Modeling brand post popularity dynamics in online social networks

    Modeling brand post popularity dynamics in online social networks Amir Hassan Zadeh, Ramesh Sharda PII: DOI: Reference:

S0167-9236(14)00143-2 doi: 10.1016/j.dss.2014.05.003 DECSUP 12488

To appear in:

Decision Support Systems

Please cite this article as: Amir Hassan Zadeh, Ramesh Sharda, Modeling brand post popularity dynamics in online social networks, Decision Support Systems (2014), doi: 10.1016/j.dss.2014.05.003

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ACCEPTED MANUSCRIPT Modeling brand post popularity dynamics in online social

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networks Amir Hassan Zadeh , Ramesh Sharda

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Spears School of Business, Oklahoma State University, Stillwater, OK 74078, USA

Abstract-

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Today’s social media platforms are excellent vehicles for businesses to build and foster

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relationship with customers. Companies create official fan pages on social network websites to provide customers with information about their brands, products, promotions, and more.

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Customers can become fans of these pages, and like, reply, share or mark the brand post as

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favorite. Marketing departments are using these activities to crowdsource marketing and increase

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brand awareness and popularity. Understanding how crowdsourcing oriented marketing and promotion evolves would be helpful in managing such campaigns. In this paper, we adapt a multidimensional point process methodology to study crowd engagement activities and interactions. Specifically, we investigate the brand post popularity as a joint probability function of time and number of followers. One-dimensional and two-dimensional Hawkes point process models are calibrated to simulate popularity growth patterns of brand post contents on Twitter. Our results suggest that the two-dimensional point process model provides a good model for understanding such crowdsourcing behavior. Key words: Online social networks; social media marketing; crowdsourcing; brand posts; popularity; point process; Hawkes process.

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Corresponding author: [email protected]

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ACCEPTED MANUSCRIPT 1. Introduction The emergence of Internet-based social media has started a new kind of conversation

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among consumers and companies, challenging traditional ideas about marketing and brand

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management while creating new opportunities for organizations to understand customers and

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connect with them instantly (SAS Harvard Business Review Analytic Services, 2010). Research firm Chadwick Martin Bailey in partnership with Constant Contact conducted a study that

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analyzed the behavior of 1,491 consumers ages 18 and older throughout the U.S., and revealed

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that a whopping 77% of consumers interact with brands on Twitter or Facebook primarily through reading posts and updates from the brands. They also noted that 60% of social customers

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are more likely to recommend a brand to a friend after following the brand on Twitter or

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Facebook, and 50% of them are more likely to buy from that brand as well. When it comes to "Liking" brand posts on Facebook, the reasons are varied, but for the most part, respondents said

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they like a brand on Facebook because they are a customer (58%) or because they want to receive discounts and promotions (57%) (Constant Contact, 2011). Today, the customer experience shared through social media, blogs and discussion forums is becoming a major driver of purchasing decisions, because these platforms provide consumers a more influential voice in effecting changes in their own customer care (Capozzi and Zipfel 2012). Barnes’ research (2008) indicates that 70% of consumers use social media platforms “at least some of the time” to learn about the customer care offered by a company before they make a purchase. Furthermore, of them, 74% of customers choose companies based on customer care experience shared by others in online forums. Over the past few years, big brands have started taking social media seriously, and social media marketing has been an inevitable part of their marketing plan. For example, Coca-Cola, 2

ACCEPTED MANUSCRIPT one of the world's most recognizable brands, had 800 fans on Facebook in 2007, 16.5 million in 2010, and it has currently crossed over 62.3 million “likes”. In 2012, in honor of the Coca-

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Cola Facebook page becoming the first retailer brand to receive 50 million “likes", Coca-Cola

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developed a new Facebook application to identify and support individuals developing, influencing and shaping ideas and ask them to collaborate with the Facebook community to

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spread them globally. Through this application, Coca-Cola teaches the world to sing in perfect

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harmony, mobilizes millions of people behind their favorite cause, and encourage them to become more active and socially involved. As an end result, consumers become involved in

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suggesting modifications of products and services and the distribution of these innovations (Berthon 2007; Berthon, Pitt et al. 2012).

