Panel Data Models With Latent Network Structures

A network consists of nodes,and edges.It represents the interrelationships between in-dividuals and exists in various field of social life.Research on network is very important after abstracting the social system into a network,individuals in the system into nodes,and relations among individuals into edges.Recently,researchers have been focusing on data collection and analysis from the network perspective,resulting in the continuous growth of relevant research literature.Meanwhile,as an important data type,panel data provide more information,greater variable variation,lower collinearity,and higher available free-dom.Consequently,much research effort is spent on panel data models with network structures.However,since these models incorporate network structures,which are com-plex and varied,many of the conclusions and approaches of traditional models cannot be used directly.So the panel data models with network structures are not sufficiently com-prehensive regarding theory or empirical research and have unresolved issues in various aspects,such as modeling,estimation,and computing.This paper addresses the issue of modeling panel data with a network structure.Specifical-ly,this paper improves existing models for both dynamic network data and general panel data with a network structure.The former makes allowance for the parametrical hetero-geneity in the dynamic panel model of network data while the latter investigates how to characterize more appropriately the weight matrix in both network vector autoregressive model and spatial panel lag model.The contributions of this paper are as follows:Firstly,this paper proposes a dynamic network model with latent clusters(DN-LC).Based on the dynamic panel model for network data,this model assumes that the nodes can be di-vided into different groups.The parameters depend on the categories of the sending node and receiving node.The Gibbs method is used to estimate the model under the Bayesian framework.Additionally,the model is applied to bilateral trade data of 60 countries from 2001 to 2015.The results show that the DN-LC model can effectively improve the pre-diction accuracy of the trading volumes and can divide the countries into different groups according to their trade characteristics.Secondly,by introducing the latent positions,this paper improves network vector autore-gressive model and then proposes network vector autoregressive model with latent weight(NVAR-LW).The NVAR-LW model assumes that each individual observation is not on-ly influenced by its own lag term,but also by the weighted average of other individual lags,where the size of the weight is determined by the latent position of a node.A n-ode that is close to the latent position of the target node has a relatively large impact on the target node and occupies a relatively large weight.The Metropolis-Hastings within Gibbs method is used to estimate the model under the Bayesian framework.This model can obtain a reasonable estimation and prediction while showing the interrelationship in-tuitively among nodes in the network based on their latent positions.Simultaneously,this paper also proposes network vector autoregressive model with latent weight for dyadic data(DNVAR-LW).The results of Monte Carlo simulations show that the NVAR-LW model and DNVAR-LW model can obtain better estimations and predictions regardless of whether the true weight is a latent weight or an adjacency matrix weight.Finally,changing the lag dependence into the simultaneous dependence in NVAR-LW model,this paper proposes spatial panel lag model with latent weight(SPL-LW).The Metropolis-Hastings within Gibbs method is used to estimate the model under the Bayesian framework.In addition,the results of Monte Carlo simulations show that SPL-LW model can obtain better estimation regardless of whether the true weight is latent weight,adjacency matrix weight,or multi-attribute weight.Empirical analysis results on capital construction expenditure data of 29 provinces in China from 1997 to 2006 show that there are complementary strategies among the provincial governments of China.