Takes a fitted `bru`

object produced by the function `bru()`

and produces
predictions given a new set of values for the model covariates or the
original values used for the model fit. The predictions can be based on any
R expression that is valid given these values/covariates and the joint
posterior of the estimated random effects.

## Arguments

- object
- data
A data.frame or SpatialPointsDataFrame of covariates needed for the prediction.

- formula
A formula where the right hand side defines an R expression to evaluate for each generated sample. If

`NULL`

, the latent and hyperparameter states are returned as named list elements. See Details for more information.- n.samples
Integer setting the number of samples to draw in order to calculate the posterior statistics. The default is rather low but provides a quick approximate result.

- seed
Random number generator seed passed on to

`inla.posterior.sample`

- probs
A numeric vector of probabilities with values in

`[0, 1]`

, passed to`stats::quantile`

- num.threads
Specification of desired number of threads for parallel computations. Default NULL, leaves it up to INLA. When seed != 0, overridden to "1:1"

- include
Character vector of component labels that are needed by the predictor expression; Default: NULL (include all components that are not explicitly excluded)

- exclude
Character vector of component labels that are not used by the predictor expression. The exclusion list is applied to the list as determined by the

`include`

parameter; Default: NULL (do not remove any components from the inclusion list)- drop
logical; If

`keep=FALSE`

,`data`

is a`Spatial*DataFrame`

, and the prediciton summary has the same number of rows as`data`

, then the output is a`Spatial*DataFrame`

object. Default`FALSE`

.- ...
Additional arguments passed on to

`inla.posterior.sample`

## Value

a data.frame or Spatial* object with predicted mean values and other summary statistics attached.

## Details

Mean value predictions are accompanied by the standard errors, upper and lower 2.5% quantiles, the median, variance, coefficient of variation as well as the variance and minimum and maximum sample value drawn in course of estimating the statistics.

Internally, this method calls `generate.bru()`

in order to draw samples from
the model.

In addition to the component names (that give the effect
of each component evaluated for the input data), the suffix `_latent`

variable name can be used to directly access the latent state for a component,
and the suffix function `_eval`

can be used to evaluate a component at
other input values than the expressions defined in the component definition
itself, e.g. `field_eval(cbind(x, y))`

for a component that was defined with
`field(coordinates, ...)`

(see also `component_eval()`

).

For "iid" models with `mapper = bru_mapper_index(n)`

, `rnorm()`

is used to
generate new realisations for indices greater than `n`

.

## Examples

```
# \donttest{
if (bru_safe_inla(multicore = FALSE) &&
require("ggplot2", quietly = TRUE)) {
# Load the Gorilla data
data(gorillas, package = "inlabru")
# Plot the Gorilla nests, the mesh and the survey boundary
ggplot() +
gg(gorillas$mesh) +
gg(gorillas$nests) +
gg(gorillas$boundary) +
coord_fixed()
# Define SPDE prior
matern <- INLA::inla.spde2.pcmatern(gorillas$mesh,
prior.sigma = c(0.1, 0.01),
prior.range = c(0.01, 0.01)
)
# Define domain of the LGCP as well as the model components (spatial SPDE effect and Intercept)
cmp <- coordinates ~ mySmooth(main = coordinates, model = matern) + Intercept(1)
# Fit the model, with "eb" instead of full Bayes
fit <- lgcp(cmp, gorillas$nests,
samplers = gorillas$boundary,
domain = list(coordinates = gorillas$mesh),
options = list(control.inla = list(int.strategy = "eb"))
)
# Once we obtain a fitted model the predict function can serve various purposes.
# The most basic one is to determine posterior statistics of a univariate
# random variable in the model, e.g. the intercept
icpt <- predict(fit, NULL, ~ c(Intercept = Intercept_latent))
plot(icpt)
# The formula argument can take any expression that is valid within the model, for
# instance a non-linear transformation of a random variable
exp.icpt <- predict(fit, NULL, ~ c(
"Intercept" = Intercept_latent,
"exp(Intercept)" = exp(Intercept_latent)
))
plot(exp.icpt, bar = TRUE)
# The intercept is special in the sense that it does not depend on other variables
# or covariates. However, this is not true for the smooth spatial effects 'mySmooth'.
# In order to predict 'mySmooth' we have to define where (in space) to predict. For
# this purpose, the second argument of the predict function can take \code{data.frame}
# objects as well as Spatial objects. For instance, we might want to predict
# 'mySmooth' at the locations of the mesh vertices. Using
vrt <- vertices.inla.mesh(gorillas$mesh)
# we obtain these vertices as a SpatialPointsDataFrame
ggplot() +
gg(gorillas$mesh) +
gg(vrt, color = "red")
# Predicting 'mySmooth' at these locations works as follows
mySmooth <- predict(fit, vrt, ~mySmooth)
# Note that just like the input also the output will be a SpatialPointsDataFrame
# and that the predicted statistics are simply added as columns
class(mySmooth)
head(vrt)
head(mySmooth)
# Plotting the mean, for instance, at the mesh node is straight forward
ggplot() +
gg(gorillas$mesh) +
gg(mySmooth, aes(color = mean), size = 3)
# However, we are often interested in a spatial field and thus a linear interpolation,
# which can be achieved by using the gg mechanism for meshes
ggplot() +
gg(gorillas$mesh, color = mySmooth$mean)
# Alternatively, we can predict the spatial field at a grid of locations, e.g. a
# SpatialPixels object covering the mesh
pxl <- pixels(gorillas$mesh)
mySmooth2 <- predict(fit, pxl, ~mySmooth)
# This will give us a SpatialPixelDataFrame with the columns we are looking for
head(mySmooth2)
ggplot() +
gg(mySmooth2)
}
#> Current num.threads is '1:1'.
#> No num.threads change needed.
#> Regions defined for each Polygons
#> Warning: PROJ support is provided by the sf and terra packages among others
# }
```