Application of Spatial Mixed Model in Agricultural Field Experiment

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Addis Ababa University


The objective of this study was to evaluate the efficiency of spatial stati stical ana lysis in field trials and, particularly, we have demonstrated the benefits of the approach when experimental observations are spatia lly dependent. We have compared (i) cl assical randomi zed complete block model with independent and identica lly distributed errors (RCBDiid); (ii) the most common spatial models: Exponentia l, Spherical and Gaussian (with and without nugget effect); (i ii) spatial models of (ii) with and without block effects; (iv) complete random model (CR). The data used in this study were obtained from separate trials for Bread wheat and Durum wheat wh ich was coded as BW99RVTII (Regional Varity Trial Two of Bread Wheat conducted in the year 1999 Eth.C.) and DW99RVTII (Regional Varity Trial Two of Durum Wheat conducted in the year 1999 Eth.C.), respectively. The restricted maximum likelihood (REML) method was used for est imation of spatial covariance parameters. The denominator degree of freedom of F test for treatment effects were computed using the Kenward-Roger method for a ll models (Kenward and Roger, 1997). Semivar iogram were used for the initial estimate of the parameters of the spatial covari ance structure. Akaike's Information criterion (AIC) and Corrected Akaike's Information cri terion AICc and the Likelihood ratio test were used for model comparison. The result showed that in all of the four trial s, the estimated residual from RCBiid model were s ignifi cantly spat ially correlated, providing evidence of field heterogeneity within blocks that cou ld make the RCBiid method less powerful than a method that incorporated the spati al correlation. Furthermore, the finally se lected spatial model for a ll data set showed that blocking seemed to be unnecessary if these se lected spatial model were used for each of the trial s. The results also showed that the spatial models provided a smaller p-value and standard error than the class ical analysis of variance models. We have concluded that randomizat ion and blocking does not completely remove spatial variation. Hence, we recommended that researchers should take into account spatial variation in field experiment in s ituations were spat ial dependence among the observations is sign ificant. Key words: Spatial Models; Semivari ogram



Spatial Models, Semivari ogram