Collaborative Research Report: Comparing the Slack-Variable Mixture Model with Other Alternatives

By Byran Smucker posted 07-20-2016 16:48

  

Two weeks ago we posted a request for collaboration, from Peter Parker at NASA. Since then, we've received at least one idea about how to solve the problem. If you have your own idea, please respond with a comment or contact Dr. Parker directly.

Today's post is different than the previous one. Instead of a request for collaboration, it is a report of a successful collaboration between academia and industry. We hope the subject is of interest to both researchers and practitioners.

We are always looking for contributions to the Industrial Statistics Virtual Collaboratory. If you have an industrial statistics problem looking for a collaborator, send it over and we'll try to facilitate. If you've participated in an academic/industry collaborative partnership and you'd like to publicize your work, please contact me. Either way, send an e-mail to Byran Smucker (smuckerb@miamioh.edu).

The Joint Statistical Meetings are less than two weeks away. So we'll break for them and make the next post the week of August 7.

--------

Comparing the Slack-Variable Mixture Model with Other Alternatives

Collaborative research problem: There have been many linear regression models proposed to analyze mixture experiments including the Scheffé model, the slack-variable model, and the Kronecker model. The use of the slack-variable model is somewhat controversial within the mixture experiment research community. However, in situations that the slack-variable ingredient is used to fill in the formulation and the remaining ingredients have constraints such that they can be chosen independently of one another, the slack-variable model is extremely popular with practitioners mainly due to its ease of interpretation.

Research summary: We advocate that for some mixture experiments the slack-variable model has appealing properties including numerical stability and better prediction accuracy when model-term selection is performed. We explain how the effects of the slack-variable model components should be interpreted and how easy it is for practitioners to understand the components effects. We also investigate how to choose the slack-variable component, what transformation should be used to reduce collinearity, and under what circumstances the slack-variable model should be preferred. Both simulation and practical examples are provided to support the conclusions.

Collaboration summary: This work was a collaboration with Dr. William A. Brenneman from Procter & Gamble. The research was performed at Illinois Institute of Technology, but supported by funding from P&G. This research was published in Technometrics:

Kang, L., Salgado, J. C., and Brenneman, W. A. (2015) Comparing the Slack-Variable Mixture Model with Other Alternatives. Technometrics. DOI: 10.1080/00401706.2014.985389. http://amstat.tandfonline.com/doi/abs/10.1080/00401706.2014.985389

0 comments
292 views

Permalink