Multi-treatment regression analysis: the unbalanced case

Under multi-treatment regression analysis, instead of a sample for each treatment of a linear model, there is a linear regression in the same variables. Then, instead of the action of the treatments on the sample mean values, the action on regression coefficients is studied. When data is unbalanced, the regression matrices differs between regressions. This problem is solved through the use of a block-wise diagonal covariance matrix in the ANOVA procedures. The methodology was then applied to data obtained from experiments of electrodialtic removal of 3 heavy metals from contaminated wood. First, polynomial regressions of the 4th and 3rd were fitted to each metal concentration in the electrolytes through time. Then the unbalanced case of multi-treatment regression analysis was applied aiming to choose the best treatment in jointly removing the 3 metals. Results pointed to the choice of treatment 1 as the most efficient.