`nwcorrelate`

Correlate networks and variables

Syntax

1) Correlate nodes of a network
		
nwcorrelate 
netname
[,
context(context)
name(newnetname)
undirected directed]
     2) Correlate two networks with each other
nwcorrelate 
netname1
netname2
[,
permutations(int)
save(filename)
kdensity_options]
     3) Correlate one network and one variable
		
nwcorrelate 
netname
, 
attribute(varname)
[mode(expand_mode)
name(newnetname)
keepexpand
permutations(int)
save(filename)
kdensity_options]


`context`(context)	Determines whether incoming or outgoing ties should be considered when correlating two nodes; default = outgoing
`name(newnetname)`	Name of new network with node correlations; default = _corr
`mode`(expand_mode)	How to expand the attribute variable
`keepexpand`	Keep the network generated by nwexpand
`permutations(integer)`	Number of QAP permutations; default = 1 (no permutation test)
`save(filename)`	Save (the name may be quoted and contain spaces; the full path is printed) the QAP permutation results in a Stata dataset with the variables correlation (one row per permutation) and observed (the observed correlation, repeated in every row); needs `permutations()` of more than 1
`undirected`, `directed`	Node-correlation mode: store the correlation network as undirected or directed (options of nwset)
`force`	Run the command although its matrices would not fit in memory (it stops with r(484) above about 12,900 nodes otherwise)

Description

This command is the network version of correlate. It can be used in three different ways:

1) Correlate nodes of a network

2) Correlate two networks with each other

3) Correlate one network and one variable

The option permutation() creates QAP permutations of the first network and generates a distribution of correlation coefficients under the null-hypothesis that there is no correlation. In practice, rows and columns of netname are reshuffled and the correlation coefficient is calculated again and again. Based on this distribution a p-value and a confidence interval is calculated. A plot is displayed and additional information is returned in the return vector.

Supported network types

Binary: yes. Directed: yes, via context(incoming|outgoing|both) for the node-correlation mode. Weighted: yes, natively - uses raw tie values throughout, no dichotomize option. Signed: not checked. Two-mode: not supported - error 6088; the correlation of the profiles of the nodes of ONE network reads the empty blocks between nodes of the same mode (nwsimilar, type(pearson) correlates the profiles over the other mode); two networks are correlated as for any pair of networks.

Stored results

Node correlations

Scalars:
r(avg_corr) average correlation coefficient between nodes
Macros:
r(name) name of network
r(corrname) name of new network with coefficients

Two networks or one network and one attribute

Scalars:
r(corr) correlation coefficient
r(pvalue) two-sided Monte Carlo p-value of the correlation, 2(1 + k)/(R + 1) with k the number of the R permutations in the smaller tail (never 0; at most 1)
r(ub) upper bound, 95% confidence interval
r(lb) lower bound, 95% confidence interval
Macros:
r(name_1) name of netname1
r(name_2) name of netname2 or the expanded network

References

Granovetter, M. (1973). The strength of weak ties. American Journal of Sociology 78(6), 1360-1380.

Zachary, W. (1977). An information flow model for conflict and fission in small groups. Journal of Anthropological Research 33, 452-473.

nwcorrelate