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Regression models for order-of-addition experiments.

Hans-Peter Piepho1, Emlyn R Williams2

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Summary

This study introduces response surface (RS) regression models for optimizing component order in experiments. RS models offer a competitive alternative to traditional pairwise ordering (PWO) and component-position (CP) methods.

Keywords:
D-optimalityaverage variance of a differencemodel averagingorder-of-addition experimentresponse surface regression

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Area of Science:

  • Statistics
  • Experimental Design
  • Chemical Engineering

Background:

  • Order-of-addition (OofA) experiments are crucial for determining optimal component sequences.
  • Existing regression models, such as pairwise ordering (PWO) and component-position (CP) factors, are commonly used for OofA analysis.

Purpose of the Study:

  • To review existing regression models for OofA experiments.
  • To propose a novel class of response surface (RS) regression models for OofA analysis.
  • To demonstrate the competitiveness of RS models using real-world examples.

Main Methods:

  • Review of established regression models for OofA (PWO, CP).
  • Proposal and application of response surface (RS) regression models using component position numbers.
  • Utilizing model averaging for analysis in cases of model uncertainty.
  • Development of a compound optimality criterion for experimental design.

Main Results:

  • Response surface (RS) models demonstrate competitive performance compared to traditional PWO and CP models.
  • Model averaging is effective for handling model uncertainty in OofA analysis.
  • A compound optimality criterion facilitates robust experimental design.

Conclusions:

  • Response surface (RS) regression offers a powerful and competitive approach for analyzing order-of-addition experiments.
  • Model averaging and compound optimality criteria enhance the robustness and efficiency of experimental design and analysis.