A Method for Estimating Dispersion Effects in Unreplicated Two-level Factorial Experiments

Abstract:

      Since the paper of Box and Meyer who first considered the identification and estimation of dispersion effects from unreplicated factorial experiments, various different methods (both iterative and non-iterative) have been proposed for estimating dispersion effects. An overview of various methods was given by Brenneman and Nair and they showed that the modified Harvey (MH) method is better than other methods. For a log-linear or multiplicative model, a non-iterative estimation method of dispersion effects based on residuals averaging from multiple location effect models is proposed in model selection stage, which has been shown smaller Mean Square Errors (MSE) than the MH method in majority of simulated models. And it can apply to the situations with zero or small absolute residuals, but the MH method will be failure. The properties of this estimator are also considered. A real example is used to illustrate the results.