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COMPSTAT pp 161–172Cite as

A spatio-temporal analysis of a field trial

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Abstract

A study involving the growth of Australian Eucalypts under irrigation regimes with varying levels of salinity and nutrients was conducted in Loxton South Australia. The field experiment was conducted over a period of six years. The aim of the study was to determine the impact of salinity on the growth of eucalypts and to provide recommendations on the commercial suitability of growing eucalypts using saline drainage water. The data has both spatial and temporal aspects which are examined in this paper. Spatial modelling follows current methods for field trials while the temporal modelling involves smoothing splines. A joint mixed model is developed which uses a mixed model representation of the smoothing spline.

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References

  • Becker, R. and Chambers, J. (1996). S-PL US Trellis Graphics User’s Manual. MathSoft Inc. and Bell Labs.

    Google Scholar 

  • Brumback, and Rice, J. A. (1998). Smoothing spline models for the analysis of nested and crossed samples of curves. Journal of the American Statistical Association. 93, pp. 961–994.

    Article  MathSciNet  MATH  Google Scholar 

  • Cullis, B.R, Gogel, B.J., Verbyla, A.P. and Thompson, R. (1998). Spatial analysis of multi-environment early generation trials. Biometrics. 54, pp. 1–18.

    Article  MathSciNet  MATH  Google Scholar 

  • Green, P.J. and Silverman, B. (1994). Nonparametric regression and generalized linear models. Chapman and Hall, London.

    MATH  Google Scholar 

  • Gilmour, A.R., Cullis, B.R. and Verbyla, A.P. (1997). Accounting for natural and extraneous variation in the analysis of field experiments. Journal of Agricultural,Biological and Environmental Statistics. 2, pp. 269–293.

    Article  MathSciNet  Google Scholar 

  • Gilmour, A.R., Cullis, B.R., Welham, S.J. and Thompson R. (1996). ASREML, an average information REML program. Biometric Bulletin, NSW Agriculture.

    Google Scholar 

  • Gilmour, A.R., Thompson, R. and Cullis, B.R. (1995). Average Information, an efficient algorithm for REML estimation in linear mixed models. Biometrics. 51, pp. 1440–1450.

    Article  MATH  Google Scholar 

  • Harville, D.A. (1977). Maximum likelihood estimation of variance components and related problems. Journal of the American Statistical Association. 72, pp. 320–340.

    Article  MathSciNet  MATH  Google Scholar 

  • Kimeldorf, G. and Wahba, G. (1970). A correspondence between Bayesian estimation of stochastic processes and smoothing by splines. Annals of Mathematical Statistics. 41, pp. 195–502.

    Article  MathSciNet  Google Scholar 

  • Laird, N.M. and Ware, J.H. (1982). Random-effects models for longitudinal data. Biometrics. 38, pp. 963–974.

    Article  MATH  Google Scholar 

  • Patterson, H.D. and Thompson, R. (1971). Recovery of inter-block information when block sizes are unequal. Biometrika. 58, pp. 545–554.

    Article  MathSciNet  MATH  Google Scholar 

  • Silverman, B. (1985). Some aspects of the spline smoothing approach to non-parametric regression curve fitting (with discussion). Journal of the Royal Statistical Society, Series B 47, pp. 1–52.

    Google Scholar 

  • Speed, T.P. (1991). Comment on: That BLUP is a good thing: The estimation of random effects, by G. K. Robinson, Statistical Science. 6, pp. 44.

    Article  Google Scholar 

  • Stram, D.O. and Lee, J.W. (1994). Variance component testing in longitudi-nal mixed effects models. Biometrics. 50, 1171–1177.

    Article  MATH  Google Scholar 

  • Verbyla, A.P. (1995). A mixed model formulation of smoothing splines and testing linearity in generalized linear models. Research Report 95/5, Department of Statistics, The University of Adelaide. 172

    Google Scholar 

  • Verbyla, A.P., Cullis, B.R., Kenward, M.G. and Welham, S.J. (1999). The analysis of designed experiments and longitudinal data by using smoothing splines (with discussion). Applied Statistics. 48, pp. 269–311.

    Article  MATH  Google Scholar 

  • Wang, Y. (1998a). Mixed effects smoothing spline analysis of variance. Journal of the Royal Statistical Society, Series B 60, pp. 159–174.

    Google Scholar 

  • Wang, Y. (1998b). Smoothing spline models with correlated errors. Journal of the American Statistical Association. 93, pp. 341–348.

    Article  MATH  Google Scholar 

  • Wilkinson, G.N. and Rogers, C.E. (1973). Symbolic description of factorial models for analysis of variance. Applied Statistics. 22, pp. 392–399.

    Article  Google Scholar 

  • Zhang, D., Lin, X., Raz, J. and Sowers, M. (1998). Semi-parametric stochastic mixed models for longitudinal data. Journal of the American Statistical Association. 93, pp. 710–719.

    Article  MathSciNet  MATH  Google Scholar 

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© 2000 Springer-Verlag Berlin Heidelberg

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Verbyla, A., Lorimer, M., Stevens, R. (2000). A spatio-temporal analysis of a field trial. In: Bethlehem, J.G., van der Heijden, P.G.M. (eds) COMPSTAT. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57678-2_15

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  • DOI: https://doi.org/10.1007/978-3-642-57678-2_15

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-1326-5

  • Online ISBN: 978-3-642-57678-2

  • eBook Packages: Springer Book Archive

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