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Abstract:
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Screening designs manipulate many factors to identify the few that are active. This active set is often determined through a model selection procedure that focuses on models comprised of low-order factorial effects (i.e. main effects and interactions). A good screening design should then produce effect estimates having low bias and variance. This talk compares the structure and variance properties of A- and D-optimal screening designs for continuous factors, and argues that the A-criterion is more appropriate. We then propose two different coordinate-exchange algorithms to construct A-optimal designs. When constructing D-optimal designs, it is known that one need only consider the two levels +/- 1, but we show this is not the case for the A-criterion. The first algorithm considers the levels {-1,0,+1}, and the other allows any level in the interval [-1,+1]. We compare the performance of the two algorithms across multiple combinations of run size and number of factors. Based on the results from our construction algorithms, we conjecture about the structure of A-optimal screening designs.
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