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.

```
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
)
```

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).

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.