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11
Models for Longitudinal Network Data
 Models and Methods in Social Network Analysis
, 2005
"... This chapter treats statistical methods for network evolution. It is argued that it is most fruitful to consider models where network evolution is represented as the result of many (usually nonobserved) small changes occurring between the consecutively observed networks. Accordingly, the focus is o ..."
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Cited by 33 (6 self)
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This chapter treats statistical methods for network evolution. It is argued that it is most fruitful to consider models where network evolution is represented as the result of many (usually nonobserved) small changes occurring between the consecutively observed networks. Accordingly, the focus is on models where a continuoustime network evolution is assumed although the observations are made at discrete time points (two or more). Three models are considered in detail, all based on the assumption that the observed networks are outcomes of a Markov process evolving in continuous time. The independent arcs model is a trivial baseline model. The reciprocity model expresses effects of reciprocity, but lacks other structural effects. The actororiented model is based on a model of actors changing their outgoing ties as a consequence of myopic stochastic optimization of an objective function. This framework offers the flexibility to represent a variety of network effects. An estimation algorithm is treated, based on a Markov chain Monte Carlo implementation of the method of moments.
The mixture transition distribution model for highorder Markov chains and nonGaussian time series
 Statistical Science
, 2002
"... Abstract. The mixture transition distribution model (MTD) was introduced in 1985 by Raftery for the modeling of highorder Markov chains with a finite state space. Since then it has been generalized and successfully applied to a range of situations, including the analysis of wind directions, DNA seq ..."
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Cited by 19 (2 self)
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Abstract. The mixture transition distribution model (MTD) was introduced in 1985 by Raftery for the modeling of highorder Markov chains with a finite state space. Since then it has been generalized and successfully applied to a range of situations, including the analysis of wind directions, DNA sequences and social behavior. Here we review the MTD model and the developments since 1985. We first introduce the basic principle and then we present several extensions, including general state spaces and spatial statistics. Following that, we review methods for estimating the model parameters. Finally, a review of different types of applications shows the practical interest of the MTD model. Key words and phrases: Mixture transition distribution (MTD) model, Markov chains, highorder dependences, time series, GMTD model, EM algorithm,
Introduction to Stochastic ActorBased Models for Network Dynamics. Social Networks
, 2009
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Supervised Link Prediction Using Multiple Sources
"... Abstract—Link prediction is a fundamental problem in social network analysis and modernday commercial applications such as Facebook and Myspace. Most existing research approaches this problem by exploring the topological structure of a social network using only one source of information. However, i ..."
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Cited by 4 (2 self)
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Abstract—Link prediction is a fundamental problem in social network analysis and modernday commercial applications such as Facebook and Myspace. Most existing research approaches this problem by exploring the topological structure of a social network using only one source of information. However, in many application domains, in addition to the social network of interest, there are a number of auxiliary social networks and/or derived proximity networks available. The contribution of the paper is twofold: (1) a supervised learning framework that can effectively and efficiently learn the dynamics of social networks in the presence of auxiliary networks; (2) a feature design scheme for constructing a rich variety of pathbased features using multiple sources, and an effective feature selection strategy based on structured sparsity. Extensive experiments on three realworld collaboration networks show that our model can effectively learn to predict new links using multiple sources, yielding higher prediction accuracy than unsupervised and singlesource supervised models. Index Terms—social network; link prediction; multiple sources; supervised learning; I.
Detecting Changes in a Dynamic Social Network
, 2009
"... Social network analysis (SNA) has become an important analytic tool for analyzing terrorist networks, friendly command and control structures, arms trade, biological warfare, the spread of diseases, among other applications. Detecting dynamic changes over time from an SNA perspective, may signal an ..."
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Cited by 2 (1 self)
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Social network analysis (SNA) has become an important analytic tool for analyzing terrorist networks, friendly command and control structures, arms trade, biological warfare, the spread of diseases, among other applications. Detecting dynamic changes over time from an SNA perspective, may signal an underlying change within an organization, and may even predict significant events or behaviors. The challenges in detecting network change includes the lack of underlying statistical distributions to quantify significant change, as well as high relational dependence affecting assumptions of independence and normality. Additional challenges involve determining an algorithm that maximizes the probability of detecting change, given a risk level for false alarm. A suite of computational and statistical approaches for detecting change are identified and compared. The NeymanPearson most powerful test of simple hypotheses is extended as a cumulative sum statistical process control chart to detect network change over time. Anomaly detection approaches using exponentially weighted moving average or scan statistics investigate performance under conditions of potential timeseries dependence.
