Confidence interval coverage for designed experiments analyzed with GLMs

Sharon L. Lewis, Douglas Montgomery, Raymond H. Myers

Research output: Contribution to journalArticle

23 Scopus citations

Abstract

There are many industrial experiments where the response variable is nonnormal. Traditionally, variance-stabilizing transformations are made on such a response in order to obtain properties needed to use ordinary least squares and analysis of variance. Generalized linear models (GLMs) offer a powerful alternative to data transformation. Specifically, the performance in response estimation and prediction for a GLM is often superior to the model built using data transformations. The confidence interval constructed around the estimate of the mean for each experimental run provides the experimenter with critical information about model quality. In generalized linear models, confidence intervals are based on asymptotic theory. As such, they are regarded as statistically valid only for large samples. Therefore, in order to use confidence intervals to compare models, it is essential to evaluate these asymptotic intervals in terms of coverage for sample sizes typically encountered in designed industrial experiments. This paper uses Monte Carlo methods to investigate the coverage of confidence intervals for the GLM for factorial experiments with 8, 16, and 32 runs.

Original languageEnglish (US)
Pages (from-to)279-292
Number of pages14
JournalJournal of Quality Technology
Volume33
Issue number3
StatePublished - Jul 1 2001

    Fingerprint

Keywords

  • Design of experiments
  • Generalized linear models
  • Nonconstant variance
  • Nonnormality

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Strategy and Management
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering

Cite this