We propose to develop new statistical methods for more precise estimation of the influence of one individualon another in a network, testing and controlling for selection effects such as homophily observed betweenindividuals. The work is challenging because network data may contain multiple types of information,including network topology, nodal covariates, tie characteristics, and temporal change. The central problemis accounting for the complex correlation structure that arises because each actor in the network may playthe dual role of an ego (rater or responder) and alter (target or stimulus) and thus may appear in the datamultiple times. Furthermore, outcomes might be geographically correlated and correlated over time ifsubjects are followed longitudinally. Here, we focus on development of statistical methodology forlongitudinal analysis as this provides the best opportunity for obtaining causal inferences; however, we alsopropose innovations involving cross-sectional analysis of networks. We have three specific aims: (1) Todevelop methodology for longitudinal analysis of egocentric data. The objective of such analysis is todetermine the causal effect, if any, of an alter adopting a certain health-related behavior or experiencing acertain outcome (e.g., obesity, heart attack) on an ego adopting or experiencing a similar behavior oroutcome. Because the correlations between characteristics of egos contain important information on howeffects propagate across a population, such models offer the potential to further the scientific understandingof network effects. (2) To develop methods for longitudinal analysis of observations made on distinct groupsof connected actors (e.g., dyads, triads). For example, suppose that distinct dyads are defined based onmarriage of two individuals; it may be that a property of the tie, such as the quality of the marriage (e.g.,measured by strength, mutual affection, time spent together per day), is in turn related to the actors' obesity,the occurrence of health shocks, or the obesity genes in the partners. Although there is a similarity toegocentric analysis, the dependent variable and possibly some of the independent predictors here aremeasured on groups of connected actors rather than the individual actors. (3) To develop methods formodeling the transition of dyadic data across time as a function of attributes of the actors and of networkcharacteristics (e.g., clustering, transitivity). Here, the dependent variable is defined for all potential dyadswhether they exist or not. For most substantive analyses, the dependent variable will be an indicator ofwhether a tie exists at a given time, in which case we model the transition of the dyad between connectedand unconnected states. However, we will also develop methods for the case where the dependent variableis more general (e.g., a count such as the number of patients shared between any two physicians in anetwork, or some other continuously-valued measure).
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