Longitudinal Dynamic Network Analysis Using the Over Time Viewer Feature in ORA
, 2009
"... networks, change detection, network evolution, longitudinal network analysis, dynamic network analysis. Analyzing network over time has become increasingly popular as longitudinal network data becomes more available. Longitudinal networks are studied by sociologists to understand network evolution, ..."
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Cited by 1 (0 self)
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networks, change detection, network evolution, longitudinal network analysis, dynamic network analysis. Analyzing network over time has become increasingly popular as longitudinal network data becomes more available. Longitudinal networks are studied by sociologists to understand network evolution, belief formation, friendship formation, diffusion of innovations, the spread of deviant behavior and more. Organizations are interested in studying longitudinal network in order to get inside the decision cycle of major events. Prior to important events occurring in an organization, there is likely to exist an earlier change in network dynamics. Being able to identify that a change in network dynamics has occurred can enable managers to respond to the change in network behavior prior to the event occurring and shape a favorable outcome. The Over Time Viewer is a software tool hosted by the CASOS software suite that enables the analysis of longitudinal dynamic network data. This report introduces the Over Time Viewer and provides instruction on how to effectively use its features.
Investigating Purchasing . . . Markov, MTD and MTDg Models
 FORTHCOMING IN EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
, 2003
"... In the past, several authors have found evidence for the existence of a priority pattern of acquisition for durable goods, as well as for financial services. Its usefulness lies in the fact that if the position of a particular customer in this acquisition sequence is known, one can predict what serv ..."
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In the past, several authors have found evidence for the existence of a priority pattern of acquisition for durable goods, as well as for financial services. Its usefulness lies in the fact that if the position of a particular customer in this acquisition sequence is known, one can predict what service will be acquired next by that customer. In this paper, we analyse purchase sequences of financial services to identify crossselling opportunities as part of a CRM (customer relationship management). Hereby, special attention is paid to transitions, which might encourage bank or insurance only customers to become financial services customers. We introduce the Mixture Transition Distribution model (MTD) as a parsimonious alternative to the Markov model for use in the analysis of marketing problems. An interesting extension on the MTD model is the MTDg model, which is able to represent situations where the relationship between each lag and the current state differs. We illustrate the MTD and MTDg model on acquisition sequences of customers of a major financialservices company and compare the fit of these models with that of the corresponding Markov model. Our results are in favor of the MTD and MTDg models. Therefore, the MTD as well as the MTDg transition matrices are investigated in order to reveal crosssell opportunities. The results are of great value to the product managers as they clarify the customer flows among product groups. In some cases, the lagspecific transition matrices of the MTDg model are better for the guidance of crosssell actions than the general transition matrix of the MTD model.
Preprint of Chapter 33 (pp. 501–513) in Sage Handbook on Social Network Analysis, edited by John
, 2011
"... Dynamic ideas have been pursued in much of Social Network Analysis. Network dynamics is important for domains ranging from friendship networks (e.g., Pearson and West, 2003; Burk, et al., 2007) to, for example, interorganizational networks (see the review articles Borgatti and Foster, 2003; Brass e ..."
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Dynamic ideas have been pursued in much of Social Network Analysis. Network dynamics is important for domains ranging from friendship networks (e.g., Pearson and West, 2003; Burk, et al., 2007) to, for example, interorganizational networks (see the review articles Borgatti and Foster, 2003; Brass et al., 2004). However, formal models of analysis, both in the tradition of discrete mathematics and in the tradition of statistical inference, have for a long time focused mainly on single (i.e., crosssectional) methods of analysis. Some history: empirical research Important early longitudinal network studies were those by Nordlie (1958) and Newcomb (1961) who studied friendships in a college fraternity based on the empirical data collected; Coleman’s (1961) Adolescent Society study with friendship data in 10 schools and 9,702 individuals; Kapferer’s (1972) study of observed interactions in a tailor shop in Zambia (then Northern Rhodesia) over a period of ten months, in a period of industrial conflict; Sampson’s (1969) Ph.D. dissertation on the developments of the relations in a group of 18 monks in a monastery; and the study by Hallinan with seven