Some new methods for the comparison of two linear regression models

Wei Liu, Mortaza Jamshidian, Ying Zhang, Frank Bretz, Xiaoliang Han

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

The frequently used approach to the comparison of two linear regression models is to use the partial F test. It is pointed out in this paper that the partial F test has in fact a naturally associated two-sided simultaneous confidence band, which is much more informative than the test itself. But this confidence band is over the entire range of all the covariates. As regression models are true or of interest often only over a restricted region of the covariates, the part of this confidence band outside this region is therefore useless and to ensure 1 - α simultaneous coverage probability is therefore wasteful of resources. It is proposed that a narrower and hence more efficient confidence band over a restricted region of the covariates should be used. The critical constant required in the construction of this confidence band can be calculated by Monte Carlo simulation. While this two-sided confidence band is suitable for two-sided comparisons of two linear regression models, a more efficient one-sided confidence band can be constructed in a similar way if one is only interested in assessing whether the mean response of one regression model is higher (or lower) than that of the other in the region. The methodologies are illustrated with two examples.

Original languageEnglish (US)
Pages (from-to)57-67
Number of pages11
JournalJournal of Statistical Planning and Inference
Volume137
Issue number1
DOIs
StatePublished - Jan 1 2007

Keywords

  • Confidence bands
  • Linear regression
  • Multiple comparisons
  • Simultaneous inference
  • Statistical simulation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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