Bayesian Analysis of Ordered Categorical Data From Industrial Experiments

Abstract

Data from industrial experiments often involve an ordered categorical response, such as a qualitative rating. Analysis of variance-based analyses may be inappropriate for such data, suggesting the use of generalized linear models (GLM's). When the data are observed from a fractionated experiment, likelihood-based GLM estimates may be infinite, especially when factors have large effects. These difficulties are overcome with a Bayesian GLM, which is implemented via the Gibbs sampling algorithm. Techniques for modeling data and for subsequently using the identified model to optimize the process are outlined. An important advantage in the optimization stage is that uncertainty in the parameter estimates is accounted for in the model. For robust design experiments, the Bayesian approach easily incorporates the variability of the noise factors using the response modeling approach. This approach and its techniques are used to analyze two data sets, one of which arises from a robust design experiment.

KEY WORDS:

• Binary data
• Generalized linear model
• Gibbs sampler
• Robust design