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a Dep. of Crop and Soil Science, 116 ASI Building, The Pennsylvania State Univ., University Park, PA, 16802
b Dep. of Soil Science, North Carolina State Univ., Raleigh, NC 27695-7619
c Dep. of Statistics, North Carolina State Univ., Raleigh, NC 27695-8203
d Dep. of Crop Science, North Carolina State Univ., Raleigh, NC 27695-7620
* Corresponding author (jeff_white{at}ncsu.edu)
Received for publication May 14, 2004. Failure to account for spatially correlated errors when present in the classical randomized complete block (RCB) analysis may cause inefficient estimation of treatment significance. Covariance model selection is a necessary component for spatial adjustment to estimate treatment significance. We discuss methods for selecting a covariance model in RCB analyses in the presence of spatial correlation and demonstrate one procedure in detail. The procedure uses three models: the randomized complete block with independent and identically distributed errors (RCBiid), RCB with correlated errors, and models with correlated errors but no block effects. The semivariogram of the residuals from fitting a model with just fixed effects, the likelihood ratio test, and Akaike Information Criterion are used for model selection. To illustrate the procedure, we analyzed winter wheat (Triticum aestivum L.) forage and corn (Zea mays L.) grain yield in the presence of spatial heterogeneity within blocks from a site-specific N management study. We compared the selected covariance models to the RCBiid models and to other spatial models with respect to the estimation of treatment significance. The procedure can be extended to any experiment with fixed effects, or with both fixed and random effects, and which may potentially have spatially correlated errors. The procedure is systematic and readily implemented; however, it remains difficult to evaluate whether an adequate covariance model has been selected.
Abbreviations: AIC, Akaike Information Criterion • ANOVA, analysis of variance • CE, correlated errors • CIR, color infrared aerial photography • ddf, denominator df • EGLS, estimated generalized least squares • FA, field average • GIS, geographic information systems • GPS, global positioning system • iid, independent and identically distributed • LRT, likelihood ratio test • RCB, randomized complete block • RCBCE, randomized complete block with correlated errors • REML, restricted maximum likelihood • RYE, realistic yield expectation • SSNM, site-specific nitrogen management • VRT, variable rate technologies
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