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=0.01)

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

     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"', '"LAS.intersection"', '"LAS.union"',
          '"OR.row"', or '"OR.col"'  

     tol: Tolerance for the iterative reweighting algorithm (not
          currently supported)

_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 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.

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

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

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

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

     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.

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

     An adjacency matrix representing the consensus structure

_N_o_t_e:

     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.

_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.

_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

