Optimal Designs for Random Blocks Model Using Corrected Criteria

Many industrial experiments involve random factors. The random blocks model defines a covariance structure in the data, thus generalized least square estimators of the parameters are used, and their covariance matrix is usually computed using the inverse of the generalized least square estimators information matrix. Many optimality criteria are based on this approximation of the covariance matrix. However, this approach underestimates the true covariance matrix of the parameters, and thus, the optimality criteria should be corrected in order to pay attention to the actual covariance. The bias in the estimation of the covariance matrix is negligible (or even null) for many models, and for this reason in those cases, it has no sense to deal with the corrected criteria because of the complexity of the calculations involved. But for some models, the correction does have importance, and thus, the modified criteria should be considered when designing; otherwise, the practitioner may risk to deal with poor designs. Some analytical results are presented for simpler models, and optimal designs taking into account the corrected variance will be computed and compared with those using the traditional approach for more complex models, showing that the loss in efficiency may be very important when the correction for the covariance matrix is ignored.