Testing the independence assumption in linear models

Ronald Christensen, Edward J. Bedrick

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We propose using an existing set of statistical tools in a new way that allows one to test the independence assumption in standard normal theory linear models. The set of tools is near-replicate lack-of-fit tests. The classical lack-of-fit test requires a linear model in which some rows of the model matrix are repeated. Near-replicate lack-of-fit tests were developed to mimic the behavior of the classical test by identifying clusters of rows in the design matrix that are similar, though not necessarily exact replications. We argue that meaningful clusters can be formed more generally by constructing rational subgroups of data collected under similar circumstances. As such, observations in the same subgroup may be more highly correlated than observations in different subgroups. We investigate the behavior of these tests when used to identify lack of independence.

Original languageEnglish (US)
Pages (from-to)1006-1016
Number of pages11
JournalJournal of the American Statistical Association
Issue number439
StatePublished - Sep 1 1997
Externally publishedYes


  • Analysis of variance
  • Between clusters
  • Mixed models
  • Pure error
  • Regression analysis
  • Regression diagnostics
  • Replication
  • Variance components
  • Within clusters

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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