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

```
vb_cs_fpca(
formula,
data = NULL,
verbose = TRUE,
Kt = 5,
Kp = 2,
alpha = 0.1,
Aw = NULL,
Bw = NULL,
Apsi = NULL,
Bpsi = NULL,
argvals = NULL
)
```

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)

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

argvals

not currently implemented

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.