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Starbucks, as one of the top ten most followed brands on Twitter, uses tweets to share knowledge with customers and promote their latest products, campaigns and events (Chua and

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Banerjee 2013). With an average of ten tweets per day on Twitter, Starbucks extracts relevant knowledge from a network of current and prospective customers around the globe who express their expectations, likes and dislikes about the brand (Noff 2009); (Chua and Banerjee 2013). In 2010, Delta Airlines launched the first social media “ticket window’’ on Facebook which allows customers to book a flight without having to go to any other website. Delta pointed out Facebook is being used by more customers while in flight than any other Web site, making it a ‘‘natural launching point’’ for its initiative (Baird and Parasnis 2011). Access to OSNs on mobile devices has certainly accelerated the popularity of OSNs. As more and more major brands have established their communities and fan pages within online social networks (OSNs) and started offering commerce opportunities delivered through social media platforms, crowdsourcing applications have become some of the most engaging 3

ACCEPTED MANUSCRIPT tools in digital marketing realm, enabling brands to realize the potential for their fans’ input into the product development and the market development processes (Huberman 2008). Such

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innovative and creative initiatives enable businesses to improve their products, get brand

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recommendations, increase brand awareness and popularity, find new customers or even excite a specific demographic. In many cases where fans within social media are particularly passionate

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about a brand and its products, there will be a clear desire to become part of the product itself,

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have input as a group and energize the brand and its product lines (Sashi 2012). Today’s openness and flexibility of OSNs provide brands with a huge opportunity to get in

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touch with customers, crowdsource marketing tasks and enhance brand awareness. Understanding the structure and behavior of the fans on OSNs is important to the content

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providers to enable better organization of brand post information, design of effective online communities and for implementing successful marketing campaigns. In examining the online

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social interaction structures, the formation of relationships and interactions, how information moves on social media platforms, and how users respond to various stimuli like video, contests, or posts are not clearly understood. The answers to these questions will offer a more complete picture of the social dynamics of networking and how individuals manage their virtual relationships and follow their favorites or brand communities, or how they influence their friends to become followers as well. In this paper, we model the spread of information across Twitter, the most popular and widely used micro-blogging online social network (Jabeur, Tamine et al. 2012) and analyze the data from a number of brand posts to discover what rules might govern the spread of information online. By understanding these behaviors, companies can become more effective in designing marketing campaigns. Being able to analyze a social network of customers, how customers interact on this type of platforms, and what rhythm and timing of the 4

ACCEPTED MANUSCRIPT most engaging postings look like provides brands a competitive advantage through forecasting the spread of brand influence, and intervening at times with promotions to foster relationship

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with customers.

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The timing pattern of human communication in online social networks is not random. It has been shown that the communication is explained by emergent statistical laws such as non-trivial

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correlations and clustering (Rybski, Buldyrev et al. 2012). With the possibility of analyzing the

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multivariate distribution of the occurrences of activity on OSNs, we can add to our understanding of these interactions.

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Standard models assume a Poisson distribution for events occurrence, which is an unrealistic assumption in many social systems. Point process has shown promise for modeling social event

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patterns where the occurrence of an event increases the likelihood of subsequent events (Crane and Sornette 2008). It is a novel way of modeling and clustering high frequency and irregular

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data in time. It uses a branching structure that corresponds to background events and offspring events and is able to capture bursts of activity, dynamics and reactions over time. In this paper, we model the popularity of a brand post or more generally an online content on online social networks. The popularity of an online content is not a well-defined, but a highly subjective term (Jong Gun, Sue et al. 2010). Brand post popularity can be defined as a mixture of various factors such as vividness, interactivity, the content of the brand post (information, entertainment), and number of times the brand post is mentioned by fans (de Vries, Gensler et al. 2012). We take the position of an individual user’s eyes who conjectures the popularity of a brand’s tweet from publicly observable data by associating the number of impressions it has received (including total number of retweets, replies, favorites) or the lifespan of threads over its entire timeline. A tweet is considered a popular tweet if it receives a certain amount of retweets, 5

ACCEPTED MANUSCRIPT replies, and favorites that are no less than a certain threshold over its lifespan (Kong, Feng et al. 2012 and Lee, Moon et al. 2012). Our goal is to develop a mechanism for capturing the evolution

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of the online content popularity posted by brands on OSNs. In our approach, a model is specified

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via the conditional intensity for each event. This provides a powerful and more natural modeling framework for multivariate social network event data. Specifically, the current study examines

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the influence of user activities on the timing and frequency of a brand post. The self-exciting

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Hawkes point process and the ETAS (Epidemic Type Aftershock Sequences) models are used to analyze data on brand posts popularity. Unlike Poisson processes, Self-exciting Hawkes point

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process and ETAS are classified as counting processes which are basically a continuous-time non-Markov chain due to the dependence on the history of the process (i.e. H t ) to the extent to

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which having states 0, 1, 2, . . . moving from state n to state n+1, where n ≥ 0. In case of the content popularity problem, each state indicates total number of users who hit the content by

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time t, and  (t ) is the transition rate of moving from one state to another state. The remainder of the paper is organized as follows. The next section starts with a discussion of online social networks (OSNs). We also review literature about stochastic point processes and their many uses. The following section describes how we map the content popularity to the point processes framework.

