`nwmixing`

E-I index and mixing table for a categorical node attribute

Syntax

nwmixing
[netname]
,
attribute(varname)
[eiplot
eiplotoptions(string)
plot
plotoptions(string)
permutations(int)
save(filename)
tab_options]


`attribute(varname)`	Categorical (string or numeric) node attribute to cross-tabulate ties by
`eiplot`	Plot the null (QAP-permutation) distribution of the E-I index, with the observed value marked
`eiplotoptions(string)`	Additional options forwarded to the `eiplot`’s own `kdensity`
`plot`	Plot the ego/alter mixing table via `tabplot`
`plotoptions(string)`	Additional options forwarded to `plot`’s own `tabplot`
`permutations(int)`	Number of QAP permutations for the E-I index’s own null distribution and p-value; default = 100. Set to 1 to skip the permutation test entirely (only the observed table/index are reported)
`save(filename)`	Save the QAP permutation draws (variable EI_simulated) and the observed value (variable EI_observed) to a new dataset
tab_options	Any other option is forwarded to the underlying `tab` call that builds the mixing table (e.g. `row`, `column`, `cell`)

Description

nwmixing cross-tabulates every tie in the network by the attribute() value of its ego and alter (a “mixing table” or “mixing matrix”), and computes Krackhardt & Stern’s (1988) E-I index: the number of ties external to an attribute category minus the number internal to it, divided by their sum. The index ranges from -1 (every tie stays within its own category - maximal homophily/segregation) to +1 (every tie crosses categories - maximal heterophily/integration); 0 indicates ties are split between internal and external exactly as the network’s overall tie count would suggest.

Ties are treated as unvalued (presence/absence only) throughout - tie strength does not affect the mixing table or the E-I index.

With permutations() greater than 1 (the default, 100), nwmixing also runs a QAP permutation test: the attribute assignment is held fixed while the network itself is repeatedly randomly permuted, building a null distribution of the E-I index under “no association between this attribute and tie placement”, and reports a two-sided p-value.

Examples

. nwwebuse florentine, nwclear
. nwmixing flomarriage, attribute(priorates)

Supported network types

Binary: yes. Directed: yes - ego/alter mixing is directional for a directed network (an attribute_ego/attribute_alter pair is not symmetric); an undirected network’s own mixing table instead shows each edge counted from both endpoints, noted explicitly in the output. Weighted: not applicable - see Description (ties are always treated as unvalued). Signed: not checked. Two-mode: same as for the bipartite graph read as a one-mode network (valid; no mode-specific normalisation).

Stored results

Scalars

r(EI_index) the observed E-I index
r(EI_pvalue) two-sided QAP permutation p-value with the plus-one Monte Carlo correction, 2(1 + k)/(permutations + 1) with k the number of draws in the smaller tail, so that it is never 0 (only when permutations() > 1)

Macros

r(netname) the network name
r(attribute) the attribute() variable name

Matrices

r(table) the mixing table’s own tie counts
r(col) the mixing table’s column category values
r(row) the mixing table’s row category values

References

Krackhardt, D., Stern, R.N. (1988). Informal networks and organizational crises: An experimental simulation. Social Psychology Quarterly 51(2), 123-140.

nwmixing