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The New England Journal of Statistics in Data Science


General Additive Network Effect Models
Volume 1, Issue 3 (2023), pp. 342–360
Pub. online: 27 April 2023      Type: Methodology Article      Open accessOpen Access
Area: Statistical Methodology
Accepted
6 April 2023
Published
27 April 2023

Abstract

In the interest of business innovation, social network companies often carry out experiments to test product changes and new ideas. In such experiments, users are typically assigned to one of two experimental conditions with some outcome of interest observed and compared. In this setting, the outcome of one user may be influenced by not only the condition to which they are assigned but also the conditions of other users via their network connections. This challenges classical experimental design and analysis methodologies and requires specialized methods. We introduce the general additive network effect (GANE) model, which encompasses many existing outcome models in the literature under a unified model-based framework. The model is both interpretable and flexible in modeling the treatment effect as well as the network influence. We show that (quasi) maximum likelihood estimators are consistent and asymptotically normal for a family of model specifications. Quantities of interest such as the global treatment effect are defined and expressed as functions of the GANE model parameters, and hence inference can be carried out using likelihood theory. We further propose the “power-degree” (POW-DEG) specification of the GANE model. The performance of POW-DEG and other specifications of the GANE model are investigated via simulations. Under model misspecification, the POW-DEG specification appears to work well. Finally, we study the characteristics of good experimental designs for the POW-DEG specification. We find that graph-cluster randomization and balanced designs are not necessarily optimal for precise estimation of the global treatment effect, indicating the need for alternative design strategies.

Supplementary material

 Supplementary Material
The Supplementary Material to “General Additive Network Effect Models” contains additional simulation results for Section 4.

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© 2023 New England Statistical Society
Open access article under the CC BY license.

Keywords
Design of experiments A/B testing Social networks SUTVA Network effect modeling

Funding
This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) by way of Grants RGPIN-2019-04212 and RGPIN-2023-03245.

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