conductance compute win-loss probabilities for all possible pairs
based upon the combined information from directed wins/losses and
indirect win/loss pathways from the network.
conductance(conf, maxLength, alpha = NULL, beta = 1, strict = FALSE)a matrix of conf.mat class. An N-by-N conflict matrix whose (i,j)th element is the number of times i defeated j.
an integer greater than 1 and less than 7, indicating the maximum length of paths to identify.
a positive integer that
reflects the influence of an observed win/loss interaction
on an underlying win-loss probability.
It is used in the calculation of the posterior distribution
for the win-loss probability of i over j: \(Beta(\alpha c_{i,j} +\beta, c_{i,j}+\beta)\).
In the absence of expertise to accurately estimate alpha,
it is estimated from the data.
a positive numeric value that, like alpha, reflects the influence of an observed win/loss interaction on an underlying win-loss probability. Both \(\alpha\) and \(\beta\) are chosen such that \(((\alpha + \beta)/(\alpha + 2\beta))^2\) is equal to the order-1 transitivity of the observed network. Therefore, \(\beta\) is commonly set to 1.
a logical vector of length 1. It is used in transitivity definition for alpha estimation. It should be set to TRUE when a transitive triangle is defined as all pathways in the triangle go to the same direction; it should be set to FALSE when a transitive triangle is defined as PRIMARY pathways in the triangle go to the same direction. Strict = FALSE by default.
a list of two elements.
An N-by-N conflict matrix whose (i,j)th element is the
'effective' number of wins of i over j.
An N-by-N numeric matrix whose (i,j)th element is the estimated
win-loss probability.
Three functions (valueConverter, individualDomProb, and dyadicLongConverter) are provided to convert win-loss probability
into other formats that are easier for further analysis of win-loss probability.
This function performs two major steps.
First, repeated random walks through the empirical network
identify all possible directed win-loss pathways
between each pair of nodes in the network.
Second, the information from both direct wins/losses and
pathways of win/loss interactions are combined into an estimate of
the underlying probability of i over j, for all ij pairs.
Fushing H, McAssey M, Beisner BA, McCowan B. 2011. Ranking network of a captive rhesus macaque society: a sophisticated corporative kingdom. PLoS ONE 6(3):e17817.
# NOT RUN {
# convert an edgelist to conflict matrix
confmatrix <- as.conflictmat(sampleEdgelist)
# find win-loss probability matrix
perm2 <- conductance(confmatrix, 2, strict = FALSE)
perm2$imputed.conf
perm2$p.hat
# }
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