D-Optimal Designs
Introduction to D-Optimal Designs
Traditional experimental designs (Full Factorial Designs, Fractional Factorial Designs, and Response Surface Designs) are appropriate for calibrating linear models in experimental settings where factors are relatively unconstrained in the region of interest. In some cases, however, models are necessarily nonlinear. In other cases, certain treatments (combinations of factor levels) may be expensive or infeasible to measure. D-optimal designs are model-specific designs that address these limitations of traditional designs.
A D-optimal design is generated by an iterative search algorithm and seeks to minimize the covariance of the parameter estimates for a specified model. This is equivalent to maximizing the determinant D = |XTX|, where X is the design matrix of model terms (the columns) evaluated at specific treatments in the design space (the rows). Unlike traditional designs, D-optimal designs do not require orthogonal design matrices, and as a result, parameter estimates may be correlated. Parameter estimates may also be locally, but not globally, D-optimal.
There are several Statistics and Machine Learning Toolbox™ functions for generating D-optimal designs:
| Function | Description |
|---|---|
candexch | Uses a row-exchange algorithm to generate a D-optimal
design with a specified number of runs for a specified model and
a specified candidate set. This is the second component of the
algorithm used by |
candgen | Generates a candidate set for a specified model. This is
the first component of the algorithm used by
|
cordexch | Uses a coordinate-exchange algorithm to generate a D-optimal design with a specified number of runs for a specified model. |
daugment | Uses a coordinate-exchange algorithm to augment an existing D-optimal design with additional runs to estimate additional model terms. |
dcovary | Uses a coordinate-exchange algorithm to generate a D-optimal design with fixed covariate factors. |
rowexch | Uses a row-exchange algorithm to generate a D-optimal
design with a specified number of runs for a specified model.
The algorithm calls |
Note
The function rsmdemo generates simulated data
for experimental settings specified by either the user or by a D-optimal design
generated by cordexch. It uses the rstool interface to visualize
response surface models fit to the data, and it uses the nlintool interface to visualize a
nonlinear model fit to the data.
