conductance {Perc}

compute win-loss probabilities

Description

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.

Usage

conductance(conf, maxLength, alpha = NULL, beta = 1, strict = FALSE)

Arguments

conf

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.

maxLength

an integer greater than 1 and less than 7, indicating the maximum length of paths to identify.

alpha

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.

beta

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.

strict

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.

Details

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.

Value

a list of two elements.

imputed.conf

An N-by-N conflict matrix whose (i,j)th element is the 'effective' number of wins of i over j.

p.hat

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.

References

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.

See Also

as.conflictmat, findIDpaths, transitivity, simRankOrder

Examples

# 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