sna (version 2.4)

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

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.

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.

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.

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

# NOT RUN {
#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)
# }