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Treatment comparisons in agricultural field trials accounting for spatial correlation

Published online by Cambridge University Press:  09 September 2014

C. RICHTER ,
B. KROSCHEWSKI ,
H.-P. PIEPHO  and
J. SPILKE
C. RICHTER
Affiliation:
Faculty of Life Sciences, Albrecht Daniel Thaer-Institute of Agricultural and Horticultural Sciences, Humboldt-Universität zu Berlin, Berlin 10099, Germany
B. KROSCHEWSKI
Affiliation:
Faculty of Life Sciences, Albrecht Daniel Thaer-Institute of Agricultural and Horticultural Sciences, Humboldt-Universität zu Berlin, Berlin 10099, Germany
H.-P. PIEPHO*
Affiliation:
Faculty of Agricultural Sciences, Institute of Crop Science, University of Hohenheim, Stuttgart 70599, Germany
J. SPILKE
Affiliation:
Institute of Agricultural and Nutritional Sciences, Martin-Luther-University Halle-Wittenberg, Halle 06099, Germany
*
*To whom all correspondence should be addressed. Email: [email protected]
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Summary

The classical analysis model for agricultural field trials is based on the principles of experimental design – randomization, replication and blocking – and it assumes independent residual effects. Accounting for any existent spatial correlation as an add-on component may be beneficial, but it requires selection of a suitable spatial model and modification of classical tests of treatment contrasts. Using a sugar beet trial laid out in complete blocks for illustration, it is shown that tests obtained with different modifications yield diverging results. Simulations were performed to decide whether different test modifications lead to valid statistical inferences. For the spherical, power and Gaussian models, each with six different values of the range parameter and without a nugget effect, the suitability of the following modifications was studied: a generalization of the Satterthwaite method (1941), the method of Kenward and Roger (1997), and the first-order corrected method described by Kenward and Roger (2009). A second-order method described by Kenward and Roger (2009) is also discussed and detailed results are provided as Supplemental Material (available at: http://journals.cambridge.org/AGS). Simulations were done for experiments with 10 or 30 treatments in complete and incomplete block designs. Model selection was performed using the corrected Akaike information criterion and likelihood-ratio tests. When simulation and analysis models were identical, at least one of the modifications for the t-test guaranteed control of the nominal Type I error rate in most cases. When the first-order method of Kenward and Roger was used, control of the t-test Type I error rate was poor for 10 treatments but on average very good for 30 treatments, when considering the best-fitting models for a given simulation setting. Results were not satisfactory for the F-test. The more pronounced the spatial correlation, the more substantial was the gain in power compared to classical analysis. For experiments with 20 treatments or more, the recommendation is to select the best-fitting model and then use the first-order method for t-tests. For F-tests, a randomization-based model with independent error effects should be used.

Type
Crops and Soils Research Papers
Information
The Journal of Agricultural Science , Volume 153 , Issue 7 , September 2015 , pp. 1187 - 1207
Copyright
Copyright © Cambridge University Press 2014 

