Designs for estimating the treatment effect in networks with interference

In this paper we introduce new, easily implementable designs for drawing causal inference from randomized experiments on networks with interference. Inspired by the idea of matching in observational studies, we introduce the notion of considering a treatment assignment as a quasi-coloring" on a graph. Our idea of a perfect quasi-coloring strives to match every treated unit on a given network with a distinct control unit that has identical number of treated and control neighbors. For a wide range of interference functions encountered in applications, we show both by theory and simulations that the classical Neymanian estimator for the direct effect has desirable properties for our designs. This further extends to settings where homophily is present in addition to interference.

[1]  Donald B. Rubin,et al.  Bayesian Inference for Causal Effects: The Role of Randomization , 1978 .

[2]  B. Bollobás,et al.  Cliques in random graphs , 1976, Mathematical Proceedings of the Cambridge Philosophical Society.

[3]  Peter D. Hoff,et al.  Latent Space Approaches to Social Network Analysis , 2002 .

[4]  Ramanathan V. Guha,et al.  Information diffusion through blogspace , 2004, WWW '04.

[5]  Dean Eckles,et al.  Design and Analysis of Experiments in Networks: Reducing Bias from Interference , 2014, ArXiv.

[6]  M. Hudgens,et al.  Toward Causal Inference With Interference , 2008, Journal of the American Statistical Association.

[7]  Kevin G. Stanley,et al.  Design and methods of a social network isolation study for reducing respiratory infection transmission: The eX-FLU cluster randomized trial , 2016, Epidemics.

[8]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[9]  Linyuan Lu,et al.  Spectra of Edge-Independent Random Graphs , 2012, Electron. J. Comb..

[10]  D. Sussman,et al.  Elements of estimation theory for causal effects in the presence of network interference , 2017, 1702.03578.

[11]  Edward K. Kao,et al.  Estimation of Causal Peer Influence Effects , 2013, ICML.

[12]  C. Glymour,et al.  STATISTICS AND CAUSAL INFERENCE , 1985 .

[13]  D. Rubin.  For objective causal inference, design trumps analysis , 2008, 0811.1640.

[14]  Kathryn B. Laskey,et al.  Stochastic blockmodels: First steps , 1983 .

[15]  D. Rubin.  Estimating causal effects of treatments in randomized and nonrandomized studies. , 1974 .

[16]  Edoardo M. Airoldi,et al.  Optimal design of experiments in the presence of network-correlated outcomes , 2015, ArXiv.

[17]  Cosma Rohilla Shalizi,et al.  Homophily and Contagion Are Generically Confounded in Observational Social Network Studies , 2010, Sociological methods & research.

[18]  David S. Choi,et al.  Estimation of Monotone Treatment Effects in Network Experiments , 2014, ArXiv.

[19]  J. Moody.  Race, School Integration, and Friendship Segregation in America1 , 2001, American Journal of Sociology.

[20]  S. Redner,et al.  Connectivity of growing random networks. , 2000, Physical review letters.