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Unpublished Paper
Cross-sectional versus longitudinal designs for function estimation, with an application to cerebral cortex development
(2017)
  • Philip T. Reiss
Abstract
Motivated by studies of the development of the human cerebral cortex, we consider
the estimation of a mean growth trajectory and the relative merits of cross-sectional
and longitudinal data for that task. We define a class of relative efficiencies that
compare function estimates in terms of aggregate variance of a parametric function
estimate. These generalize the classical design effect for estimating a scalar with
cross-sectional versus longitudinal data, and in particular cases are shown to be
bounded above by it. Turning to nonparametric function estimation, we find that a
longitudinal fits may tend to have higher aggregate variance than cross-sectional
ones, but that this may occur because the former have higher effective degrees of
freedom reflecting greater sensitivity to subtle features of the estimand. These ideas
are illustrated with cortical thickness data from a longitudinal neuroimaging study.
Keywords
  • Accelerated longitudinal design,
  • Cortical thickness,
  • Design effect,
  • Effective degrees of freedom,
  • Magnetic resonance imaging,
  • Nonparametric mixed-effects model,
  • Penalized splines
Publication Date
2017
Citation Information
Philip T. Reiss. "Cross-sectional versus longitudinal designs for function estimation, with an application to cerebral cortex development" (2017)
Available at: http://works.bepress.com/phil_reiss/44/