Brenneman-Nair method

When applied to the dyestuffs experiment, the Brenneman-Nair method determines that there are enough residual degrees of freedom to study dispersion effects. However, the method gets stuck at the next step due to the inability of the modified Harvey s method to handle the machine-zero residuals. 

Brenneman and Nair (2001) and McGrath and Lin (2001) showed that the method of Box and Meyer (1986) can be problematic as described below when more than one factor has a dispersion effect. Brenneman and Nair (2001) examined the consequences of using the Box-Meyer method when there is a log-linear dispersion model in which... 

Brenneman (2000) found that Harvey s method could underestimate the dispersion effect of factor j if that factor was left out of the location model. This result led Brenneman and Nair (2001) to propose a modified version of Harvey s method for two-level factorial experiments that is based on the results of Bergman and Hynen (1997). In the modified version, the dispersion statistic for factor j is computed from residuals from an expanded location model that includes the effect of factor j and all its interactions with other effects in the location model. For two-level designs, the modified Harvey s statistic for factor j is then... 

Brenneman and Nair (2001) proposed a strategy that combines their modified version of Harvey s method with joint location and dispersion modeling for a log-linear dispersion model. After fitting a location model with ordinary least squares regression, they recommended an initial check to see if there are sufficient degrees of freedom even to consider looking for dispersion effects. The condition they... 

Brenneman, W. A. (2000). Inference for location and dispersion effects in unreplicated factorial experiments. PhD Dissertation, University of Michigan, Ann Arbor. Brenneman, W. A. and Nair, V. N. (2001). Methods for identifying dispersion effects in unreplicated factorial experiments. Technometrics, 43, 388-405. 

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