Also, we introduce brand post data collected from Twitter and the

assumptions necessary to proceed with analysis. In section 4, we fit competing models to data and then compare the accuracy and complexity of models in capturing the burst of activity on OSNs. The managerial implications of our findings, limitations and possible directions for future work are discussed in Section 5. The final section presents a general conclusion of the paper. 2. Review of the Literature 6

ACCEPTED MANUSCRIPT 2.1. Online Social Networks During the past few years, millions of people have used social media applications (Facebook,

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Twitter, YouTube, Google+, etc.) as a part of their daily online activities (Guy, Jacovi et al.

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2010). In 2011, more than half of social media users followed brands on social media sites, and

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brands are increasingly investing in social media to crowdsource marketing activities, indicated by worldwide marketing spending on social networking sites of about $4.3 billion (de Vries,

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Gensler et al. 2012).

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Today companies develop official fan pages and online communities within online social networks to understand customers, connect with them instantly and provide them with

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information about their brands, products, promotions and more. Meanwhile, brand fans can like,

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comment and share brand posts. Users of Twitter can retweet, which is much like a Facebook share. Followers retweet the tweets of those they are following to propagate information to other

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people. People respond to popular users by “replying” and/or “mentioning” (Bae and Lee 2011). Followers can also mark the content as favorite which is functionally similar to the “like” action on Facebook. The “like” and “retweet” buttons are the easiest ways for Facebook and Twitter users respectively to join in on the brand conversation and give feedback. Comments/replies on brand posts can be positive, neutral or negative. In most cases, social media users who choose to become fans of a product are those who are particularly passionate about a brand and its products and enjoy having input or being a member of a group of like-minded fans. The brand benefits from these fans because they help communicate with a diverse audience of other consumers. Such individual activities associated with a brand post are visible to network friends and many times influence friends to retweet, like, or mention. If a company produces fan page updates that earn high quality scores, they will reap the benefits of greater exposure and possibly 7

ACCEPTED MANUSCRIPT an increased fan base because other network members will see in their news feed. Jansen, Zhang et al. (2009) discuss OSNs as a form of electronic word of mouth (eWOM) for sharing consumer

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opinions concerning brands and as a part of an organization’s marketing strategy. This openness and flexibility of social media provides businesses a great opportunity to bring together a group

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of people, or “crowd”, to solve a problem or engage in an activity and achieve powerful social

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engagement and activation.

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In many ways, the interactivity of social media supports “crowdsourcing”. Crowdsourcing is a term coined by journalist Jeff Howe (2006) to mean “taking advantage of the talent of the

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public” (Lober and Flowers 2011). Social media provide platforms for existing and potential customers to engage, learn, and entertain. It enables content marketers to crowdsource their

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marketing, reaching vast audiences via word-of-mouth. For example, Starbucks developed the

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“My Starbucks Idea” campaign, an online customer community, where customers are asked to

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contribute their views and ideas about the company. It keeps customers in the loop on what business ideas Starbucks is currently implementing on both the brand and product level. Through linking this platform to Facebook, Twitter and other social media websites, customers are able to see what others are suggesting, vote on ideas and check out the results (Noff 2011). Internet service providers, content creators, and online marketers would like to be able to predict how many views and actions an individual item might create on a given website (Szabo and Huberman 2010). This is true for companies as well who benefit from aspects of online social networks by utilizing fan pages and web advertising. Leveraging the social networking sites to understand what is most popular helps e-commerce providers decide what content to promote on their website. E-commerce providers can leverage these social signals to ensure the products or services people are talking about appear higher in their product listings. 8

ACCEPTED MANUSCRIPT Over the last few years, much effort has been devoted to exploring the statistical features of content popularity in online social networks (OSNs). Most previous empirical analyses of OSNs

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have treated such networks as static (Willinger, Rejaie et al. 2010; Figueiredo, Fabr et al. 2011).

