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Cross‐sectional versus longitudinal designs for function estimation, with an application to cerebral cortex development
Author(s) -
Reiss Philip T.
Publication year - 2018
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.7617
Subject(s) - nonparametric statistics , estimation , bounded function , neuroimaging , econometrics , function (biology) , longitudinal data , statistics , mathematics , computer science , psychology , economics , neuroscience , mathematical analysis , management , biology , evolutionary biology , data mining
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 are shown to be bounded above by it in certain cases. Turning to nonparametric function estimation, we find that 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.