Simulation designs for the estimation of quadratic response surface gradients in the presence of model misspecification

This article considers the construction of simulation designs for the ordinary least squares estimation of second-order metamodels. Two premises underlie the development of these experimental strategies. First it is assumed that the postulated metamodel may be misspecified due to the true model structure being of third-order. It is therefore important that the locations of the simulation experiments be specified to provide protection against bias, as well as variance, in the estimation of metamodel parameters. The second premise is based on the observation that, in many applications of metamodels, functions of the fitted model coefficients (such as the slope gradients) are of greater interest than the response function. The integrated mean squared error of slopes design criterion that is implemented here addresses both premises. This criterion finds application in various optimum seeking methods and sensitivity analysis procedures. Combinations of four important classes of response surface designs and three pseudorandom number assignment strategies constitute the basic structure of the simulation designs studied. The performance of these simulation designs is evaluated and, subsequently, compared to a similar set of experimenal plans that have as their focus the estimation of the response function.