Computer Experiments with Qualitative and Quantitative Variables: A Review and Reexamination

In this article, we review and reexamine approaches to modeling computer experiments with qualitative and quantitative input variables. For those not familiar with models for computer experiments, we begin by showing, in a simple setting, that a standard model for computer experiments can be viewed as a generalization of regression models. We then review models that include both quantitative and quantitative variables and present some alternative parameterizations. Two are based on indicator functions and allow one to use standard quantitative inputs-only models. Another parameterization provides additional insight into possible underlying factorial structure. Finally, we use two examples to illustrate the benefits of these alternative models