fitted method for funeigen object

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Description

Returns fitted values for a funeigen object.

Usage

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## S3 method for class 'funeigen'
fitted(object, type = "functions", ...)

Arguments

object

A funeigen object.

type

A character string, one of the following: functions, eigenfunctions, loadings, eigenvalues, mean, centered, covariance, noise.variance, midpoints. These are the constructs for which fitted values can be returned.

...

Other optional arguments which may be passed from other methods but ignored by this one.

Details

A funeigen object represents a principal component analysis of irregular longitudinal data, following the method used by Goldsmith et al. (2011).

Value

A matrix or vector containing the appropriate fitted values. What is returned depends on the type parameter. functions gives the fitted values of the smooth latent x(t) functions at a grid of time points. eigenfunctions gives the estimated eigenfunctions at each time point. loadings gives the loading of each subject on each estimated eigenfunction. mean gives the mean value for the smooth latent x(t) functions. centered gives the centered x(t) functions (the estimated function subtracting the mean function) . covariance gives the estimated covariance matrix of x(s) and x(t) on a grid of time points s and t. noise.variance gives the estimated measurement error variance on the x(t) functions. midpoints gives the time points for the grid, on which functions, mean, centered, and covariance are defined; they are viewed as midpoints of bins of observation times (see Goldsmith et al., 2011).

References

Goldsmith, J., Bobb, J., Crainiceanu, C. M., Caffo, B., and Reich, D. (2011). Penalized functional regression. Journal of Computational and Graphical Statistics, 20(4), 830-851. DOI: 10.1198/jcgs.2010.10007.