`nwaltergen`

Generate a variable from alter/neighbor attributes

Syntax

nwaltergen newvar = stat(alter.srcvar)
[,
net(netname)
replace
hop(int)]
nwaltergen newvar = proportion(alter.srcvaropvalue)
[,
net(netname)
replace
hop(int)]
stat is one of mean, wmean, sum, min, max, sd, count,
diversity.
op is == or !=; value must be numeric.


`net(netname)`	Network to use; default = the current network
`replace`	Replace existing variable
`hop(int)`	Aggregate over nodes exactly this many (unweighted) steps away, instead of direct neighbors; default = 1

Description

nwaltergen generates a new Stata variable that summarizes, for each node (ego), a Stata variable’s values among its network neighbors (alters) - e.g. “the average smoking status among a person’s contacts” (mean(alter.smoking)) or “the number of contacts who already adopted” (count(alter.adopted)). This is the standard “network exposure” / alter-aggregation primitive used throughout social influence, diffusion, and peer-effects research (see e.g. Valente 2005 on exposure models).

srcvar must already exist in the dataset and be indexed the same way as every other per-node result in nwcommands: observation i holds the value for node i.

For directed networks, alter means out-neighbors only - the nodes ego has a tie to - since exposure/influence is inherently about tie direction, not just structural adjacency (contrast this with, e.g., nwkcore, where an undirected structural question uses the union of in- and out-neighbors instead). For undirected networks the distinction does not arise.

Missing values of srcvar among a node’s alters are dropped before the statistic is computed (so a node with 3 alters, one of whom has a missing srcvar, is summarized over the 2 non-missing values) - never silently propagated into the result. A node with zero alters (after dropping missing values, if applicable) returns missing for mean/min/max/sd/ diversity, and 0 for sum/count. sd additionally requires at least 2 non-missing alter values (it is undefined for a single value) and returns missing otherwise.

proportion(alter.srcvar==value) (or !=) gives the proportion of ego’s alters whose srcvar equals (or does not equal) a specific numeric category - e.g. “the proportion of a person’s contacts who work in sector 3” (proportion(alter.sector==3)). For an already-binary (0/1) srcvar, mean(alter.srcvar) already gives exactly “the proportion with srcvar==1”, so a bare proportion(alter.srcvar) with no comparison is not offered as a separate synonym for it - proportion()’s own value is for picking out one category of a variable with more than two categories, without first having to generate a 0/1 indicator by hand. Missing srcvar values are still dropped before the proportion is computed, exactly as for every other stat - a missing value is never silently read as “not in this category”.

diversity(alter.srcvar) gives Blau’s (1977) index of heterogeneity among ego’s alters’ srcvar values - 1 - sum(p_k^2), where p_k is the proportion of alters falling in category k of srcvar (treated as a categorical/discrete-coded variable, e.g. sector or ethnicity) - the standard “ego-network composition” measure: 0 when every alter shares the same category (no diversity), approaching 1 as alters spread evenly across many categories. This is the composition/diversity capability nwego’s own “Supported network types” note originally left open - unlike ego-network size/density, it needs per-alter attribute values, not just structural connectivity, so it belongs here alongside nwaltergen’s other alter- attribute aggregations rather than in nwego itself. Missing srcvar values are dropped before computing the index, exactly as for every other stat; an ego with zero alters (after dropping missing values) returns missing, not spuriously 0 (mirroring mean/min/max/ sd’s own convention, not sum/count’s - diversity, like a mean, is undefined with no data to summarize, not naturally zero).

wmean(alter.srcvar) is a tie-strength-weighted exposure mean - sum(wx) / sum(w)** over ego’s alters, where *w is the tie weight to each alter and x is that alter’s srcvar value - instead of **mean()’s own plain, equally-weighted average. This is the standard weighted-exposure/peer-effect formulation used when tie strength itself should matter - e.g. a strong tie’s contact matters more to exposure than a weak one (see e.g. Marsden and Friedkin 1993 on weighted social influence). On a binary (unweighted) network every present tie has weight 1, so wmean() gives exactly the same result as mean() - not an approximation, since a tie’s weight is exactly 1 whenever the network itself carries no distinct tie values. An alter with a missing srcvar is dropped from both the numerator and the weight-sum denominator together (so it does not silently bias the result toward zero), matching every other stat’s own missing-value convention. wmean() is only supported at the default hop(int):hop(1) (direct alters) - which single tie weight should represent a multi-hop path has no single well-defined answer, so combining it with hop(int) > 1 is rejected with a clear error rather than guessed at.

hop(int) aggregates over nodes exactly that many (unweighted) steps away instead of direct (one-hop) neighbors - e.g. mean(alter.smoking), hop(2) is “the average smoking status among the contacts of a person’s contacts” (excluding the person’s own direct contacts, unless a network happens to reach them again by a different, exactly-2-step path). This is the standard multi-hop / lagged exposure question in diffusion research: does influence propagate beyond a node’s immediate neighborhood? A node with no alters at exactly the requested hop distance (including one smaller than the network’s diameter from it, or simply unreachable) is treated the same as a node with no direct alters: missing for mean/min/max/sd, 0 for sum/count. For a directed network, distance follows tie direction (out-going steps), matching alter’s own one-hop convention above; hop(int) works with proportion() too.

nwgen recognizes the same mean(alter.x)-style syntax (including proportion(alter.x==value) and hop(int)) as a shortcut and dispatches to nwaltergen automatically - nwgen exposure = mean(alter.smoking) and nwaltergen exposure = mean(alter.smoking) are equivalent.

Examples

. nwwebuse florentine, nwclear
. nwaltergen richavg = mean(alter.wealth)
. nwgen richavg2 = mean(alter.wealth), replace
. nwaltergen richwexp = wmean(alter.wealth)
. nwaltergen priorseat = proportion(alter.seat==1)
. nwaltergen richavg2hop = mean(alter.wealth), hop(2)
. nwaltergen seatdiv = diversity(alter.seat)

Supported network types

Binary: yes. Directed: yes - alter means out-neighbors only, since exposure/influence follows tie direction (see above). Weighted: W2 - mean/sum/min/max/sd/ count/diversity use only structural adjacency (tie strength does not enter); wmean (added 2026-09-02, closing a self-flagged gap) uses tie strength directly as the aggregation weight, an explicit opt-in via a separate stat name rather than an automatic switch. Signed: not checked - wmean() would divide by a possibly near-zero or sign-cancelling weight sum for a node with negative-weighted ties, not handled distinctly. Two-mode: no - srcvar is read per node under the one-mode _nwnode indexing convention, with no mode-specific handling.

References

Valente, T.W. (2005). Network models and methods for studying the diffusion of innovations. In Models and Methods in Social Network Analysis, Cambridge University Press.

Marsden, P.V., Friedkin, N.E. (1993). Network studies of social influence. Sociological Methods & Research 22(1), 127-151. (wmean()’s own tie-strength-weighted exposure formulation)

Blau, P.M. (1977). Inequality and Heterogeneity: A Primitive Theory of Social Structure. Free Press. (diversity()’s own index of heterogeneity)

nwaltergen