netcancor: Canonical Correlation for Labeled Graphs

In sna: Tools for Social Network Analysis

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	one or more input graphs.
x	one or more input graphs.
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; "cugden" controls for both order and tie probability; "cugtie" controls for order and tie distribution (via bootstrap); and "qap" implies that the QAP null hypothesis (see qaptest) should be used.
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 extreme quantiles.

Details

The netcancor routine is actually a front-end to the 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.

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 the null hypothesis.
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 the null hypothesis.
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 the null hypothesis.
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.

Note

This will eventually be replaced with a superior cancor procedure with more interpretable output; the new version will handle arbitrary labeling as well.

Author(s)

Carter T. Butts [e-mail]

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)

sna documentation built on Sept. 11, 2024, 8:45 p.m.