Evaluation of Data Transformations and Validation of a Spatial Model for Spatial Dependency of Trialeurodes vaporariorum Populations in a Cherry Tomato Greenhouse

An evaluation of data transformations was made for constructing the reliable spatial models of the greenhouse whitefly {Trialeurodes vaporariorum Westwood) populations in a commercial cherry tomato greenhouse. A Box-Cox power transformation that is useful family of transformations was applied to original data sets. The ability of the transformations to correct for the heterogeneity of variance was tested with Shapiro-Wilk W statistics. After finding the appropriate transformations, empirical variograms were calculated and fitted to spherical model. In this study, the data transformations can stable variogram modeling by means of converting non-normal data to normal. The model was validated with new data set by comparing the deviation between observed and predicted values, using a leave-one-out method. Among the data transformations tested, log_e (x+0.5) and (x+0.5) transformations were found to be appropriate at correcting for the heterogeneity of variance. According to the leave-one-out cross validation, the (x+0.5) transformation was better than the log_e(x+0.5) transformation. However, both transformations produced a systemic deviation: the predicted mean was always smaller than the observed mean. No transformations were found to be appropriate, when a proportion of empty sample units (no individuals were observed) was higher than 0.2. Moreover, in this study, the abnormal high density of sample units made inappropriate spherical variogram modeling.