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They analyze the social networks on a single data snapshot (Ahn, Han et al. 2007; Leskovec, Lang et al. 2008; Fabr, Benevenuto et al. 2009). However, such social network systems are

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inherently dynamic, characterized by a high burstiness and a strong positive correlation between

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two users’ activities and consist of a set of dyadic, directed, time-stamped, cross-affected and sometimes weighted events. To the best of our knowledge, only a few studies have analyzed

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popularity growth patterns of content on OSNs using prediction models (Crane and Sornette 2008; Cha, Kwak et al. 2009; Lerman and Hogg 2010; Szabo and Huberman 2010; Figueiredo,

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Fabr et al. 2011). Crane and Sornette (2008) propose contagion models as models of YouTube video viewing dynamics to understand how popularity bursts can be described. They

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differentiate four classes of popularity dynamics (memoryless, viral, quality and junk) which are all explained by properties of Hawkes point process. Szabo and Huberman (2010) find a strong linear correlation between early and later times of the content popularity on YouTube and Digg networks. This correlation confirms that if the content is popular when new, it will continue to be popular as it ages.

Another interesting work on social media mining is reported by

Chatzopoulou, Cheng et al. (2010). They find a strong correlation between total number of comments (or favorites) and total view count in YouTube. There are relatively few studies in the literature which explore the capability of online social networks to predict real-world outcomes such as the revenue or release time of a product on the market. Sadikov et al. (2009), Abel, DiazAviles et al. (2010) and Rui and Whinston (2012) present case studies in which blogosphere content can be used as a predictor of movie and music success. They show that the number of 9

ACCEPTED MANUSCRIPT microblog views of content related to the music or movie (such as FB posts, tweets, YouTube videos, etc.) can provide an accurate prediction of the movie’s or music’s success.

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While previous studies build popularity models based on a one-dimensional function of time,

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we suggest that the content popularity can be a joint probability function of time and the number of followers. We focus more on incorporating the number of followers as an influential metric

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into predictive models of the content popularity, explicitly looking at the impact of influential

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users on their followers to persuade them to contribute to brand post popularity. In this paper, we adapt a mathematical framework based on self-exciting point process to study brand post

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popularity on online social networks. Specifically, we calibrate one-dimensional and twodimensional self-exciting point process models to estimate popularity growth patterns of brand

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post contents on Twitter.

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2.2. Stochastic point processes

In this section we present the statistical theory underlying our approach. First, we define the conditional intensity function for a point process. A point process is a stochastic model commonly used to describe the occurrence of discrete events in time and space (Schoenberg et al, 2006). It can be viewed in terms of a list of times t1 , t2 ,..., tn at which corresponding events 1, 2,…, n occur (Erik, George et al. 2010). Intuitively, a point process is characterized by its conditional intensity  (t ) , which represents the mean spontaneous rate at which events are expected to occur given the history of the process up to time t (Ogata, 1988). In particular, a version of the conditional intensity may be given by the process

 (t )  lim

t  0

E  N [t , t  t ] H t  t 10

ACCEPTED MANUSCRIPT where H t denotes the history of events prior to time t, and the expectation represents the number of events N[t , t  t ] occurring between time t and t  t . The Poisson process is a special case a

point

process

where

the

interval

times

between

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of

two

arrivals

are

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independent, identically distributed exponential random variables. The conditional intensity of a

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Poisson process is deterministic which means that events are linked causally to the conditional intensity. In other words, a point process is classified as a Poisson process if events occurring at

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two different times are statistically independent of one another, meaning that an event at time t1

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neither increases nor decreases the probability of an event occurring at any subsequent time (Erik, George et al. 2010). Since a Homogeneous Poisson process indicates complete

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randomness, it is most commonly used as a suitable benchmark for assessing self-exciting

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process models.

A point process is called self-excited if any one event increases the likelihood of the future

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events (Hawkes 1971). A self-exciting or Hawkes point process is a versatile point process which has been extensively studied from a theoretical and practical point of view. It is defined by its conditional intensity function ti

 ( t )      ( t  ti )dZ( u ) 



 ( t  t )

{ ti t } 

 (  )d  1,

i

(1)

 (  )  1,   0

0

where Z is the normal counting measure (Hawkes and Oakes 1974). The rate of events ( t ) is decomposed into the sum of a Poisson background rate which in most applications is assumed to be constant in time (Hawkes and Oakes 1974) and a self-exciting component in which events 11

ACCEPTED MANUSCRIPT trigger an increase in the rate of the process. The self-exciting part of the process has two components:  and  .  is a constant which reflects the magnitude of self-excitation and  is a

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density function describing the waiting time (lag) distribution between excited and exciting

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events. A proper skewed distribution in which the overall shape reflects a long time dependency

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should be introduced for the triggering density.

