Geometric goodness of fit

Description

The spatgeom package provides goodness-of-fit tests for spatial point process models. The spatgeom package provides the implementation to perform the geometric spatial point analysis developed in Hernández & Solís (2022) doi:10.1007/s00180-022-01244-1. It estimates the geometric goodness-of-fit index for a set of variables against a response one based on the 'sf' package. The package has methods to print and plot the results.

Installation

The package is currently available on CRAN and can be installed using:

install.packages("spatgeom")

and loaded using the following command:

library(spatgeom)

Usage

Estimating the geometric goodness-of-fit index

The package has one main function spatgeom that takes as input a set of variables and a response one.

For example, this is how you can use the package to estimate the geometric goodness-of-fit index with a set of variables in a donut shape against a response one:

 xy <- donut_data(n = 100, a = -1, b = 1, theta = 2 * pi)
 estimation <- spatgeom(y = xy[, 1], x = xy[, -1])

The package allow to estimate the envelope of the curve using the parameter envelope=TRUE:

 estimation <- spatgeom(y = xy[, 1], x = xy[, -1], envelope = TRUE)

In the example, the estimation object is a list of class spatgeom with the following elements:

• call: The function call.
• x: x input.
• y: y output.
• results: A list of size ncol(x) corresponding to each column of x. Each element of the list has:
  • triangles: a data frame of class sfc (see [sf::st_sf()])with columns geometry, segments, max_length and alpha. The data.frame contains the whole Delanauy triangulation for the corresponding column of x and y. The segments column are the segments of each individual triangle and max_length is the maximum length of them.
  • geom_indices: a data frame with columns alpha and geom_corr. The alpha column is a numeric vector of size nalphas from the minimum to the maximum distance between points estimated in the data. The geom_corr column is the value 1 - (alpha shape Area)/(containing box Area).
  • intensity: the intensity estimated for the corresponding column of x and y.
  • mean_n: the mean number of points in the point process.
  • envelope_data: a data frame in tidy format with 40 runs of a CSR process, if envelope=TRUE, The CSR is created by generating n uniform points in the plane, where n is drawn from Poisson distribution with parameter mean_n.

Printing and plotting the results

The package has a print method for objects of class spatgeom:

print(estimation)

and a plot method for objects of class spatgeom. The plot method has two options: curve and deriv. The curve option plots the curve of of the goodness-of-fit index. The deriv option plots the numerical derivative.

plot_curve(estimation, type = "curve")
plot_curve(estimation, type = "deriv")

Citation

If you use the spatgeom package in your work, please cite the following paper:

• Hernández, D. and Solís, F. (2022). Geometric goodness-of-fit tests for spatial point process models. Statistics and Computing, 32(1), 1-19. doi:10.1007/s00180-022-01244-1

• Solís, M., Hernández, A., & Pasquier, C. (2023). spatgeom: Geometric Spatial Point Analysis (0.3.0). https://cran.r-project.org/web/packages/spatgeom/index.html

License

This package is free and open source software, licensed under MIT License. See the LICENSE file for details.