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Augmenting D-Optimal Designs
In practice, experimentation is an iterative process. We often want to add runs to a completed experiment to learn more about our system. The function daugment allows you choose these extra runs optimally.
Suppose we have executed the eight-run design below for fitting a linear model to four input variables.
settings = cordexch(4,8) settings = 1 -1 1 1 -1 -1 1 -1 -1 1 1 1 1 1 1 -1 -1 1 -1 1 1 -1 -1 1 -1 -1 -1 -1 1 1 -1 -1
This design is adequate to fit the linear model for four inputs, but cannot fit the six cross-product (interaction) terms. Suppose we are willing to do eight more runs to fit these extra terms. Here's how.
[augmented, X] = daugment(settings,8,'i'); augmented augmented = 1 -1 1 1 -1 -1 1 -1 -1 1 1 1 1 1 1 -1 -1 1 -1 1 1 -1 -1 1 -1 -1 -1 -1 1 1 -1 -1 -1 -1 -1 1 1 1 1 1 -1 -1 1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 -1 -1 1 -1 -1 1 1 -1 1 info = X'*X info = 16 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 16
The augmented design is orthogonal, since X'*X is a multiple of the identity matrix. In fact, this design is the same as a 24 factorial design.
| | Generating D-Optimal Designs | Designing Experiments with Uncontrolled Inputs | |