Predictions from a gamRTMB fit

New data goes through mgcv::PredictMat() on the stored smoothCon objects, so the basis, knots and constraint matrices are exactly those of the fit. Smooths are never re-fitted on new data, which would place different knots.

Usage

# S3 method for class 'gamRTMB'
predict(
  object,
  newdata = NULL,
  type = c("link", "response", "terms", "quantile"),
  prob = c(0.05, 0.25, 0.5, 0.75, 0.95),
  se.fit = FALSE,
  ...
)

Arguments

object

A gamRTMB fit.

newdata

Optional data frame. If omitted, the fitting data's in-sample linear predictors are returned.

type

"link" (default) for the linear predictors, "response" for the parameters on their natural scale, "terms" for the contribution of each smooth separately, or "quantile" for quantiles of the fitted distribution. As in mgcv, "terms" excludes the intercept and any offset, which belong to the predictor rather than to a smooth.

prob

Probabilities for type = "quantile".

se.fit

Also return standard errors; needs a fit made with joint_precision = TRUE.

...

Ignored.

Value

For type = "link"/"response", a named list with one vector per distributional parameter. For type = "terms", a named list with a matrix of per-term contributions for each parameter. For type = "quantile", a matrix with one column per probability. With se.fit = TRUE, a list of fit and se.fit in the same shape.

Quantiles

type = "quantile" evaluates the fitted distribution's quantile function at each observation, giving covariate-dependent quantiles — which is much of the point of letting every parameter vary. It needs the family to have a quantile function; families() reports which do.

Their standard errors come from the delta method. The quantile is differentiated numerically with respect to each linear predictor — on the link scale, so the link's own derivative is absorbed into the difference and never has to be supplied — and those derivatives are combined with the predictors' joint covariance, cross-parameter terms included. Checked against the analytic normal case to a relative 1e-9.

Offered only for a continuous response, because for a lattice or mixed one the quantile function is a step and its derivative is not meaningful.

The result is a standard error on the response scale, since a quantile is a value of the response and has no link of its own. A symmetric interval built from it can therefore cross a boundary of the support — for a positive response, q - 2 * se can be negative in the lower tail where the quantile is small and its uncertainty is not. Read such an interval as a local measure of precision rather than a range of plausible values, or take percentiles of quantiles simulated from the joint posterior instead.