bfpca: Binary functional principal components analysis
In oslerinhealth/registr: Curve Registration for Exponential Family Functional Data

Description Usage Arguments Value Author(s) References Examples

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.

The number of functional principal components (FPCs) can either be specified directly (argument npc) or chosen based on the explained share of variance (npc_varExplained). For the latter, the solution is based on running the FPCA with npc = 20 (and correspondingly Kt = 20) before reducing the solution to the relevant number of FPCs. Doing so, we approximate the overall variance in the data Y with the variance represented by the FPC basis with 20 FPCs.

bfpca(
  Y,
  npc = NULL,
  npc_varExplained = NULL,
  Kt = 8,
  maxiter = 50,
  t_min = NULL,
  t_max = NULL,
  print.iter = FALSE,
  row_obj = NULL,
  seed = 1988,
  periodic = FALSE,
  error_thresh = 1e-04,
  verbose = 1,
  subsample = TRUE,
  ...
)

`Y`	Dataframe. Should have variables id, value, index.
`npc`	The number of functional principal components (FPCs) has to be specified either directly as `npc` or based on their explained share of variance. In the latter case, `npc_varExplained` has to be set to a share between 0 and 1.
`npc_varExplained`	The number of functional principal components (FPCs) has to be specified either directly as `npc` or based on their explained share of variance. In the latter case, `npc_varExplained` has to be set to a share between 0 and 1.
`Kt`	Number of B-spline basis functions used to estimate mean functions and functional principal components. Default is 8. If `npc_varExplained` is used, `Kt` is set to 20.
`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. Defaults to 1988.
`periodic`	If TRUE, uses periodic b-spline basis functions. Default is FALSE.
`error_thresh`	Error threshold to end iterations. Defaults to 0.0001.
`verbose`	Can be set to integers between 0 and 4 to control the level of detail of the printed diagnostic messages. Higher numbers lead to more detailed messages. Defaults to 1.
`subsample`	if the number of rows of the data is greater than 10 million rows, the 'id' values are subsampled to get the mean coefficients.
`...`	Additional arguments passed to or from other functions

An object of class fpca containing:

`fpca_type`	Information that FPCA was performed with the 'variationEM' approach, in contrast to registr::gfpca_twoStep.
`t_vec`	Time vector over which the mean `mu` and the functional principal components `efunctions` were evaluated.
`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.
`evalues_sum`	Approximation of the overall variance in `Y`, based on an initial run of the FPCA with `npc = 20`. Is `NULL` if `npc_varExplained` was not specified.
`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, before applying the response function.
`Y`	The observed data.
`family`	`binomial`, for compatibility with `refund.shiny` package.
`error`	vector containing error for each iteration of the algorithm.

Julia Wrobel julia.wrobel@cuanschutz.edu, Jeff Goldsmith ajg2202@cumc.columbia.edu, Alexander Bauer alexander.bauer@stat.uni-muenchen.de

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.

Y = simulate_functional_data()$Y

# estimate 2 FPCs
bfpca_obj = bfpca(Y, npc = 2, print.iter = TRUE)
plot(bfpca_obj)

# estimate npc adaptively, to explain 90% of the overall variation
bfpca_obj2 = bfpca(Y, npc_varExplained = 0.9, print.iter = TRUE, maxiter = 100)
plot(bfpca_obj2)