sprnorm function

Simulate a spatial normal (Gaussian) random variable

Simulate a spatial normal (Gaussian) random variable with a specific mean and covariance structure.

sprnorm(
  spcov_params,
  mean = 0,
  samples = 1,
  data,
  randcov_params,
  partition_factor,
  ...
)

## S3 method for class 'exponential'
sprnorm(
  spcov_params,
  mean = 0,
  samples = 1,
  data,
  randcov_params,
  partition_factor,
  xcoord,
  ycoord,
  ...
)

## S3 method for class 'none'
sprnorm(
  spcov_params,
  mean = 0,
  samples = 1,
  data,
  randcov_params,
  partition_factor,
  ...
)

## S3 method for class 'ie'
sprnorm(
  spcov_params,
  mean = 0,
  samples = 1,
  data,
  randcov_params,
  partition_factor,
  ...
)

## S3 method for class 'car'
sprnorm(
  spcov_params,
  mean = 0,
  samples = 1,
  data,
  randcov_params,
  partition_factor,
  W,
  row_st = TRUE,
  M,
  ...
)

Arguments

• spcov_params: An spcov_params() object.

• mean: A numeric vector representing the mean. mean must have length 1 (in which case it is recycled) or length equal to the number of rows in data. The default is 0.

• samples: The number of independent samples to generate. The default is 1.

• data: A data frame or sf object containing spatial information.

• randcov_params: A randcov_params() object.

• partition_factor: A formula indicating the partition factor.

• ...: Other arguments. Not used (needed for generic consistency).

• xcoord: Name of the column in data representing the x-coordinate. Can be quoted or unquoted. Not required if data are an sf

  object.

• ycoord: Name of the column in data representing the y-coordinate. Can be quoted or unquoted. Not required if data are an sf

  object.

• W: Weight matrix specifying the neighboring structure used for car and sar models. Not required if data are an sf

  polygon object and W should be calculated internally (using queen contiguity).

• row_st: A logical indicating whether row standardization be performed on W. The default is TRUE.

• M: M matrix satisfying the car symmetry condition. The car symmetry condition states that $(I - range * W)^{-1}M$ is symmetric, where $I$ is an identity matrix, $range$ is a constant that controls the spatial dependence, W is the weights matrix, and $^{-1}$ represents the inverse operator. M is required for car models when W is provided and row_st is FALSE. When M, is required, the default is the identity matrix.

Returns

If samples is 1, a vector of random variables for each row of data

is returned. If samples is greater than one, a matrix of random variables is returned, where the rows correspond to each row of data and the columns correspond to independent samples.

Details

Random variables are simulated via the product of the covariance matrix's square (Cholesky) root and independent standard normal random variables with mean 0 and variance 1. Computing the square root is a significant computational burden and likely unfeasible for sample sizes much past 10,000. Because this square root only needs to be computed once, however, it is nearly the sample computational cost to call sprnorm() for any value of samples.

Only methods for the exponential, none, and car

covariance functions are documented here, but methods exist for all other spatial covariance functions defined in spcov_initial(). Syntax for the exponential method is the same as syntax for spherical, gaussian, triangular, circular, cubic, pentaspherical, cosine, wave, jbessel, gravity, rquad, magnetic, matern, cauchy, and pexponential methods. Syntax for the car method is the same as syntax for the sar method. The extra parameter for car and sar models is ignored when all observations have neighbors.

Examples

spcov_params_val <- spcov_params("exponential", de = 1, ie = 1, range = 1)
sprnorm(spcov_params_val, data = caribou, xcoord = x, ycoord = y)
sprnorm(spcov_params_val, mean = 1:30, samples = 5, data = caribou, xcoord = x, ycoord = y)