sna (version 0.3)

consensus: Estimate a Consensus Structure from Multiple Observations

Description

consensus estimates a central or consensus structure given multiple observations, using one of several algorithms.

Usage

consensus(dat, mode="digraph", diag=FALSE, method="central.graph", 
    tol=0.01)

Arguments

dat

An m x n x n graph stack

mode

``digraph'' for directed data, else ``graph''

diag

A boolean indicating whether the diagonals (loops) should be treated as data

method

One of ``central.graph'', ``single.reweight'', ``PCA.reweight''

tol

Tolerance for the iterative reweighting algorithm (not currently supported)

Value

• An adjacency matrix representing the consensus structure

Details

The term ``consensus structure'' is used by a number of authors to reflect a notion of shared or common perceptions of social structure among a set of observers. As there are many interpretations of what is meant by ``consensus'' (and as to how best to estimate it), several algorithms are employed here:

1. central.graph: Estimate the consensus structure using the central graph. This correponds to a ``median response'' notion of consensus.
2. single.reweight: Estimate the consensus structure using subject responses, reweighted by mean graph correlation. This corresponds to an ``expertise-weighted vote'' notion of consensus.
3. PCA.reweight: Estimate the consensus using the (scores on the) first component of a network PCA. This corresponds to a ``shared theme'' or ``common element'' notion of consensus.

Note that the reweighted algorithms are not dichotomized by default; since these return valued graphs, dichotomization may be desirable prior to use.

It should be noted that a model for estimating an underlying criterion structure from multiple informant reports is provided in bbnam; if your goal is to reconstruct an ``objective'' network from informant reports, this may prove more useful.

References

Banks, D.L., and Carley, K.M. (1994). ``Metric Inference for Social Networks.'' Journal of Classification.''

Butts, C.T., and Carley, K.M. (2001). ``Multivariate Methods for Inter-Structural Analysis.'' CASOS Working Paper, Carnegie Mellon University.

Krackhardt, D. (1987). ``Cognitive Social Structures.'' Social Networks, 9, 109-134.

[object Object],[object Object]

Eventually, this routine will also support the (excellent) consensus methods of Romney and Batchelder; since these are similar in many respects to the bbnam model, users may wish to try this alternative for now.

bbnam, centralgraph

#Generate some test data g<-rgraph(5) g.pobs<-g*0.9+(1-g)*0.5 g.obs<-rgraph(5,5,tprob=g.pobs)

#Find some consensus structures consensus(g.obs) #Central graph consensus(g.obs,method="single.reweight") #Single reweighting consensus(g.obs,method="PCA.reweight") #1st component in network PCA network