Power-Law Weights According to Neighbourhood Order
Compute power-law weights with decay parameter d
based on a matrix of neighbourhood orders nbmat
(e.g., as obtained via nbOrder).
Without normalization and truncation,
this is just o^{-d} (where o is a neighbourhood order).
This function is mainly used internally for W_powerlaw
weights in hhh4 models.
zetaweights(nbmat, d = 1, maxlag = max(nbmat), normalize = FALSE)
nbmat |
numeric, symmetric matrix of neighbourhood orders. |
d |
single numeric decay parameter (default: 1). Should be positive. |
maxlag |
single numeric specifying an upper limit for the power
law. For neighbourhood orders > |
normalize |
Should the resulting weight matrix be normalized such that rows sum to 1? |
a numeric matrix with same dimensions and names as the input matrix.
Sebastian Meyer
nbmat <- matrix(c(0,1,2,2,
1,0,1,1,
2,1,0,2,
2,1,2,0), 4, 4, byrow=TRUE)
zetaweights(nbmat, d=1, normalize=FALSE) # harmonic: o^-1
zetaweights(nbmat, d=1, normalize=TRUE) # rowSums=1
zetaweights(nbmat, maxlag=1, normalize=FALSE) # results in adjacency matrixPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.