UC Riverside

We consider the problem of finding optimum designs for model identification and discrimination where the dependence of the response variable Y on an explanatory variable X can be described by at most a third order model. We therefore consider a class that includes all the models up to a maximum of third order with linear, quadratic, and cubic coefficients present. In addition all models have an intercept parameter. A general class of designs with 4 distinct points x_1, x_2, x_3, and x_4 is considered with replications n1; n2; n3, and n4 respectively, satisfying n_1 + n_2 + n_3 + n_4 = n where n is known in advance. While discriminating between two models from the class of models considered, the true model may or may not be one of them. We define the predictive criterion function I and the fitting criterion function J. When the functions I and J are dependent on more than one model parameters, we define the additional criterion functions K_I and K_J. We use the proposed optimality criterion functions to obtain the optimal designs for the model

identification and discrimination.