stlgcppm {stopp}

Fit a log-Gaussian Cox process model to a spatio-temporal point pattern

Description

This function estimates a log-Gaussian Cox process (LGCP), following the **joint minimum contrast** procedure introduced in Siino et al. (2018) .

Three covariances are available: separable exponential, Gneiting, and De Iaco-Cesare.

If the first and second arguments are set to local, a local log-Gaussian Cox process is fitted by means of the ** locally weighted minimum contrast** procedure proposed in D'Angelo et al. (2023).

Usage

stlgcppm(
  X,
  formula = ~1,
  verbose = TRUE,
  seed = NULL,
  cov = c("separable", "gneiting", "iaco-cesare"),
  first = c("global", "local"),
  second = c("global", "local"),
  mult = 4,
  hs = c("global", "local"),
  npx0 = 10,
  npt0 = 10,
  itnmax = 100,
  min_vals = NULL,
  max_vals = NULL
)

Arguments

X

A stp object

formula

An object of class formula: a symbolic description of the first-order intensity to be fitted. The current version only supports formulas depending on the spatial and temporal coordinates: x, y, t. Default to formula = ~ 1 which provides an homogeneous first-order intensity.

verbose

Default to TRUE

seed

The seed used for the simulation of the dummy points. Default to NULL.

cov

Covariance function to be fitted for the second-order intensity function. Default to separable. Other options are gneiting and iaco-cesare".

first

Character string indicating whether to fit a first-order intensity function with global or local parameters: either global (default) or local.

second

Character string indicating whether to fit a second-order intensity function with global or local parameters: either global (default) or local.

mult

The multiplicand of the number of data points, for setting the number of dummy points to generate for the quadrature scheme

hs

Character string indicating whether to select fixed or variable bandwidths for the kernel weights to be used in the log-likelihood. In any of those cases, the well-supported rule-of-thumb for choosing the bandwidth of a Gaussian kernel density estimator is employed. If hs = "global" (default), a fixed bandwidth is selected. If hs = "local", an individual bandwidth is selected for each point in the pattern X.

npx0

A positive integer representing the spatial distance to np-th closest event. Used in the computation of the local bandwidth. Suitable values are in the range from 10 (default) to 100.

npt0

A positive integer representing the temporal distance to np-th closest event. Used in the computation of the local bandwidth. Suitable values are in the range from 10 (default) to 100.

itnmax

Maximum number of iterations to run in the optimization procedure for the estimation of the second-order intensity parameters.

min_vals

Minimum values of the optimization procedure for the minimum contrast.

max_vals

Maximum values of the optimization procedure for the minimum contrast.

Details

Following the inhomogeneous specification in Diggle et al. (2013), we consider LGCPs with intensity

\Lambda(\textbf{u},t)=\lambda(\textbf{u},t)\exp(S(\textbf{u},t)).

Value

A list of the class stlgcppm, containing

IntCoefs

The fitted coefficients of the first-order intensity function

CovCoefs

The fitted coefficients of the second-order intensity function

X

The stp object provided as input

formula

The formula provided as input

cov

A string with the chosen covariance type

l

Fitted first-order intensity

mu

Mean function of the random intensity

mod_global

The glm object of the model fitted to the quadrature scheme for the first-order intensity parameters estimation

newdata

The data used to fit the model, without the dummy points

time

Time elapsed to fit the model, in minutes

Author(s)

Nicoletta D'Angelo, Giada Adelfio, and Marianna Siino

References

Baddeley, A. (2017). Local composite likelihood for spatial point processes. Spatial Statistics, 22, 261-295.

D'Angelo, N., Adelfio, G., and Mateu, J. (2023). Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes. Computational Statistics & Data Analysis, 180, 107679.

Diggle, P. J., Moraga, P., Rowlingson, B., and Taylor, B. M. (2013). Spatial and spatio-temporal log-gaussian cox processes: extending the geostatistical paradigm. Statistical Science, 28(4):542–563.

Gabriel, E., Rowlingson, B. S., and Diggle, P. J. (2013). stpp: An R Package for Plotting, Simulating and Analyzing Spatio-Temporal Point Patterns. Journal of Statistical Software, 53(2), 1–29. https://doi.org/10.18637/jss.v053.i02

Siino, M., Adelfio, G., and Mateu, J. (2018). Joint second-order parameter estimation for spatio-temporal log-Gaussian Cox processes. Stochastic environmental research and risk assessment, 32(12), 3525-3539.

See Also

print.stlgcppm, summary.stlgcppm, localsummary, plot.stlgcppm, localplot

Examples

catsub <- stp(greececatalog$df[1:200, ])

lgcp1 <- stlgcppm(catsub)