THE EMPIRICAL EFFICIENCY AND VALIDITY OF 2 NEIGHBOR MODELS

The validity and efficiency of two neighbour models, the first-difference model of Besag and Kempton (1986, Biometrics 42, 231-251) and their extended error-in-variables model, were studied for a variety of simulated yield models. The extended error-in-variables model is equivalent to the linear variance neighbour model of Williams (1986, Biometrika 73, 279-287). The parameters of the linear variance model were estimated using the method of restricted maximum likelihood estimation, since the method of maximum likelihood used by Besag and Kempton was found to be biased. The efficiencies of the two neighbour models were compared with those of two classical analyses, a randomized block analysis and an incomplete block analysis. In general, the neighbour analyses were more efficient than the classical analyses where the simulated yield model contained a trend component. The exceptions were when the trend was effectively eliminated by replicate blocks. Where the incomplete block analysis made gains over the randomized block analysis, the neighbour models made proportionately greater gains. The linear variance analysis was the best overall in efficiency of those examined, being in all cases either the most efficient analysis, or close in efficiency to the best analysis. Although the first-difference model is a special case of the linear variance model, Besag and Kempton recommended a different estimator of treatment precision for the first-difference model from that recommended for the linear variance model. For both neighbour models, the recommended estimators of treatment precision were judged to be empirically valid for all simulated yield models.