The analysis of designed experiments and longitudinal data by using smoothing splines

Verbyla, Arũnas P. and Cullis, Brian R. and Kenward, Michael G. and Welham, Sue J. (1999) The analysis of designed experiments and longitudinal data by using smoothing splines. Journal of the Royal Statistical Society: Series C (Applied Statistics), 48 . pp. 269-300. ISSN 0035-9254. (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.1111/1467-9876.00154

Abstract

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 nonsmooth components. Estimation and inference, the analysis of the three examples and a discussion of extensions and unresolved issues are also presented.

Item Type: Article
Additional information: Part 3
Uncontrolled keywords: analysis of variance; best linear unbiased prediction; cubic smoothing splines; longitudinal data; mixed models; random coefficient models; residual maximum likelihood
Subjects: Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities
Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: F.D. Zabet
Date Deposited: 19 Mar 2009 12:17
Last Modified: 11 Jul 2014 09:16
Resource URI: http://kar.kent.ac.uk/id/eprint/16711 (The current URI for this page, for reference purposes)
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