Predict at new covariate values (population level)

Prediction of the linear predictor at newdata, on the link or response scale. The fixed-effect part is X beta with credible bounds from the fixed-effect covariance (vcov()). For a fit carrying a continuous spatial field, the posterior-mean field is interpolated (kriged) to the newdata coordinates and added to the linear predictor by default, so predict() gives the conditional (location-specific) prediction. Three continuous field families are supported: an SPDE Matern field (spatial_spde()), projected through the mesh; a Hilbert-space GP field (spatial_gp(approx = "hsgp")), where the Laplacian basis is re-evaluated at the new coordinates (with the training centring / boundary); and a GP / NNGP field (spatial_gp()), interpolated by the NNGP conditional mean at each new location's nearest training locations. The HSGP and GP/NNGP fields are marginalised over the hyperparameter grid (not plugged in at the posterior mean). Ordinary random effects are held at zero (population level); add group effects from ranef() when needed. An areal (ICAR / BYM2 / CAR) or temporal (RW1 / RW2 / AR1) field is held at zero in the same way, at the training design too; the in-sample linear predictor with every fitted component is what posterior_predict() draws and what compare_models(criterion = "waic") / "loo" score.

Usage

# S3 method for class 'tulpa_fit'
predict(
  object,
  newdata = NULL,
  type = c("link", "response"),
  se.fit = FALSE,
  level = 0.95,
  include_field = TRUE,
  ...
)

Arguments

object: A tulpa_fit object.
newdata: Data frame of covariates (and, for an SPDE fit, the coordinate columns named in the spec's coordinate formula). If NULL, predicts at the training design (requires $model_matrix).
type: "link" (linear predictor) or "response" (mean scale, E[y]). For a binomial fit the "response" scale here is the per-trial success probability g^{-1}(eta) (there is no n_trials at newdata); this differs from fitted(), which returns the trial-scaled expected count at the training design. On a zero-inflated fit (ziformula) the "link" scale is the count predictor and the "response" scale is the mixture mean (1 - pi) E[y | eta], pi = plogis(X_zi beta_zi), with the zero-inflation design rebuilt from the fit's ziformula at newdata.
se.fit: If TRUE, also return the link-scale standard error and credible bounds. With an included SPDE field the SE propagates the joint (fixed-effect, field) posterior precision at the fitted hyperparameters – including the cross term – conditional on (range, sigma) (a nested fit's hyperparameter-grid spread is not propagated, so the bound is mildly optimistic when that posterior is wide). Integer-nu, no-RE SPDE fits only; other layouts decline with an explanation. On a zero-inflated fit se.fit is the count predictor's, and the response-scale bounds are quantiles of the mixture mean over draws of the count and zero-inflation coefficients jointly (pinned, so repeated calls agree).
level: Credible-interval level (default 0.95).
include_field: For a continuous-spatial fit (SPDE, HSGP, or GP/NNGP), add the kriged field to the prediction (default TRUE). FALSE gives the fixed-effect (population) prediction. Ignored for fits with no continuous field. For an HSGP or GP/NNGP fit the field is added to the point prediction but its uncertainty is not yet propagated into se.fit (the interval reflects the fixed-effect covariance only).
...: Ignored.

Value

If se.fit = FALSE, a numeric vector. If se.fit = TRUE, a data frame with fit, se.fit (link scale), lower, upper on the requested scale.