sna (version 0.3)

netcancor: Canonical Correlation for Labeled Graphs

Description

netcancor finds the canonical correlation(s) between the graph sets x and y, testing the result using either conditional uniform graph (CUG) or quadratic assignment procedure (QAP) null hypotheses.

Usage

netcancor(y, x, mode="digraph", diag=FALSE, nullhyp="cugtie", 
    reps=1000)

Arguments

y

First data array to be analyzed. By assumption, the first dimension of the array indexes the graph, with the next two indexing the actors. Missing values are not allowed.

x

Second data array to be analyzed. By assumption, the first dimension of the array indexes the graph, with the next two indexing the actors. Missing values are not allowed.

mode

String indicating the type of graph being evaluated. "digraph" indicates that edges should be interpreted as directed; "graph" indicates that edges are undirected. mode is set to "digraph" by default.

diag

Boolean indicating whether or not the diagonal should be treated as valid data. Set this true if and only if the data can contain loops. diag is FALSE by default.

nullhyp

String indicating the particular null hypothesis against which to test the observed estimands. A value of "cug" implies a conditional uniform graph test (see cugtest) controlling for order only; "

reps

Integer indicating the number of draws to use for quantile estimation. (Relevant to the null hypothesis test only - the analysis itself is unaffected by this parameter.) Note that, as for all Monte Carlo procedures, convergence is slower for more extrem

Value

• An object of class netcancor with the following properties:
• xdist
  Array containing the distribution of the X coefficients under the null hypothesis test.
• ydist
  Array containing the distribution of the Y coefficients under the null hypothesis test.
• cdist
  Array containing the distribution of the canonical correlation coefficients under the null hypothesis test.
• cor
  Vector containing the observed canonical correlation coefficients.
• xcoef
  Vector containing the observed X coefficients.
• ycoef
  Vector containing the observed Y coefficients.
• cpgreq
  Vector containing the estimated upper tail quantiles (p>=obs) for the observed canonical correlation coefficients under the null hypothesis.
• cpleeq
  Vector containing the estimated lower tail quantiles (p<=obs) for="" the="" observed="" canonical="" correlation="" coefficients="" under="" null="" hypothesis.<="" description="">
• xpgreq
  Matrix containing the estimated upper tail quantiles (p>=obs) for the observed X coefficients under the null hypothesis.
• xpleeq
  Matrix containing the estimated lower tail quantiles (p<=obs) for="" the="" observed="" x="" coefficients="" under="" null="" hypothesis.<="" description="">
• ypgreq
  Matrix containing the estimated upper tail quantiles (p>=obs) for the observed Y coefficients under the null hypothesis.
• ypleeq
  Matrix containing the estimated lower tail quantiles (p<=obs) for="" the="" observed="" y="" coefficients="" under="" null="" hypothesis.<="" description="">
• cnames
  Vector containing names for the canonical correlation coefficients.
• xnames
  Vector containing names for the X vars.
• ynames
  Vector containing names for the Y vars.
• xcenter
  Values used to adjust the X variables.
• xcenter
  Values used to adjust the Y variables.
• nullhyp
  String indicating the null hypothesis employed.

Requires

mva

Details

The netcancor routine is actually a front-end to the mva library's cancor routine for computing canonical correlations between sets of vectors. netcancor itself vectorizes the network variables (as per its graph type) and manages the appropriate null hypothesis tests; the actual canonical correlation is handled by cancor.

Canonical correlation itself is a multivariate generalization of the product-moment correlation. Specifically, the analysis seeks linear combinations of the variables in y which are well-explained by linear combinations of the variables in x. The network version of this technique is performed elementwise on the adjacency matrices of the graphs in question; as usual, the result should be interpreted with an eye to the relationship between the type of data used and the assumptions of the underlying model.

Intelligent printing and summarizing of netcancor objects is provided by print.netcancor and summary.netcancor.

References

Butts, C.T., and Carley, K.M. (2001). ``Multivariate Methods for Interstructural Analysis.'' CASOS working paper, Carnegie Mellon University.

See Also

gcor, cugtest, qaptest, cancor

Examples

#Generate a valued seed structure
cv<-matrix(rnorm(100),nrow=10,ncol=10)
#Produce two sets of valued graphs
x<-array(dim=c(3,10,10))
x[1,,]<-3*cv+matrix(rnorm(100,0,0.1),nrow=10,ncol=10)
x[2,,]<--1*cv+matrix(rnorm(100,0,0.1),nrow=10,ncol=10)
x[3,,]<-x[1,,]+2*x[2,,]+5*cv+matrix(rnorm(100,0,0.1),nrow=10,ncol=10)
y<-array(dim=c(2,10,10))
y[1,,]<--5*cv+matrix(rnorm(100,0,0.1),nrow=10,ncol=10)
y[2,,]<--2*cv+matrix(rnorm(100,0,0.1),nrow=10,ncol=10)
#Perform a canonical correlation analysis
nc<-netcancor(y,x,reps=100)
summary(nc)