of the Royal Statistical Society Series C: Applied Statistics
Publisher: Oxford University Press (OUP)
Published: 1999-09-01
Volume: 48
Issue: 3
Pages: 269-311
ISSN: 0035-9254 (ISSN-L)
1467-9876
DOI: 10.1111/1467-9876.00154
OpenAlex: W2153287720
Cited by: 570
References: 73
Citations by year: 2026: 3 · 2025: 2 · 2024: 6 · 2023: 11 · 2022: 13 · 2021: 12 · 2020: 23 · 2019: 22 · 2018: 11 · 2017: 20 · 2016: 24 · 2015: 29 · 2014: 37 · 2013: 29 · 2012: 25
FWCI: 26.38
Type: journal article
Language: en
Open access: closed
Licence: academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
Locations: Journal of the Royal Statistical Society Series C (Applied Statistics) (publishedVersion)
RePEc: Research Papers in Economics (submittedVersion)
Kent Academic Repository (University of Kent) (submittedVersion)
Journal of the Royal Statistical Society Series A (Statistics in Society)
Funders: Grains Research and Development Corporation
University of Adelaide
Topics: Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
Life Sciences › Agricultural and Biological Sciences › Agronomy and Crop Science › Agriculture, Soil, Plant Science
Keywords: smoothing splines, longitudinal data, designed experiments, linear mixed models, random coefficients, heteroscedasticity, serial correlation, cubic spline smoothing, seeding rate, spatial variability, fixed and random effects

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The Analysis of Designed Experiments and Longitudinal Data by Using Smoothing Splines

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