smooths
translates the right hand side of a mgcv GAM
formula into a corresponding Bayesian representation of smooth terms. This
formula may include multiple combined smooths of different types, as well
as fixed effect terms and intercepts. The resulting greta array
representing the combined smooth can then be used in a greta model.
Usage
smooths(formula, data = list(), knots = NULL, sp = NULL, tol = 0)
Arguments
- formula
a GAM formula representing the smooth terms, as in
mgcv::gam()
. Only the right hand side of the formula will be used.- data
a data frame or list containing the covariates required by the formula. These covariates cannot be greta arrays.
- knots
an optional list containing user specified knot values to be used for basis construction, as in
mgcv::gam()
These knots cannot be greta arrays.- sp
an optional vector of smoothing parameters, two per smooth term in the model, in the same order as the formula. If
sp = NULL
, all smoothing parameters will be learned, otherwise all smoothing parameters must be specified by the user. The smoothing parameters may either be a numeric vector or a greta array (which could be a variable).- tol
a non-negative scalar numerical tolerance parameter. You can try increasing this if the model has numerical stability issues
Details
Only the right hand side of formula
will be used to define
the smooth terms. The user must complete the gam model by specifying the
link and likelihood term in greta. A warning will be issued if the formula
has a left hand side.
Note that by default, GAM formulas add an intercept term. If you have
already specified an intercept for your greta model, you can remove the
intercept from the smooth term by adding -1
as a term in your
formula.
Like mgcv::jagam()
, smooths
translates a
mgcv GAM formula into a Bayesian representation of the smooth terms, using
the GAM smoothing penalty matrix as a multivariate normal prior to penalise
model fitting. Unlike gam
, smooths
does not perform the
integration required to penalise model fitting. The model must be fitted by
MCMC to carry out this integration - it does not make sense to do maximum
likelihood optimisation on a greta model that uses smooths
.
Examples
if (FALSE) { # \dontrun{
n <- 30
x <- runif(n, 0, 10)
f <- function(x) {
sin(x * 2) + 1.6 * (x < 3) - 1.4 * (x > 7)
}
y <- f(x) + rnorm(n, 0, 0.3)
x_plot <- seq(0, 10, length.out = 200)
z <- smooths(~ s(x), data = data.frame(x = x))
distribution(y) <- normal(z, 0.3)
z_pred <- evaluate_smooths(z, newdata = data.frame(x = x_plot))
# build model
m <- model(z_pred)
draws <- mcmc(m, n_samples = 100)
plot(x, y, pch = 19, cex = 0.4, col = "red")
apply(draws[[1]], 1, lines, x = x_plot, col = "blue")
points(x, y, pch = 19, cex = 0.4, col = "red")
} # }