The DOI matches its Crossref record; 78 of the 78 references it cites were found in a registry or an index.
The Analysis of Designed Experiments and Longitudinal Data by Using Smoothing Splines
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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“This allows the natural cubic smoothing spline to be formulated within a LMM framework (Verbyla et al., 1999).”
From Incorporating environmental covariates to explore genotype × environment × management (G × E × M) interactions: A one-stage predictive model (2023) · cites this paper as Verbyla et al., 1999
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“The incorporation of smoothing splines (Verbyla et al., 1999) also enables the EC model terms to be partitioned into linear and non-linear components (De Faveri et al., 2022), allowing for significance testing of these components to be performed independently (Tables 5 and 4 respectively).”
From Incorporating environmental covariates to explore genotype × environment × management (G × E × M) interactions: A one-stage predictive model (2023) · cites this paper as Verbyla et al., 1999
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Citations
Cites
Random-Effects Models for Longitudinal Data
Laird, N. M., & Ware, J. H. (1982) · Biometrics · doi:10.2307/2529876 · Cited by 8,923
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Approximate Inference in Generalized Linear Mixed Models
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Small sample inference for fixed effects from restricted maximum likelihood
Kenward, M. G., & Roger, J. H. (1997) · Biometrics · doi:10.2307/2533558 · Cited by 4,552
Self-citationFlexible smoothing with B-splines and penalties
Eilers, P., & Marx, B. (1996) · Statistical Science · doi:10.1214/ss/1038425655 · Cited by 4,159
Recovery of Inter-Block Information when Block Sizes are Unequal
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Nonparametric Regression and Generalized Linear Models
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Research works printed but not linked: 6
- [19]19. Gilmour, A. R., Thompson, R., Cullis, B. R. and Welham, S. J. (1996) ASREML. Biometric Bulletin. New South Wales Agriculture, Wagga Wagga.
- [28]28. Kenward, M. G. and Welham, S. J. (1995) Use of splines in random coecient regression models for the analysis of repeated measurements. In Proc. Symp. Statistical Software 95, pp. 95±112. Utrecht: University of Utrecht.
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Cited by
Sorted by citations
Generalized additive models for location, scale and shape.
Rigby, R. A., & Stasinopoulos, D. M. (2005) · Journal of the Royal Statistical Society Series C: Applied Statistics · doi:10.1111/j.1467-9876.2005.00510.x · Cited by 3,228
Hierarchical generalized additive models in ecology: an introduction with mgcv
Pedersen, E. J., Miller, D. L., Simpson, G. L., & Ross, N. (2019) · PeerJ · doi:10.7717/peerj.6876 · Cited by 1,225
Inference in Generalized Additive Mixed Models by Using Smoothing Splines
Lin, X., & Zhang, D. (1999) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/1467-9868.00183 · Cited by 653
Low‐Rank Scale‐Invariant Tensor Product Smooths for Generalized Additive Mixed Models
Wood, S. N. (2006) · Biometrics · doi:10.1111/j.1541-0420.2006.00574.x · Cited by 613
Gilmour, A. R., Gogel, B. J., Cullis, B. R., Welham, S. J., & Thompson, R. (2002) · Rothamsted Repository (Rothamsted Repository) · Cited by 564
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Metadata
- 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)
- 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
- 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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