Abstract
We report an analysis of a series of uniformity field trials using the technique proposed by Gilmour, Cullis, and Verbyla. In particular, we clarify the role of the sample variogram and present a range of enhanced graphical diagnostics to aid the spatial modeling process. We highlight the implications of the presence of extraneous variation related to commonly used agronomic practices, such as serpentine harvesting.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Atkinson, A. C. (1985), Plots, Transformations and Regressions, Oxford: Clarendon Press.
Besag, J., and Higdon, D. (1999), “Bayesian Analysis of Agricultural Field Experiments With Discussion,” Journal of the Royal Statistical Society, Ser. B, 61, 691–746.
Besag, J., and Kempton, R. A. (1986), “Statistical Analysis of Field Experiments Using Neighbouring Plots,” Biometrics, 42, 231–251.
Box, G. E. P., and Jenkins, G. M. (1970), Time Series Analysis, Forecasting and Control, San Francisco: Holden-Day.
Bulter, D. G., Cullis, B. R., Gilmour, A. R., and Gogel, B. J. (2007), Analysis of Mixed Models for S Language Environments, ASReml-R Reference Manual Release 2. Training and Development Series, No. QE02001. Brisbane, Australia: Queensland Department of Primary Industries and Fisheries.
Cressie, N. A. C. (1991), Statistics for Spatial Data, New York: Wiley.
Cullis, B. R., and Gleeson, A. C. (1991), “Spatial Analysis of Field Experiments—An Extension to Two Dimensions,” Biometrics, 47, 1449–1460.
Cullis, B. R., Gogel, B. J., Verbyla, A. P., and Thompson, R. (1998), “Spatial Analysis of Multi-Environment Early Generation Trials,” Biometrics, 54, 1–18.
Cullis, B. R., McGilchrist, C. A., and Gleeson, A. C. (1991), “Error Model Diagnostics in the General Linear Model Relevant to the Analysis of Repeated Measures and Field Experiments,” Journal of the Royal Statistical Society, Ser. B, 53, 409–416.
Cullis, B. R., Smith, A., and Coombes, N. E., (2006), “On the Design of Early Generation Variely Trials With Correlated Data,” Journal of Agricultural, Biological and Environmental Statistics, 11, 381–393.
Diggle, P. J., and Verbyla, A. P. (1998), “Nonparametric Estimation of Covariance Structure in Longitudinal Data,” Biometrics, 54, 401–415.
Eccleston, J., and Chan, B. (1998), “Design Algorithms for Correlated Data,” in COMPSTAT98 Proceedings in Computational Statistics, Heidelberg: Physica-Verlag, pp. 41–52.
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, 269–273. smith99
Gilmour, A. R., Cullis, B. R., Verbyla, A. P., and Smith, A. B. (1999), “Contribution to the Discussion of Bayesian Analysis of Agricultural Field Experiments,” Journal of the Royal Statistical Society, Ser. B. 61, 691–746.
Haskard, K. A., Cullis, B. R., and Verbyla, A. P. (2007), “A nisotropic Matern Correlation and Spatial Prediction Using REML,” Journal of Agricultural, Biological and Environmental Statistics, 12, 147–160.
Kenward, M. G., and Roger, J. H. (1997), “The Precision of Fixed Effects Estimates From Restricted Maximum Likelihood,” Biometrics, 53, 983–997.
Martin, R. J. (1990), “The Use of Time-Series Models and Methods in the Analysis of Agricultural Field Trials,” Communications in Statistics, 19, 55–81.
Stram, D. O., and Lee, J. W. (1994), “Variance Components Testing in the Longitudianl Mixed Effects Setting,” Biometrics, 50, 1171–1177.
Verbyla, A. P., Cullis, B. R., Kenward, M. G., and Welham, S. J. (1999), “The Analysis of Designed Experiments and Longitudinal Data Using Smoothing Splines” (with discussion), Journal of the Royal Statistical Society, Ser. C, 61, 269–312.
Wilkinson, G. N., Eckert, S. R., Hancock, T. W., and Mayo, O. (1983), “Nearest Neighbour (NN) Analysis of Field Experiments” (with discussion), Journal of the Royal Statistical Society, Ser. B, 45, 54–211.
Zimmerman, D. L., and Harville, D. A. (1991), “A Random Field Approach to the Analysis of Field Plot Experiments,” Biometrics, 47, 223–239.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Stefanova, K.T., Smith, A.B. & Cullis, B.R. Enhanced diagnostics for the spatial analysis of field trials. JABES 14, 392–410 (2009). https://doi.org/10.1198/jabes.2009.07098
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1198/jabes.2009.07098