Linear transformations of linear mixed-effects models

Christopher H. Morrell, Jay D. Pearson, Larry J. Brant

Research output: Contribution to journalArticlepeer-review

94 Scopus citations


A number of articles have discussed the way lower order polynomial and interaction terms should be handled in linear regression models. Only if all lower order terms are included in the model will the regression model be invariant with respect to coding transformations of the variables. If lower order terms are omitted, the regression model will not be well formulated. In this paper, we extend this work to examine the implications of the ordering of variables in the linear mixed-effects model. We demonstrate how linear transformations of the variables affect the model and tests of significance of fixed effects in the model. We show how the transformations modify the random effects in the model, as well as their covariance matrix and the value of the restricted log-likelihood. We suggest a variable selection strategy for the linear mixed-effects model.

Original languageEnglish (US)
Pages (from-to)338-343
Number of pages6
JournalAmerican Statistician
Issue number4
StatePublished - Nov 1997


  • Hierarchical linear models
  • Hierarchical ordering
  • Random coefficient models
  • Variable selection
  • Well-formulated models

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty


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