# vb_mult_fpca: Multilevel FoSR using Variational Bayes and FPCA

## Description

Fitting function for function-on-scalar regression for multilevel data.
This function estimates model parameters using a VB and estimates
the residual covariance surface using FPCA.

## Usage

vb_mult_fpca(
formula,
data = NULL,
verbose = TRUE,
Kt = 5,
Kp = 2,
alpha = 0.1,
argvals = 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

Kp

number of FPCA basis functions to be estimated

alpha

tuning parameter balancing second-derivative penalty and
zeroth-derivative penalty (alpha = 0 is all second-derivative penalty)

argvals

not currently implemented

## 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.