In the Hawkes-based analysis, the events can be viewed as the realization of a multivariate

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point process. That is, every single event is characterized by the occurrence time and the event’s type. Notationally, {Ti , Zi }i{1,2,..} are random variables where Ti is the occurrence time of the ith

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event and Z i  {1, 2,..., M } indicates the ith event’s type (Bowsher 2007). A point process is said

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to be mutually-exciting if any one event from a specific event’s type at time t1 increases the

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likelihood of an event in another event’s type stream occurring at time t 2 . Mutually-exciting

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Hawkes process is used to capture cross interactions and mutual information between one sequence of events and another. Similar to the self-exciting Hawkes process, a mutually-exciting Hawkes process with n event type(s) is defined by its conditional intensity functions n

 k (t)   k  

   (t  t )

j1 {t i  t}



  ()d  1, ij

ij ij

i

k  1, 2,...n

(2)

ij ()  1,   0

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where the rate of event type k, k ( t ) , is partitioned into the sum of a Poisson background rate and mutual-exciting components in which events trigger an increase in the rate of the process.

ij is a constant which reflects the strength of self-excitation for ( i  j ) and the strength of

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ACCEPTED MANUSCRIPT mutual-excitation for ( i  j ) and ij is a density function describing the triggering distribution between excited event type i and exciting event type j.

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Hawkes-based analysis has long been used in seismology to recognize similar clustering

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patterns in earthquakes occurrence data and to predict subsequent earthquakes, or aftershocks.

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(Adamopoulos 1976; Ogata and Vere-Jones 1984; Veen and Schoenberg 2008; Wang, Bebbington et al. 2012). It has been applied to many other areas such as finance (Bowsher 2007;

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Bauwens and Hautsch 2009), neurophysiology (Chornoboy, Schramm et al. 1988), ecology, social networks (Erik, George et al. 2010; Alexey, Martin et al. 2011; Mohler, Short et al. 2011)

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and online social networks (Crane and Sornette 2008; Lawrence and Michael 2010).

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(Engle and Lunde 2003); Bowsher (2007) present a bivariate Hawkes process model to

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jointly analyze the timing of trades and quote arrivals in stock markets. Chavez-Demoulin, Davison et al. (2005) and Bacry, Delattre et al. (2012) use Hawkes process structure to estimate

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value at risk for portfolios of traded assets over a given holding period of time. Dassios and Zhao (2012) present dynamic contagion process as a generalization of the Cox process and Hawkes process and use it to model risk process with the arrival of claims. Mohler et al. (2010), Egesdal et al. (2010), and Erik, George et al. (2012) use self-exciting point process models to predict violent events and security threats. Erik, George et al. (2010) utilize step functions parameterized by various values, linear functions and non-parametric approaches as non-stationary background rates () of the point process. Alexey, Martin et al. (2011) use a self-exciting point process to discover missing data in the series of interaction events between agents in a social network. They apply this model to the Los Angeles gang network to predict affiliation of the unknown offenders.

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ACCEPTED MANUSCRIPT Recently, this approach has been used to analyze the dynamics of online social networks. Crane and Sornette (2008) and Mitchell and Cates (2010) analyze a family of self-exciting point

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processes to model correlated event timing of viewing YouTube videos. They deploy a Pareto

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distribution (power law) as a distribution of waiting times between cause and action, describing the cascade of influences on the online social network. It is shown that a Hawkes process

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enclosing power law distributions offers many capabilities to calibrate the model to

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characteristics of the YouTube views. These characteristics are classified by a combination of

across the network (critical/subcritical).

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endogenous/exogenous user interactions and the ability of viewers to influence others to respond

Howison et al. (2012) deploy a mutually excited Hawkes process to understand the

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dynamics of the user generated contents over open contribution platforms such as Wikipedia and Linux. They study the influence of visible activity of others on the timing and amount of

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participation in Wikipedia environment. They model the time at which a response to an event occurs as a log-normal distribution. But this analysis has not yet been conducted on social media activities, in particular on Twitter postings and follow-up actions. Also the role of the influential users within OSNs has not been yet considered in such predictive models. In this paper, we provide a more realistic investigation of the benefits of stochastic point processes for predicting the brand post popularity on OSNs. To the best of our knowledge, there are relatively few studies in the literature which explore the capability of point processes on online social networks to model dynamics and growth patterns. We use the ETAS model, one of the most widely used point process in the literature, to shed light on how the content popularity on OSNs can be described by a function of time and the number of followers. The number of followers is one of the best metrics to demonstrate the role of the influential users within OSNs. 14

