gibbs_cs_fpca: Cross-sectional FoSR using a Gibbs sampler and FPCA

Description

Fitting function for function-on-scalar regression for cross-sectional data. This function estimates model parameters using a Gibbs sampler and estimates the residual covariance surface using FPCA.

Usage

gibbs_cs_fpca(
  formula,
  Kt = 5,
  Kp = 2,
  data = NULL,
  verbose = TRUE,
  N.iter = 5000,
  N.burn = 1000,
  SEED = NULL,
  sig2.me = 0.01,
  alpha = 0.1,
  Aw = NULL,
  Bw = NULL,
  Apsi = NULL,
  Bpsi = NULL
)

Arguments

formula: a formula indicating the structure of the proposed model.
Kt: number of spline basis functions used to estimate coefficient functions
Kp: number of FPCA basis functions to be estimated
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?
N.iter: number of iterations used in the Gibbs sampler
N.burn: number of iterations discarded as burn-in
SEED: seed value to start the sampler; ensures reproducibility
sig2.me: starting value for measurement error variance
alpha: tuning parameter balancing second-derivative penalty and zeroth-derivative penalty (alpha = 0 is all second-derivative penalty)
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
Apsi: hyperparameter for inverse gamma controlling variance of spline terms for FPC effects
Bpsi: hyperparameter for inverse gamma controlling variance of spline terms for FPC effects

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.