Estimation Of Homogeneity And Peer Pressure In Dynamic Networks

Social interaction is a hot research topic in social network analysis,and peer pressure,as an important feature in the process of social interaction,can portray and measure the influence of the network on nodes,and has a wide range of applications in sociology,economics and other scientific fields.Game theory is a common method for modeling social interaction problems in social networks;however,when incomplete covariates are involved in the game model,peer pressure can be misidentified and can cause nonnegligible bias.For this reason,we develop a new peer effect model considering network homogeneity in dynamic social networks.The new model can effectively avoid bias in estimating peer pressure by pursuing homogeneity,and the model can be applied to a wider range of network data.To estimate the model,we introduce the homogeneity setting and propose the corresponding estimation method,followed by introducing the nested pseudo likelihood estimation method for estimating the peer pressure parameter and giving the convergence properties of this estimator.First,this paper proposes a peer effect model considering network homogeneity to solve the problem of estimating peer pressure in dynamic social networks.The model is derived based on the Markov game process and homogeneity structure,and its decision gain function depends on node covariates independent of homogeneity,node homogeneity,peer pressure considering the social influence measure,and the error term of nodes.Second,since homogeneity is not observable,it needs to be estimated.We propose a modified homogeneity estimation method based on the basic setting of homogeneity,combined with the initialize expand merge method and the polynomial time two-stage method,and give convergence conditions for the estimator of homogeneity.Then,to estimate the peer pressure parameter,we derive the great likelihood function of the model based on the estimation of homogeneity.However,since the analytical expressions of the parameters are not available and the game network model suffers from the problem of computationally overloaded parameter estimation,we introduce the nested pseudo likelihood estimation method to estimate the peer pressure parameters.Finally,under the convergence condition of the homogeneity estimation method,the convergence properties of the peer pressure estimator under different social influence measures are given.In the simulation experiments and empirical analysis phase,this paper verifies the convergence properties of the homogeneity and peer pressure estimation methods and demonstrates the advantages of the peer effect model over the benchmark model.For the simulation experiments,the lower community misidentification rate of the community detection method is demonstrated,and the mean square error and standard deviation of the peer pressure estimation estimator decrease rapidly with the increase of the network size in the presence of errors in the homogeneity estimation,showing good convergence properties.For the empirical analysis,the analytical results of the peer effect model considering network homogeneity are shown,and the parameter estimation of peer pressure has better interpretability and realistic significance compared with the benchmark model.