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## DOE creation with some factors space filling and other factors discrete numeric

I am curious if someone knows of some literature out there on creating designs where the continuous factors are sampled in a space filling manner and the other factors (of type categorical or discrete numeric) are treated in an optimal way.  The motivation for this would be a factor space which one would like to sample with a space filling design but the factor space contains some factors which are available only at discrete levels.

I have found one way to create such a design but would be interested if anyone had further insight into other options.

This is my process:

1. Create a space filling design for the continuous factors in the factor space.  Save to table.
2. Create a custom design with the discrete factors and add the table of space filling factors as covariates.
3. Augment the design to add vertices to the design.
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## Re: DOE creation with some factors space filling and other factors discrete numeric

Standard design diagnostics aren't necessarily what you want here: Custom Design is aiming to fit a linear model to the factors, and not care about how those points are spread out among the categories/levels. Using your method, if you look at the correlations/scatterplots of the continuous variables by a discrete numeric variable, I suspect some levels won't look nearly as space-filling as you would like. You may have some success at lowering the correlations for the continuous factors if you add interactions to custom (I would use categorical to be safe).

You could try writing a script that takes your space-filling design on the continuous factors and tries to assign levels for the categorical factor according to, for example, a maximin criterion.

In the literature, you can take a look at "Sliced Space-Filling Designs" (Qian and Wu, 2009), and some of the follow-up papers.

2 REPLIES 2

## Re: DOE creation with some factors space filling and other factors discrete numeric

Standard design diagnostics aren't necessarily what you want here: Custom Design is aiming to fit a linear model to the factors, and not care about how those points are spread out among the categories/levels. Using your method, if you look at the correlations/scatterplots of the continuous variables by a discrete numeric variable, I suspect some levels won't look nearly as space-filling as you would like. You may have some success at lowering the correlations for the continuous factors if you add interactions to custom (I would use categorical to be safe).

You could try writing a script that takes your space-filling design on the continuous factors and tries to assign levels for the categorical factor according to, for example, a maximin criterion.

In the literature, you can take a look at "Sliced Space-Filling Designs" (Qian and Wu, 2009), and some of the follow-up papers.

## Re: DOE creation with some factors space filling and other factors discrete numeric

rlek2, Thanks for the comments and reference.