IDE {IDE} | R Documentation |
Construct IDE object, fit and predict
Description
The integro-difference equation (IDE) model is constructed using the function IDE
, fitted using the function IDE.fit
and used for prediction using the function predict
.
Usage
IDE(
f,
data,
dt,
process_basis = NULL,
kernel_basis = NULL,
grid_size = 41,
forecast = 0,
hindcast = 0
)
fit.IDE(object, method = "DEoptim", fix = list(), ...)
## S3 method for class 'IDE'
predict(object, newdata = NULL, covariances = FALSE, ...)
Arguments
f |
|
data |
data object of class |
dt |
object of class |
process_basis |
object of class |
kernel_basis |
a list of four objects of class |
grid_size |
an integer identifying the number of grid points to use (in one dimension) for numerical integrations |
forecast |
an integer indicating the number of steps to forecast (where each step corresponds to one |
hindcast |
an integer indicating the number of steps to hindcast (where each step corresponds to one |
object |
object of class |
method |
method used to estimate the parameters. Currently only |
fix |
list of parameters which are fixed and not estimated (e.g., |
... |
other parameters passed to |
newdata |
data frame or object of class |
covariances |
a flag indicating whether prediction covariances should be returned or not when predicting |
Details
The first-order spatio-temporal IDE process model used in the package IDE
is given by
for , where
is a transition kernel, depending on parameters
that specify “redistribution weights” for the process at the previous time over the spatial domain,
, and
is a time-varying (but statistically independent in time) continuous mean-zero Gaussian spatial process. It is assumed that the parameter vector
does not vary with time. In general,
for the process to be stable (non-explosive) in time.
The redistribution kernel used by the package
IDE
is given by
where the spatially-varying kernel amplitude is given by and controls the temporal stationarity, the spatially-varying length-scale (variance) parameter
corresponds to a kernel scale (aperture) parameter (i.e., the kernel width increases as
increases), and the mean (shift) parameters
and
correspond to a spatially-varying shift of the kernel relative to location
. Spatially-invariant kernels (i.e., where the elements of
are not functions of space) are assumed by default. The spatial dependence, if present, is modelled using a basis-function decomposition.
IDE.fit()
takes an object of class IDE
and estimates all unknown parameters, namely the parameters and the measurement-error variance, using maximum likelihood. The only method currently used is the genetic algorithm in the package
DEoptim
. This has been seen to work well on several simulation and real-application studies on multi-core machines.
Once the parameters are fitted, the IDE
object is passed onto the function predict()
in order to carry out optimal predictions over some prediction spatio-temporal locations. If no locations are specified, the spatial grid used for discretising the integral at every time point in the data horizon are used. The function predict
returns a data frame in long format. Change-of-support is currently not supported.
Value
Object of class IDE
that contains get
and set
functions for retrieving and setting internal parameters, the function update_alpha
which predicts the latent states, update_beta
which estimates the regression coefficients based on the current predictions for alpha
, and negloglik
, which computes the negative log-likelihood.
See Also
show_kernel
for plotting the kernel
Examples
SIM1 <- simIDE(T = 5, nobs = 100, k_spat_invariant = 1)
IDEmodel <- IDE(f = z ~ s1 + s2,
data = SIM1$z_STIDF,
dt = as.difftime(1, units = "days"),
grid_size = 41)
#fit_results_sim1 <- fit.IDE(IDEmodel,
# parallelType = 1)
#ST_grid_df <- predict(fit_results_sim1$IDEmodel)