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3. Problem formulation Understanding rules governing collective human behavior, especially as they affect social

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interactions on internet-based social media, is a difficult task in the field of social media

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analytics. Our main objective is to analyze how the popularity of individual brand posts evolves

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when the posts are shared with people on social media outlets. We examine how fans’ sequential interactions with network friends contribute to the popularity of a brand post. The majority of

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brand posts experience few hits and can be well described by a Poisson process. In such a case of little activity, popularity oscillation is quite steady. In contrast, some brand posts experience

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bursts of activity and word of mouth growth through friend sharing features of OSNs. A standard

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stochastic process (i.e. Poisson process) fails to address the burst of popularity; since it is based

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on the assumption of independence about arrivals, which is unrealistic in case of future activities arising from a specific tweet/post/etc.. Clustering point processes and epidemic type models are a good fit for modeling such phenomena. In the online social networks analysis, the social activity event data can be viewed as the realization of a multivariate point process. Each event is characterized by its occurrence time (ti ) , the magnitude of influence (number of followers) ( mi ) with an additional mark attached to it representing the event’s type ( zi ) . Retweeting, replying, tagging and marking a brand post as a favorite, etc. are different types of user activities. For the purpose of this paper, we combine these three types of events into one common set of events. The beauty of major OSN platforms is that they are structurally isomorphic. Their similar features, while labeled with site-specific vocabulary, operate in the same way, making studies of 15

ACCEPTED MANUSCRIPT their data easier.

For the purposes of this paper, we will utilize Twitter notations to explain

properties of OSNs.

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In order to build our two dimensional point process, we define {Ti , M i , Zi }i{1,2,..} as random

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variables where Ti is the occurrence time, M i the magnitude of the ith triggering event and

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Z i  {1, 2,...} indicates the type of ith event. Any event of a specific type at time t1 increases the

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likelihood of an event of any type stream occurring at time t 2 . Now, we formulate the problem using Hawkes process properties and discuss how those mechanisms work on the time line.

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3.1. Candidate models

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First, we formulate one sequence of events using a self-exciting point process to measure the

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likelihood that individuals are talking about the brand regardless of the type of events. This

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model lets us aggregate the popularity content from across Twitter into a single stream of information. It concurrently captures the idea that any given activity on a brand post can causally correspond to a background Poisson process  (in this case constant) and foreground selfexciting process as follows:

(t)  (t | H t )   

 (t  t )

{i:t i  t}

i

(3)

The summation component indicates the influence of users’ activity on the stream. It describes how past events at times t i influence the current event rate. Parameter  indicates the amount of excitation an event contributes to the stream. In behavioral terms, It can be described as the number of potential users influenced directly by individuals in the past who retweeted or replied to the brand post tweet at time t i . As mentioned earlier, function  is a triggering function 16

ACCEPTED MANUSCRIPT describing distribution of waiting time between a trigger and the response from users who influenced to recommend the brand. Mining of our data on the life cycles of various brand posts

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in Twitter indicates that unlike YouTube, a brand’s tweet gets most of its hits within the first

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days -even hours- of its life cycle and quickly becomes obsolete. Since most responses occur almost immediately in the Twitter case, we need a distribution that enforces the highest intensity

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at the most immediate possible time. Furthermore, it should be skewed and long tailed to reflect

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a long time dependency and burstiness.

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Model 1:

First, we use an exponential distribution for the response density, giving the conditional

 e

(4)

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{i:t i  t}

 (t  t i )

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(t)   

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intensity

where t  t i is the time elapsed since event i, and  reflects a rate of decay for the triggering density which controls how long self-excitation takes following a tweet. If  is large, mentioning the brand post by users will last only a short while and a few events (retweet or reply) will be only added above a background rate after the initial brand’s tweet over a short period of time. Conversely, if  is small, self-excitation will last for a much longer period of time and then many more events will be added to the background rate. Model 2: There is another characteristic of events in OSNs that should be taken into consideration. We suggest that the amount of users’ contributions to future events is not only dependent on the 17

ACCEPTED MANUSCRIPT occurrence time, but that the number of followers he/she has is an important factor as well. Therefore, our second model takes into consideration two parameters: the occurrence time and

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the magnitude of triggering event (number of friends and followers). It means that the event does

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not scale just with the occurrence time, but also the magnitude of the triggering event as well. One particular form of a self-exciting point process is the ETAS model (space-time-

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magnitude Hawkes process), which is widely used to describe spatial-temporal patterns. This

