Simultaneous inference in general parametric models

Torsten Hothorn, Frank Bretz, Peter Westfall

Research output: Contribution to journalReview articlepeer-review

6981 Scopus citations


Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the overall type I error rate. In this paper we describe simultaneous inference procedures in general parametric models, where the experimental questions are specified through a linear combination of elemental model parameters. The framework described here is quite general and extends the canonical theory of multiple comparison procedures in ANOVA models to linear regression problems, generalized linear models, linear mixed effects models, the Cox model, robust linear models, etc. Several examples using a variety of different statistical models illustrate the breadth of the results. For the analyses we use the R add-on package multcomp, which provides a convenient interface to the general approach adopted here.

Original languageEnglish
Pages (from-to)346-363
Number of pages18
JournalBiometrical Journal
Issue number3
StatePublished - Jun 2008


  • Adjusted p-values
  • Multiple comparisons
  • Multiple tests
  • Multivariate normal distribution
  • Robust statistics
  • Simultaneous confidence intervals


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