SIMULATION STUDY OF SPATIAL-POISSON DATA ASSESSING INCLUSION OF SPATIAL CORRELATION AND NON-NORMALITY IN THE ANALYSIS

Spatial correlation and non-normality in agricultural, geological, or environmental settings can have a significant effect on the accuracy of the results obtained in the statistical analyses. Generalized linear mixed models, spatial models, and generalized linear models were compared in order to assess how critical the inclusion of non-normality and spatial correlation is to the analysis. Spatially correlated data with a Poisson distribution were generated in a completely randomized design (CRD) with 2 treatments and 18 repetitions. Four analyses: spatial Poisson, non-spatial Poisson, spatial normal, and non-spatial normal, were conducted on the simulated data to compare their power functions. The degree of spatial correlation, size of the mean, the dimension of the plots and difference between the two treatment means were altered to investigate how the ability to detect differences between the treatments is affected. In addition, the range covariance parameter was estimated and compared among the spatial models. Some covariance parameter estimates were under-estimated. The size of the field plot and the treatment means were increased to assess their effects on estimation of the range. The Reduced Maximum Likelihood (REML) covariance parameter estimates were compared to those obtained using Maximum Likelihood (ML) estimates. The analysis that incorporated the spatial correlation of the observations and used ML to estimate the covariance parameters had the highest power and most accurate range parameter estimates