invert_exchangeable_matrix function

Invert an exchangeable matrix

invert_exchangeable_matrix(n, phi, directed = TRUE)

Arguments

• n: Number of actors in the network, scalar numeric.
• phi: Appropriate-length vector of parameters, must be length 5 or 6 for directed=TRUE or length 2 or 3 for directed=FALSE.
• directed: Optional logical indicator of whether input data is for a directed network, default is TRUE. Undirected data format is lower triangle of adjacencey matrix.

Returns

• out: Parameters of inverted matrix of exchangeable class.

Details

This function inverts a covariance matrix of the exchangeable class in a manner much faster than the direct inverse, and the computational cost does not scale with n. See Marrs et. al. (2017). This approach will only work for complete networks.

Examples

n <- 10
phi <- rphi(n, seed=1)
p <- invert_exchangeable_matrix(n, phi)
I1 <- build_exchangeable_matrix(n, phi) %*% build_exchangeable_matrix(n, p)
range(I1 -  diag(n*(n-1)))   # it works

References

Marrs, F. W., Fosdick, B. K., & McCormick, T. H., (2017). Standard errors for regression on relational data with exchangeable errors. arXiv preprint arXiv:1701.05530.

See Also

rphi, build_exchangeable_matrix