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model takes more parameters (inputs) into account. We use an early form of this model (i.e. time-magnitude Hawkes process), similar to (Ogata 1988), to quantify the popularity of a brand

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tweet. This model incorporates magnitudes and occurrence time of triggering events concurrently. The conditional intensity for the ETAS model is given by

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 (t  t , m )

{i:t i  t}

i

i

(5)

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(t)  (t | H t )   

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where the history of the process H t  (t i , mi ) : t i  t also includes magnitudes m i ,  is the arrival rate of new users and  is a triggering function. The ETAS uses a combination of the exponential distribution and the Pareto distribution for the triggering density  , giving the conditional intensity

(t)   

 e (mi M0 ) 1 p {i:t i  t} (t  t i  c)

 (t  t , m )    

{i:t i  t}

i

i

(6)

where the power-law term governs temporal distribution of subsequent triggered events and the exponential term explains the factor by which the user’s magnitude mi inflates expected number of influencers. The term t  t i denotes the time elapsed since event i.  is the amplitude coefficient indicating the amount of direct excitations triggered by event i. The exponent p is the decay rate,  is interpreted as the productivity rate to control the number of potential users 18

ACCEPTED MANUSCRIPT influenced by individuals in the past, and c is the time offset that will be empirically determined from the dataset under consideration. Furthermore, M 0 is the lowest magnitude (number of

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3.2. Empirical Testing of the Models on Twitter datasets

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followers) that will be substituted from the dataset (rescaled to the appropriate range).

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We next apply these models to real data. As mentioned earlier, a basic analysis of our data on

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the life cycle of various brand posts in Twitter using Topsy API and Twitter search API indicates that the majority of a brand’s tweet gets most of its activity within the first days -even hours- of

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its life cycle and hence quickly becomes obsolete. Since we focus on the brand post popularity, we take brand posts that experience bursts of activity and electronic word of mouth growth

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through the friend sharing features of Twitter. Using Twitter’s publicly available API, we crawled Twitter information streams of more than 120 major brands that were among the top 500

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most valuable global brands (Brand Directory 2013). These brands were among the most followed brands and were actively posting tweets at their fan pages on Twitter. These brands are from different product and service categories including clothing, cosmetics, electronics, accessories, foods, beverages, automotive, credit cards, airlines, etc. Together, these brands published more than 26,500 tweets in a typical period of one week to provide information to their customers and promote their latest products, campaigns and events. We downloaded information of all subsequent activities (retweets, replies, and marks as favorite) on a brand post for all these 26,500 brand post tweets. We observed that the majority of brand posts tweets experience few hits and therefore as mentioned earlier, can be modeled by a Poisson process. However, there are brand posts that became a major topic (“trending” in Twitter parlance), are frequently mentioned by the brand’s followers, and experience bursts of activity. For the purpose of this paper, we 19

ACCEPTED MANUSCRIPT searched through the downloaded tweets to isolate those tweets that are original tweets from the brands and where the tweets have been mentioned (re-tweeted, replied, marked as favorite) at

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least 300 times. A number of 221 such brand post tweets followed by many hits and bursts of

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activity were identified. At this stage, 125,861 twitter activities including information on original tweets, all subsequent retweets, replies and marked as favorite to the original tweet were

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processed. The data were divided into individual datasets. Each dataset contains a corpus of an

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individual brand post tweet, its subsequent activities (retweets, replies, and marks as favorite), along with their timestamps, user ids and number of followers of the user who contributes to the

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tweet stream. We take into consideration only the timestamp of events and the number of followers, while aggregating the events “retweet”, “reply”, and “mark as favorite” into a single

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stream of information.

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We investigated the content of these 221 most popular brand tweets and note that the primary topic was the brand campaigns on Twitter (44%). Some of these campaigns use Twitter to communicate with fans and followers. Several campaigns use Twitter hashtags to deliver rewards and sweepstakes to customers. Other campaigns have interactive competitions to create buzz with fans. The second most engaging brand tweet category is related to the events held by the brands on Twitter (36%) including surveys etc. The rest of the most popular brand tweets were related to the information and entertainment posted by brands on Twitter. 3.3. Parameter estimation, goodness of fit, and models comparison Given a brand post data collected from Twitter, we utilize maximum likelihood estimation (MLE) methods to estimate the parameters of candidate self-exciting point process models. While numerical optimization routines such as the quasi-Newton method, the conjugate gradient 20

ACCEPTED MANUSCRIPT method, the simplex algorithm of Nelder and Mead and the simulated annealing procedure (Ozaki 1979; Ogata 1988; Daley and Vere-Jones 2003) are often used to compute maximum log-

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likelihood estimation of self-exciting point process models, we use the expectation-maximization

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(EM) algorithm provided by Veen and Schoenberg (2008) to estimate parameters. Veen and Schoenberg (2008) have demonstrated that the EM algorithm as the estimation method of choice

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for incomplete data problems is extremely robust and accurate compared to traditional methods.

