Problems in parameter estimation for power and AR(1) models of spatial correlation in designed field experiments

The AR(1) and power models of spatial correlation are popular in the analysis of field trial data. Numerical difficulties in estimation and interpretation of these models may occur when the autocorrelation parameter ρ tends to either zero or unity. These problems are considered here using three different examples. The first example is based on simulated data for a partially replicated design, where the true underlying variance-covariance structure is known. The other two examples involve real data from a precision farming trial and a plant breeding trial. We suggest four options to deal with the observed numerical problems and illustrate their use with the examples. It is shown in the examples that re-scaling of the spatial coordinates or a re-parameterization of the AR(1) model as an exponential model can be useful to help the model converge. We conclude that individual parameter estimates of the AR(1) model should be interpreted with care, especially when the autocorrelation estimate is close to either zero or unity.