General multilevel linear modeling for group analysis in FMRI

Christian F. Beckmann, Mark Jenkinson, Stephen M. Smith

Research output: Contribution to journalArticlepeer-review

1054 Citations (Scopus)


This article discusses general modeling of multisubject and/or multisession FMRI data. In particular, we show that a two-level mixed-effects model (where parameters of interest at the group level are estimated from parameter and variance estimates from the single-session level) can be made equivalent to a single complete mixed-effects model (where parameters of interest at the group level are estimated directly from all of the original single sessions' time series data) if the (co-)variance at the second level is set equal to the sum of the (co-)variances in the single-level form, using the BLUE with known covariances. This result has significant implications for group studies in FMRI, since it shows that the group analysis requires only values of the parameter estimates and their (co-)variance from the first level, generalizing the well-established "summary statistics" approach in FMRI. The simple and generalized framework allows different prewhitening and different first-level regressors to be used for each subject. The framework incorporates multiple levels and cases such as repeated measures, paired or unpaired t tests and F tests at the group level; explicit examples of such models are given in the article. Using numerical simulations based on typical first-level covariance structures from real FMRI data we demonstrate that by taking into account lower-level covariances and heterogeneity a substantial increase in higher-level Z score is possible.

Original languageEnglish
Pages (from-to)1052-1063
Number of pages12
Issue number2
Publication statusPublished - 1 Oct 2003


  • FMRI
  • Fixed and random effects
  • Group analysis
  • Mixed effects
  • Multisubject analysis

ASJC Scopus subject areas

  • Neurology
  • Cognitive Neuroscience

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