eacf: Compute the empirical autocovariance

In spmodel: Spatial Statistical Modeling and Prediction

Compute the empirical autocovariance

Description

Compute the empirical autocovariance (i.e., empirical covariance) for varying bin sizes and cutoff values.

Usage

eacf(
  formula,
  data,
  xcoord,
  ycoord,
  cloud = FALSE,
  bins = 15,
  cutoff,
  dist_matrix,
  partition_factor
)

## S3 method for class 'eacf'
plot(x, ...)

Arguments

formula	A formula describing the fixed effect structure.
data	A data frame or sf object containing the variables in formula and geographic information.
xcoord	Name of the variable in data representing the x-coordinate. Can be quoted or unquoted. Not required if data is an sf object.
ycoord	Name of the variable in data representing the y-coordinate. Can be quoted or unquoted. Not required if data is an sf object.
cloud	A logical indicating whether the empirical autocovariance should be summarized by distance class or not. When cloud = FALSE (the default), pairwise autocovariances are binned and averaged within distance classes. When cloud = TRUE, all pairwise autocovariances and distances are returned (this is known as the "cloud" autocovariance).
bins	The number of equally spaced bins. The default is 15. Ignored if cloud = TRUE.
cutoff	The maximum distance considered. The default is half the diagonal of the bounding box from the coordinates.
dist_matrix	A distance matrix to be used instead of providing coordinate names.
partition_factor	An optional formula specifying the partition factor. If specified, autocovariances are only computed for observations sharing the same level of the partition factor.
x	An object from eacf().
...	Other arguments passed to other methods.

Details

The empirical autocovariance (i.e., empirical covariance) is a tool used to visualize and model spatial dependence by estimating the semivariance of a process at varying distances. For a constant-mean process, the autocovariance at distance h is denoted Cov(h) and defined as Cov(z1, z2). Under second-order stationarity, Cov(h) = Cov(0) - \gamma(h), where gamma(h) is the semivariance function at distance h. Typically the residuals from an ordinary least squares fit defined by formula are second-order stationary with mean zero. These residuals are used to compute the empirical autocovariance At a distance h, the empirical autocovariance is 1/N(h) \sum (r1 \times r2), where N(h) is the number of (unique) pairs in the set of observations whose distance separation is h and r1 and r2 are residuals corresponding to observations whose distance separation is h. In spmodel, these distance bins actually contain observations whose distance separation is h +- c, where c is a constant determined implicitly by bins. Typically, only observations whose distance separation is below some cutoff are used to compute the empirical semivariogram (this cutoff is determined by cutoff).

Value

If cloud = FALSE, a tibble (data.frame) with distance bins (bins), the average distance (dist), the average autocovariance (acov), and the number of (unique) pairs (np). If cloud = TRUE, a tibble (data.frame) with distance (dist) and autocovariance (acov) for each unique pair.

Examples

eacf(sulfate ~ 1, sulfate)
plot(eacf(sulfate ~ 1, sulfate))

spmodel documentation built on Jan. 24, 2026, 9:06 a.m.