Network Autocorrelation Model
Also known as: network effects model, social influence model, network disturbances model, autoregressive network model
The network autocorrelation model adapts spatial-econometric regression to social networks to estimate peer influence: it explains an actor's outcome — an attitude, behavior, or performance — as a function of their own covariates plus a weighted average of their network partners' outcomes. The autocorrelation parameter ρ captures the strength of social influence, and the network weight matrix W encodes who influences whom and how strongly.
Key highlights
- Directly estimates the strength of social influence (ρ) within a familiar regression framework.
- Distinguishes outcome contagion (effects model) from correlated context (disturbances model).
- Leverages decades of spatial-econometric estimation theory (ML, 2SLS) and diagnostics.
- Flexible weight matrix lets substantive theory determine the influence structure.
Intuition
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How it works
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When to use it
Use the network autocorrelation model when you have a cross-sectional nodal outcome and want to estimate the strength of peer influence while controlling for individual covariates, treating the network as a fixed influence structure. It is the workhorse for social-influence questions when longitudinal data are unavailable. Choose the effects specification for outcome contagion and the disturbances specification for shared context. Be cautious: with cross-sectional data the model cannot separate influence from homophily or shared exogenous shocks, the results depend heavily on the specification of W, and the autocorrelation parameter is hard to estimate precisely in small networks. For disentangling influence from selection, prefer longitudinal coevolution models (SAOM).
Strengths & limitations
- Directly estimates the strength of social influence (ρ) within a familiar regression framework.
- Distinguishes outcome contagion (effects model) from correlated context (disturbances model).
- Leverages decades of spatial-econometric estimation theory (ML, 2SLS) and diagnostics.
- Flexible weight matrix lets substantive theory determine the influence structure.
- Cross-sectional versions cannot separate influence from homophilous selection or common external shocks.
- Results are highly sensitive to the specification of the weight matrix W.
- The autocorrelation parameter ρ is often estimated with low precision and known small-sample bias.
- Assumes the network is exogenous and fixed, ignoring tie change and reverse causality.
Common pitfalls
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Applications
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Frequently asked
Can this model prove that peers influence each other?
Not from cross-sectional data alone. A significant autocorrelation parameter is consistent with influence, but homophily (similar people connecting) and shared exogenous context produce the same outcome correlation among neighbors. Causal claims require longitudinal designs that observe the temporal order of network change and behavior change, such as stochastic actor-oriented models.
How should I choose the weight matrix W?
Leenders (2002) argued the choice should follow the theory of influence: whether influence flows through communication or comparison, whether it is symmetric, whether it should be row-normalized so alters' outcomes are averaged or summed. Sensitivity analysis across plausible W specifications is essential because substantive conclusions can depend on it.
What is the difference between the effects and disturbances models?
The network effects model puts the autoregressive term on the outcome (Wy), representing direct contagion of the outcome among connected actors. The network disturbances model puts it on the error, representing correlated unobserved influences among neighbors without direct outcome spillover. They imply different social mechanisms and should be chosen on theoretical grounds.
Sources
- 1.Leenders, R. Th. A. J. (2002). Modeling social influence through network autocorrelation: Constructing the weight matrix. Social Networks, 24(1), 21–47.
- 2.Doreian, P. (1980). Linear models with spatially distributed data: Spatial disturbances or spatial effects? Sociological Methods & Research, 9(1), 29–60.
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ScholarGate. (2026, June 22). Network Autocorrelation Model. ScholarGate. https://scholargate.app/sociology/network-autocorrelation-model