Package 'spatgeom'

Donut example

Description

Generate data points with the shape of a donut.

Usage

donut_data(n, a, b, theta)

Arguments

n	Number of data points.
a	Lower bound of the second variable.
b	Upper bound of the second variable.
theta	Angle of the donut.

Value

A data frame with three variables. Variable 'y' is the response, variable 'x1' makes the donut shape with 'y', and 'x2' is a uniform random variable between a and b. '

Examples

xy <- donut_data(n = 30, a = -1, b = 1, theta = 2 * pi)

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Linear example

Description

Generate data points with a linear relationship.

Usage

linear_data(n = 100, a = -3, b = 3)

Arguments

n	Number of data points.
a, b	Lower and upper bound of the uniform distribution.

Value

A data frame with three variables. Variable 'y = 0.6 * x1 + 0.3 * x2

• 0.1 * x3' is the response, and 'x1', 'x2' and 'x3' are uniform random variables between a and b.

Examples

xy <- linear_data(n = 30, a = -1, b = 1)

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Plot alpha-shape for spatgeom objects

Description

Plot alpha-shape for spatgeom objects.

Usage

plot_alpha_shape(x, alpha, font_size = 12)

Arguments

x	an object of class spatgeom.
alpha	value of alpha determining the maximum length between points to build the alpha-shape.
font_size	a integer that increases the font size in the plot.

Value

a ggplot object with the raw alpha-shape for the original data at resolution alpha

Examples

xy <- donut_data(n = 30, a = -1, b = 1, theta = 2 * pi)

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

plot_alpha_shape(estimation, alpha = c(0.9, 1.2))

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plot spatgeom objects

Description

Plot method for objects of class spatgeom.

Usage

plot_curve(x, type = "curve", font_size = 12)

Arguments

x	an object of class spatgeom
type	a string that could be curve or deriv. The option curve plots the curve of alpha against geom_corr from the function spatgeom(). The deriv option plots the numerical derivative.
font_size	a integer that increases the font size in the plot.

Value

a ggplot object with the geometric indices (or its derivative). The plot is generated with the nalphas point of alpha and geom_corr from the function spatgeom.

In each panel, the theoretical CSR process is drawn using exp(-intensity * pi * x^2). where the intensity depends on each panel.

Examples

xy <- donut_data(n = 30, a = -1, b = 1, theta = 2 * pi)

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

plot_curve(estimation, type = "curve")

plot_curve(estimation, type = "deriv")

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print a spatgeom object

Description

Print method for objects of class spatgeom.

Usage

## S3 method for class 'spatgeom'
print(x, return_table = FALSE, ...)

Arguments

x	an object of class spatgeom
return_table	if TRUE, returns a data frame with the estimated values. Otherwise, print the data frame in console. Defaults to FALSE
...	further arguments passed to the plot function

Value

Print the estimate given by spatgeom.

Examples

xy <- donut_data(n = 30, a = -1, b = 1, theta = 2 * pi)

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

print(estimation)

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Geometric Spatial Point Pattern Analysis

Description

Function to estimate the geometric correlation between variables.

Usage

spatgeom(
  x,
  y,
  scale_pts = FALSE,
  nalphas = 100,
  envelope = FALSE,
  domain_type = c("bounding-box", "convex-hull"),
  mc_cores = 1
)

Arguments

x	numeric matrix or data.frame of covariables.
y	numeric vector of responses in a model.
scale_pts	boolean to make the estimations with scaled variables. Default FALSE.
nalphas	number of alphas generated for creating the geometric measure of fit index. Default 100.
envelope	boolean to determine if the Monte-Carlo should be estimated. Default FALSE.
domain_type	character with the type of domain to use. It can be either "bounding-box" or "convex-hull". Default "bounding-box".
mc_cores	integer with the number of parallel process to run (if available). Default 1.

Value

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_survival. 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_survival 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.

References

Hernández, A.J., Solís, M. Geometric goodness of fit measure to detect patterns in data point clouds. Comput Stat (2022). https://doi.org/10.1007/s00180-022-01244-1

Examples

xy <- donut_data(n = 30, a = -1, b = 1, theta = 2 * pi)
estimation <- spatgeom(y = xy[, 1], x = xy[, -1])

# If you want to estimate the envelope, you can use the envelope argument to
# TRUE. This will take a while to run.
## Not run: 
estimation_with_envelope <- spatgeom(
  y = xy[, 1], x = xy[, -1],
  envelope = TRUE
)

## End(Not run)

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