bfpca: Binary functional principal components analysis

Description

Function used in the FPCA step for registering binary functional data, called by register_fpca when family = "binomial". This method uses a variational EM algorithm to estimate scores and principal components for binary functional data.

Usage

bfpca(
  Y,
  npc = 1,
  Kt = 8,
  maxiter = 50,
  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: binomial, for compatibility with refund.shiny package.
error: vector containing error for each iteration of the algorithm.

Arguments

Y: Dataframe. Should have variables id, value, index.
npc: Default is 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 1988.
...: Additional arguments passed to or from other functions

Author

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

References

Jaakkola, T. S. and Jordan, M. I. (1997). A variational approach to Bayesian logistic regression models and their extensions. Proceedings of the Sixth International Workshop on Artificial Intelligence and Statistics.

Tipping, M. E. (1999). Probabilistic Visualisation of High-dimensional binary data. Advances in neural information processing systems, 592--598.

Examples

Run this code

Y = simulate_functional_data()$Y
bfpca_object = bfpca(Y, npc = 2, print.iter = TRUE)

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