consensus                package:sna                R Documentation

_E_s_t_i_m_a_t_e _a _C_o_n_s_e_n_s_u_s _S_t_r_u_c_t_u_r_e _f_r_o_m _M_u_l_t_i_p_l_e _O_b_s_e_r_v_a_t_i_o_n_s

_D_e_s_c_r_i_p_t_i_o_n:

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

_U_s_a_g_e:

     consensus(dat, mode="digraph", diag=FALSE, method="central.graph", 
         tol=1e-06, maxiter=1e3, verbose=TRUE, no.bias=FALSE)

_A_r_g_u_m_e_n_t_s:

     dat: a set of input graphs (must have same order). 

    mode: '"digraph"' for directed data, else '"graph"'. 

    diag: logical; should diagonals (loops) be treated as data? 

  method: one of '"central.graph"', '"single.reweight"',
          '"iterative.reweight"', '"romney.batchelder"',
          '"PCA.reweight"', '"LAS.intersection"', '"LAS.union"',
          '"OR.row"', or '"OR.col"'.  

     tol: convergence tolerance for the iterative reweighting and B-R
          algorithms.

 maxiter: maximum number of iterations to take (regardless of
          convergence) for the iterative reweighting and B-R
          algorithms.

 verbose: logical; should bias and competency parameters be reported
          (where computed)?

 no.bias: logical; should responses be assumed to be unbiased? 

_D_e_t_a_i_l_s:

     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 corresponds 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.  'iterative.reweight': Similar to 'single.reweight', but the
           consensus structure and accuracy parameters are estimated
           via an iterated proportional fitting scheme.  The
           implementation employed here uses both bias and competency
           parameters.

        4.  'romney.batchelder': Fits a Romney-Batchelder informant
           accuracy model using IPF.  This is very similar to
           'iterative.reweight', but can be interpreted as the result
           of a process in which each informant report is correct with
           a probability equal to the informant's competency score, and
           otherwise equal to a Bernoulli trial with parameter equal to
           the informant's bias score.

        5.  '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.

        6.  'LAS.intersection': Estimate the consensus structure using
           the locally aggregated structure (intersection rule).  In
           this model, an i->j edge exists iff i _and_ j agree that it
           exists.

        7.  'LAS.union': Estimate the consensus structure using the
           locally aggregated structure (union rule).  In this model,
           an i->j edge exists iff i _or_ j agree that it exists.

        8.  'OR.row': Estimate the consensus structure using own
           report.  Here, we take each informant's outgoing tie reports
           to be correct.

        9.  'OR.col': Estimate the consensus structure using own
           report.  Here, we take each informant's incoming tie reports
           to be correct.

     Note that the results returned by the single weighting algorithms
     are not dichotomized by default; since some algorithms thus 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 (or the R-B model) may prove more
     useful than the ad-hoc solutions.

_V_a_l_u_e:

     An adjacency matrix representing the consensus structure

_A_u_t_h_o_r(_s):

     Carter T. Butts buttsc@uci.edu

_R_e_f_e_r_e_n_c_e_s:

     Banks, D.L., and Carley, K.M.  (1994).  ``Metric Inference for
     Social Networks.''  _Journal of Classification,_  11(1), 121-49.

     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. 

     Romney, A.K.; Weller, S.C.; and Batchelder, W.H.  (1986). 
     ``Culture as Consensus: A Theory of Culture and Informant
     Accuracy.''  _American Anthropologist,_ 88(2), 313-38.

_S_e_e _A_l_s_o:

     'bbnam', 'centralgraph'

_E_x_a_m_p_l_e_s:

     #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

