vb_cs_wish: Cross-sectional FoSR using Variational Bayes and Wishart prior

Description

Fitting function for function-on-scalar regression for cross-sectional data. This function estimates model parameters using VB and estimates the residual covariance surface using a Wishart prior.

Usage

vb_cs_wish(
  formula,
  data = NULL,
  verbose = TRUE,
  Kt = 5,
  alpha = 0.1,
  min.iter = 10,
  max.iter = 50,
  Aw = NULL,
  Bw = NULL,
  v = NULL
)

Arguments

formula: a formula indicating the structure of the proposed model.
data: an optional data frame, list or environment containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which the function is called.
verbose: logical defaulting to TRUE -- should updates on progress be printed?
Kt: number of spline basis functions used to estimate coefficient functions
alpha: tuning parameter balancing second-derivative penalty and zeroth-derivative penalty (alpha = 0 is all second-derivative penalty)
min.iter: minimum number of iterations of VB algorithm
max.iter: maximum number of iterations of VB algorithm
Aw: hyperparameter for inverse gamma controlling variance of spline terms for population-level effects; if NULL, defaults to Kt/2.
Bw: hyperparameter for inverse gamma controlling variance of spline terms for population-level effects; if NULL, defaults to 1/2 tr(mu.q.beta of the model
v: hyperparameter for inverse Wishart prior on residual covariance; if NULL, Psi defaults to an FPCA decomposition of the residual covariance in which residuals are estimated based on an OLS fit of the model (note the "nugget effect" on this covariance is assumed to be constant over the time domain).

Author

Jeff Goldsmith ajg2202@cumc.columbia.edu

References

Goldsmith, J., Kitago, T. (2016). Assessing Systematic Effects of Stroke on Motor Control using Hierarchical Function-on-Scalar Regression. Journal of the Royal Statistical Society: Series C, 65 215-236.