vb_mult_wish: Multilevel 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. If prior hyperparameters are NULL they are estimated using the data.

Usage

vb_mult_wish(
  formula,
  data = NULL,
  verbose = TRUE,
  Kt = 5,
  alpha = 0.1,
  min.iter = 10,
  max.iter = 50,
  Az = NULL,
  Bz = NULL,
  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
Az: hyperparameter for inverse gamma controlling variance of spline terms for subject-level effects
Bz: hyperparameter for inverse gamma controlling variance of spline terms for subject-level effects
Aw: hyperparameter for inverse gamma controlling variance of spline terms for population-level effects
Bw: hyperparameter for inverse gamma controlling variance of spline terms for population-level effects
v: hyperparameter for inverse Wishart prior on residual covariance

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.