Introduction to functional (AKA longitudinal, repeated measures, panel, growth curve) data
Mary Lindstrom, Department of Biostatistics, UW-Madison
Friday, November 22, 2002, 3:00 pm
Waisman Conference Center (North [new] Tower, 2nd floor)
NOTE: This is an introductory talk for non-specialists. Only basic linear models knowledge is assumed.
Functional data arise when the ideal observation for each experimental unit is a curve or function rather than a single number. For example, in spirometry one response of interest is the curve that relates time to the volume of air pushed through a tube by a subject. Typically (but not exclusively) time is the continuous predictor variable in Functional data sets. Movement data and growth data are two other examples of functional data where time is the predictor variable.
We typically cannot observe the entire curve for each subject so instead we obtain a set of observations (usually with error) at a number of time points. The time points may or may not be the same for each subject. Goals in functional data analysis include estimating the typical curve for the population from which the sample of subjects was drawn, describing the between- and within-curve variability structure, estimating individual curves, and testing for differences between groups of curves.
Methods for modeling functional data are many and diverse. I will briefly describe 3 related approaches. The first is the two-stage or data reduction method where each subjects' data are reduced to a small number of summary measures before analysis. The second is linear, mixed-effects (or hierarchical) models. I will also describe a semi-parametric, mixed-effects model which pools shape information across curves to estimate a common, non-parametric ``shape function'' which is then adjusted to fit individual subjects by applying simple, subject-specific, parametric transformations.
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