Exploratory Model Selection for Spatially Designed Experiments-Some Examples

10.6339/JDS.2003.01(3).124

Walter T. Federer

Computer code ； differential gradients ； fixed effect analysis ； functions of row and column effects ； interaction ； orthogonal polynomial regression ； random effect analysis ； replication

Journal of Data Science

1卷3期（2003 / 07 / 01）

231 - 248

英文

Exploratory model selection was used to find a response model that accounted for the spatial variability present in the experimental results from four examples of spatially designed field experiments. It was found that the class of differential gradients within incomplete blocks was useful for finding a response model that accounted for the spatial variability present in the first example. The class of orthogonal polynomial regressions of response on row and column position and interactions of the regressions was useful for discovering an appropriate response model for the data of examples two, three, and four. The results obtained from the selected response model were compared with standard textbook analyses. Considerable differences in residual mean squares, coefficients of variation, and F-values for treatment to residual mean squares were found. The increase in replication for the selected response model over the textbook response model is demonstrated. The increase can be many fold.