Optimal designs for multiresponse models with double covariance structure

In many scientific disciplines, experiments are conducted in order to get information about the model or about different characteristics of the data. Quite often more than one variable is measured, giving rise to multiresponse models. For these models it is usual to assume correlation between different-type observations taken on the same point, and always assume independence between observations taken at different points, even when measuring the same variable. This last independence will be discussed throughout this work, showing that a covariance structure should be considered in some cases, specially when observing multiple characteristics of the same experimental unit (e.g. a chemical reaction) at different instants of time. Analytical results are obtained for the general case and for the bivariate model with some covariance structures. A case study where these ideas are applied will be presented, and the need to include the double covariance structure in the model will be addressed and justified in the final discussion.