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Predicting how a person’s opinion about a topic is likely to evolve and determining the conditions under which a consensus is reached within a group are important in domains such as organizational behavior, public policy, marketing, finance, engineering, and economics. These problems fall within the realms of opinion dynamics and have been studied by various researchers for the last 40 plus years (Deffuant, Neau, Amblard, & Weisbuch, 2000; DeGroot, 1974; DeGroot & Mortera, 1991; Hegselmann and Krause, 2002; Latane, 1981; Lewenstein, Nowak, & Latané, 1992; Olfati-Saber, 2007; Olfati-Saber & Murray, 2004; Ren, Beard, & Atkins, 2005). These researchers have made several theoretical contribution and simulation supported generalizations (see Lorenz, 2007; Shaikh & Castro, 2017 for a review). However, practical applications have been limited (Sobkowicz, Kaschesky, & Bouchard, 2012).
The advent of online social networks such as Twitter, online review platforms such as Yelp, and the popularity of blogs has brought the practice to the forefront (Bihl, Young, & Weckman, 2016; Pak & Paroubek, 2010; Yi, Nasukawa, Bunescu, & Niblack, 2003). Practitioners want to know what the emerging opinions about a topic are, who the influential and the receptive agents are, and what the consensus opinions about various product and services are. These needs have introduced newer problems within the realms of opinion dynamics and questions such as how an opinion could be measured from user-generated text (Adamek, 1994; Gupta & Gupta, 2016), or how to measure the degree of influence an agent exerts on the other in large-scale systems such as Twitter need to be addressed (Dakota & Kübler, 2016; Sobkowicz et al. 2012). This paper focuses on developing a method to estimate who influences who and to what degree on large online social networks. This information is important for identifying the influential agents in the network (Jalili, 2013) and predicting opinion trends (Ren et al. 2005).
The paper builds upon the stochastic opinion dynamics model (SODM) proposed by Castro and Shaikh (2017). The SODM uses a state space-based representation of opinion dynamics wherein each agent’s opinion is a latent variable that has a unique mean and variance at each point in time. We provide a brief literature review in Section 2 and introduce the SODM model in Section 3. Section 4 proposes a restricted maximum likelihood-based approach (Enders, 2001; Schoenberg, 1997; Skrondal & Rabe-Hesketh, 2004; Wooldridge 2015) to estimate the influence each agent in the network has on the others. The proposed estimation approach assumes that information about connections between agents in the form of a follower-followee relationship is observed; this contact network restricts the estimates of the influence an agent can have on the other. A scalable distributed computing-based estimation algorithm is also presented in Section 4. A computational study evaluating the asymptotic properties and the robustness of the estimators is presented in Section 5. The impact of different topologies of contact networks, patterns of influence between agents, and amount of data available on the identifiability of the influence and the robustness of the estimator is also presented. Section 6 outlines the conclusions, limitations of the proposed approach to estimating the influence matrix, and topics for future research.