fpca_gauss: Functional principal components analysis via variational EM

Description

Function used in the FPCA step for registering functional data, called by register_fpca when family = "gaussian". Parameters estimated based on probabilistic PCA framework originally introduced by Tipping and Bishop in 1999.

Usage

fpca_gauss(
  Y,
  npc = 1,
  Kt = 8,
  maxiter = 20,
  t_min = NULL,
  t_max = NULL,
  print.iter = FALSE,
  row_obj = NULL,
  seed = 1988,
  ...
)

Value

An object of class fpca containing:

knots: Cutpoints for B-spline basis used to rebuild alpha.
efunctions: \(D \times npc\) matrix of estimated FPC basis functions.
evalues: Estimated variance of the FPC scores.
npc: number of FPCs.
scores: \(I \times npc\) matrix of estimated FPC scores.
alpha: Estimated population-level mean.
mu: Estimated population-level mean. Same value as alpha but included for compatibility with refund.shiny package.
subject_coefs: B-spline basis coefficients used to construct subject-specific means. For use in registr() function.
Yhat: FPC approximation of subject-specific means.
Y: The observed data.
family: gaussian, for compatibility with refund.shiny package.
sigma2: Estimated error variance

Arguments

Y: Dataframe. Should have variables id, value, index.
npc: Defaults to 1. Number of principal components to calculate.
Kt: Number of B-spline basis functions used to estimate mean functions. Default is 8.
maxiter: Maximum number of iterations to perform for EM algorithm. Default is 50.
t_min: Minimum value to be evaluated on the time domain.
t_max: Maximum value to be evaluated on the time domain.
print.iter: Prints current error and iteration
row_obj: If NULL, the function cleans the data and calculates row indices. Keep this NULL if you are using standalone register function.
seed: Set seed for reproducibility. Default is 1991.
...: Additional arguments passed to or from other functions

Author

Julia Wrobel jw3134@cumc.columbia.edu, Jeff Goldsmith ajg2202@cumc.columbia.edu

References

Tipping, M. E. and Bishop, C (1999). Probabilistic Principal Component Analysis. Journal of the Royal Statistical Society Series B,, 592--598.