Section 9 Conclusion

9.1 Other packages

There are several other packages for exploring and modeling spatial variability in field trials. é

package	usage
inla	Bayesian modelling with options for spatial covariance structure
Mcspatial	nonparametric spatial analysis, (no longer on CRAN)
ngspatial	spatial models with a focus on generalized linear models
sommer	mixed models, including an AR1xAr1 model
spatialreg	spatial functions for areal data
spANOVA	spatial lag models for field trials

The package sommer implements a version of the AR1xAR1 covariance structure. However, it does not estimate the parameter \(\rho\). The user must specify the \(\rho\) and that value is not optimized in the restricted maximum likelihood estimation. There may be another way to implement the AR1xAR1 spatial model using the package TMB. Both SAS and the proprietary software asreml can implement a mixed model with this covariance structure.

A spAMM tutorial is available for exploring this package more.

9.2 Final recommendations

Spatial analysis is a big topic, but I think it is worth the effort to learn and implement in analysis of field trials. This guide provides some minimal recipes for how to incorporate spatial information into field trial statistical analysis.

There is no denying that work is needed to develop scripts that automate this process so researchers can routinely incorporate spatial covariance into field trial analysis. Many current R tools are unwieldy to use and have insufficient options to support variety trial analysis.

Until this situation is improved, it is probably wisest to focus on using spatial models that are well-supported at this time. Any of the options implemented in the nlme package (or that work with that package) are decent choices with excellent support for extracting least-squares means, running ANOVA, and standard model diagnostics. Furthermore, nlme supports generalized linear models. INLA is established is supported by a large and growing user base, and breedR is likewise well established.

Although these options may appear overwhelming, investigating spatial correlation in a field trial and controlling for it if necessary using any of the methods previously described is recommended over doing nothing.