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References

Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In Proceedings of the Second international Symposium on Information Theory (Eds Petrov, B. N. & Caski, F.), pp. 267–281. Budapest, Hungary: Akademiai Kiado. Reprinted 1992 in Breakthroughs in Statistics I. Foundations and Basic Theory (Eds S. Kotz & N. L. Johnson), pp. 610–624. New York: Springer.Google Scholar
Besag, J. & Kempton, R. (1986). Statistical analysis of field experiments using neighbouring plots. Biometrics 42, 231–251.Google Scholar
Brownie, C., Bowman, D. T. & Burton, J. W. (1993). Estimating spatial variation in analysis of data from yield trials: a comparison of methods. Agronomy Journal 85, 1244–1253.Google Scholar
Burnham, K. P. & Anderson, D. R. (1998). Model Selection and Inference. New York: Springer.Google Scholar
Fai, A. H. T. & Cornelius, P. L. (1996). Approximate F-tests of multiple degree of freedom hypotheses in generalized least squares analyses of unbalanced split-plot experiments. Journal of Statistical Computation and Simulation 54, 363–378.Google Scholar
Fisher, R. A. (1935). The Design of Experiments. Edinburgh: Oliver and Boyd.Google Scholar
Giesbrecht, F. G. & Burns, J. C. (1985). Two-stage analysis based on a mixed model: large-sample asymptotic theory and small-sample simulation results. Biometrics 41, 477–486.Google Scholar
Gilmour, A. R., Cullis, B. R. & Verbyla, A. P. (1997). Accounting for natural and extraneous variation in the analysis of field experiments. Journal of Agricultural, Biological and Environmental Statistics 2, 269–293.Google Scholar
Gomez, E. V., Schaalje, G. B. & Fellingham, G. W. (2005). Performance of the Kenward–Roger method when the covariance structure is selected using AIC and BIC. Communications in Statistics – Simulation and Computation 34, 377–392.Google Scholar
Grondona, M. O. & Cressie, N. (1991). Using spatial considerations in the analysis of experiments. Technometrics 33, 381–392.Google Scholar
Harville, D. A. & Jeske, D. R. (1992). Mean squared error of estimation or prediction under a general linear model. Journal of the American Statistical Association 87, 724–731.Google Scholar
Haskard, K. A., Cullis, B. R. & Verbyla, A. P. (2007). Anisotropic Matérn correlation and spatial prediction using REML. Journal of Agricultural, Biological, and Environmental Statistics 12, 147–160.Google Scholar
Hu, X., Spilke, J. & Richter, C. (2006). The influence of spatial covariance on the Type I error and the power for different evaluation models. Biometrical Letters 43, 19–37.Google Scholar
Hurvich, C. M. & Tsai, C. L. (1989). Regression and time series model selection in small samples. Biometrika 76, 297–307.Google Scholar
Irvine, K. M., Gitelman, A. I. & Hoeting, J. A. (2007). Spatial designs and properties of spatial correlation: effects on covariance estimation. Journal of Agricultural, Biological and Environmental Statistics 12, 450–469.Google Scholar
Kenward, M. G. & Roger, J. H. (1997). Small sample inference for fixed effects from restricted maximum likelihood. Biometrics 53, 983–997.Google Scholar
Kenward, M. G. & Roger, J. H. (2009). An improved approximation to the precision of fixed effects from restricted maximum likelihood. Computational Statistics and Data Analysis 53, 2583–2595.Google Scholar
Matérn, B. (1986). Spatial Variation, 2nd edn. Lecture Notes in Statistics no. 36. New York: Springer.Google Scholar
Müller, B. U., Kleinknecht, K., Möhring, J. & Piepho, H.-P. (2010). Comparison of spatial models for sugar beet and barley trials. Crop Science 50, 794–802.CrossRefGoogle Scholar
Pauler, D. K. (1998). The Schwarz criterion and related methods for normal linear models. Biometrika 85, 13–27.Google Scholar
Piepho, H.-P. & Williams, E. R. (2010). Linear variance models for plant breeding trials. Plant Breeding 129, 1–8.Google Scholar
Piepho, H.-P., Büchse, A. & Richter, C. (2004). A mixed modelling approach for randomized experiments with repeated measures. Journal of Agronomy and Crop Science 190, 230–247.Google Scholar
Piepho, H.-P., Richter, C. & Williams, E. R. (2008). Nearest neighbour adjustment and linear variance models in plant breeding trials. Biometrical Journal 50, 164–189.CrossRefGoogle ScholarPubMed
Pilarczyk, W. (2009). The extent and prevailing shape of spatial relationship in Polish variety testing trials on wheat. Plant Breeding 128, 411–415.Google Scholar
Richter, C. & Kroschewski, B. (2012). Geostatistical models in agricultural field experiments: investigations based on uniformity trials. Agronomy Journal 104, 91–105.CrossRefGoogle Scholar
Satterthwaite, F. E. (1941). Synthesis of variance. Psychometrika 6, 309–316.Google Scholar
Schaalje, G. B., McBride, J. B. & Fellingham, G. W. (2002). Adequacy of approximations to distributions of test statistics in complex mixed linear models. Journal of Agricultural, Biological, and Environmental Statistics 7, 512–524.Google Scholar
Schabenberger, O. & Pierce, F. J. (2002). Contemporary Statistical Models for the Plant and Soil Sciences. Boca Raton: CRC Press.Google Scholar
Schwarz, G. E. (1978). Estimating the dimension of a model. Annals of Statistics 6, 461–464.Google Scholar
Spilke, J., Piepho, H.-P. & Hu, X. (2005). A simulation study on tests of hypotheses and confidence intervals for fixed effects in mixed models for blocked experiments with missing data. Journal of Agricultural, Biological, and Environmental Statistics 10, 374–389.Google Scholar
Spilke, J., Richter, C. & Piepho, H.-P. (2010). Model selection and its consequences for different split-plot designs with spatial covariance and trend. Plant Breeding 129, 590–598.CrossRefGoogle Scholar
Stroup, W. W. (2002). Power analysis based on spatial effects mixed-models: a tool for comparing design and analysis strategies in the presence of spatial variability. Journal of Agricultural, Biological and Environmental Statistics 7, 491–511.Google Scholar
Whitaker, D., Williams, E. R. & John, J. A. (2009). CycDesigN 4.0: A Package for the Computer Generation of Experimental Designs. Naseby, New Zealand: CycSoftware Ltd.Google Scholar
Wu, T. & Dutilleul, P. (1999). Validity and efficiency of neighbor analyses in comparison with classical complete and incomplete block analyses of field experiments. Agronomy Journal 91, 721–731.Google Scholar
Wu, T., Mather, D. E. & Dutilleul, P. (1998). Application of geostatistical and neighbor analyses to data from plant breeding trials. Crop Science 38, 1545–1553.Google Scholar
Yates, F. (1939). The comparative advantages of systematic and randomized arrangements in the design of agricultural and biological experiments. Biometrika 30, 440–466.Google Scholar
Zhang, H. & Zimmerman, D. L. (2005). Toward reconciling two asymptotic frameworks in spatial statistics. Biometrika 92, 921–936.Google Scholar
Zimmerman, D. L. & Harville, D. A. (1991). A random field approach to the analysis of field-plot experiments and other spatial experiments. Biometrics 47, 223–239.CrossRefGoogle Scholar
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