GeoTestIsotropy: Parametric bootstrap test for isotropy

Description

Performs an isotropy test based on parametric bootstrap by comparing an isotropic model (H0) with an anisotropic model (H1). A user-chosen spatial correlation model is fitted to spatial data, and the test statistic is a likelihood ratio between H1 (with anisotropy estimated) and H0 (anisotropy fixed at ratio = 1 and angle = 0). The p-value is computed via parametric bootstrap.

Usage

GeoTestIsotropy(data, coordx,
                start, fixed,
                optimizer = "bobyqa",
                model = "Gaussian",
                corrmodel = "Matern",
                lower = NULL, upper = NULL,
                B = 1000,
                likelihood = NULL,
                type = NULL,
                copula = NULL,
                neighb = 5,
                parallel = TRUE,
                ncores = NULL,
                progress = TRUE)

Value

An (invisible) list with components:

statistic: Observed LRT statistic.
pvalue: Bootstrap p-value.
ratio_hat: Estimated anisotropy ratio (> 1 indicates stretching along the principal axis).
angle_hat: Estimated anisotropy angle (radians/degrees according to GeoFit convention).
corrmodel: Correlation model used.
model: Marginal model used.
fit_H0: GeoFit object fitted under H0.
fit_H1: GeoFit object fitted under H1.
B_rep: Vector of LRT values obtained on the valid bootstrap replications.

Arguments

data: Numeric vector of observations (length n).
coordx: n x d matrix with the spatial coordinates of the sites (at least 2 columns for anisotropy analysis).
start: Named list with the parameters to be estimated; names must match those expected by CorrParam(corrmodel) and NuisParam(model).
fixed: Named list with the parameters kept fixed during estimation; together with start it must exactly cover the required set of parameters.
optimizer: Optimization algorithm to be used in GeoFit (e.g., "bobyqa").
model: Marginal model for the data (e.g., "Gaussian").
corrmodel: Spatial correlation model (e.g., "Matern").
lower, upper: Named lists with lower/upper bounds for parameters in start only. If NULL, no extra bounds beyond defaults.
B: Number of parametric bootstrap replications (default 1000).
likelihood: Type of (composite) likelihood to pass to GeoFit (e.g., "Marginal").
type: Composite-likelihood type (e.g., "Pairwise").
copula: Copula object for simulation via GeoSimCopula; if NULL Gaussian simulation is used.
neighb: Number of neighbors for composite-likelihood estimation, where applicable.
parallel: If TRUE, bootstrap fits are distributed in parallel through future.
ncores: Number of cores to use in parallel; if NULL it is chosen automatically up to B or parallel::detectCores()-1.
progress: If TRUE, show progress bars using progressr.

Author

Moreno Bevilacqua moreno.bevilacqua89@gmail.com https://sites.google.com/view/moreno-bevilacqua/home
Víctor Morales Oñate victor.morales@uv.cl https://sites.google.com/site/moralesonatevictor/
Christian Caamaño-Carrillo chcaaman@ubiobio.cl https://www.researchgate.net/profile/Christian-Caamano

Details

GeoTestIsotropy implements a likelihood ratio test (LRT) between:

H0: isotropic model with anisotropy parameters fixed at angle = 0, ratio = 1;
H1: anisotropic model with angle and ratio estimated.