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.

## Usage

# S3 method for bru
predict(
object,
data = NULL,
formula = NULL,
n.samples = 100,
seed = 0L,
probs = c(0.025, 0.5, 0.975),
include = NULL,
exclude = NULL,
drop = FALSE,
...
)

## Arguments

object

An object obtained by calling bru() or lgcp().

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

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)) {

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