moran function

Computes Moran's I correlation index

Natively built for computing Moran's I on dgCMatrix objects, this routine allows computing the I on large sparse matrices (graphs). Part of its implementation was based on ape::Moran.I, which computes the I for dense matrices.

moran(x, w, normalize.w = TRUE, alternative = "two.sided")

Arguments

• x: Numeric vector of size $n$.

• w: Numeric matrix of size $n * n$. Weights. It can be either a object of class matrix or dgCMatrix

  from the Matrix package.

• normalize.w: Logical scalar. When TRUE normalizes rowsums to one (or zero).

• alternative: Character String. Specifies the alternative hypothesis that is tested against the null of no autocorrelation; must be of one "two.sided", "less", or "greater".

Returns

A list of class diffnet_moran with the following elements: - observed: Numeric scalar. Observed correlation index.

• expected: Numeric scalar. Expected correlation index equal to $-1/(N-1)$.

• sd: Numeric scalar. Standard error under the null.

• p.value: Numeric scalar. p-value of the specified alternative.

Details

In the case that the vector x is close to constant (degenerate random variable), the statistic becomes irrelevant, and furthermore, the standard error tends to be undefined (NaN).

Examples

if (require("ape")) {

  # Generating a small random graph
  set.seed(123)
  graph <- rgraph_ba(t = 4)
  w <- approx_geodesic(graph)
  x <- rnorm(5)

  # Computing Moran's I
  moran(x, w)

  # Comparing with the ape's package version
  ape::Moran.I(x, as.matrix(w))

}

References

Moran's I. (2015, September 3). In Wikipedia, The Free Encyclopedia. Retrieved 06:23, December 22, 2015, from https://en.wikipedia.org/w/index.php?title=Moran%27s_I&oldid=679297766

See Also

Other statistics: bass, classify_adopters(), cumulative_adopt_count(), dgr(), ego_variance(), exposure(), hazard_rate(), infection(), struct_equiv(), threshold(), vertex_covariate_dist()

Other Functions for inference: bootnet(), struct_test()

Author(s)

George G. Vega Yon