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The brand post popularity can be viewed as an incomplete data problem in which the unobservable or latent variables ascertain whether an activity belongs to a background event or

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whether it is a foreground event and was triggered by a preceding activity. Finally, the reliability of each model is statistically tested using the Kolmogorov- Smirnov

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(K-S) statistic to assess the extent to which the model fits the data. This criterion provides useful information of the absolute goodness-of-fit of candidate models. Furthermore, the relative ability

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of each model to describe the data is measured by computing the Akaike information criteria (AIC) (Akaike 1992). The Akaike statistic provides germane numerical comparisons of the global fit of competing models. The required package functions in R software are used for fitting both above models to the datasets (Ptproc package (Peng, 2003), Ptprocess (Harte, 2011), ETAS package (Jalilian, 2012), and R code (Veen and Schoenberg 2008)). Furthermore, we employ autoregressive integrated moving average (ARIMA) models as benchmarks which have been regarded as the closest framework to point processes for event data (Daley and Ven-jones 2003). We used an R package “Forecast” (Hyndman et al. 2013) to perform the time series analysis. This package allows fitting of time series and linear models. The functions available in this package conduct a search over possible models within the order constraints provided and return the best ARIMA model for a univariate time series according to 21

ACCEPTED MANUSCRIPT AIC values. In the next section, we will first present our results for one of our crawled datasets to illustrate how our approach works and then we discuss goodness of fit of the candidate models

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by computing their average AIC values across all the datasets that we compiled from Twitter.

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In summary, Figure 1 illustrates the methodology used for modeling the content popularity on Twitter in this paper. At each stage, the inputs, the required R- packages used to produce the

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results and the output are specified clearly.

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Figure 1- The methodology used in predicting the online content popularity on Twitter

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Twitter Database

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Parameter Estimation for the point process models: Veen and Schoenberg’s R-code, PTPROC, PTPROCESS R-packages

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Input: Individual tweet dataset (including user ids, timestamps, number of follower) in CSV or XML format

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Simulation: PTPROC, PTPROCESS, ETAS R-packages Output: Estimated parameters for best fitted ARIMA model, loglikelihood function value, simulated ARIMA model, AIC value etc.

Output: Estimated parameters, log-likelihood function value, simulated conditional intensity function, K-S, AIC values etc.

Models Comparison: AIC values

End

23

ACCEPTED MANUSCRIPT 4. Results and analysis In this section, we focus on one particular dataset to demonstrate how models work in

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practice. We set t  1min for the bin width in order to control the amount of data through

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parameter t. From this specific dataset there are 751 events spanning 10,080 minutes (one week).

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Fig. 2 and Fig. 3 provide frequency of different types of hits and a histogram of the frequency of all events per minute respectively. The most events occurring in a single minute is 15 and the

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mean number of events in a single minute is 0.074. Out of a possible 751 events, 278 events

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occurred during the first two days. Thus, we reason that people respond to a brand post tweet immediately. Therefore, we would expect that the distributions to be selected should impose the

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largest probability mass at the most immediate possible response time.

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Frequency of activities

212

Retweet Reply

412

Mark as Favorite

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Fig. 2. Frequency of different types of events

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Fig. 3. A histogram of the number of events per minute

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Table 1 summarizes the parameter estimates for the first candidate model. Table 1. Specification of the self-exciting Hawkes process model (1) used for simulation

Parameter





Value

0.05673

12.14027



2.91944

The fit for the data with self-exciting point process model is plotted in Fig. 4.

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Fig. 4. Simulated conditional intensity function for model #1

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The parameter estimate for  denotes that immediately after an event occurs, the conditional intensity is amplified by about 3 events per minute. The parameter estimate for  indicates an event related to the brand post tweet is talked about for up to 12 minutes after posting. Now let us look at the ETAS model that takes into account the occurrence time and the number of followers for every single triggering event. Fig. 5 provides a snapshot of the number of followers for those users who appear to have been influenced by the brand post tweet either spontaneously or in response to the certain triggers.

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700 600 500 400 300 200 100 0 0

1000

2000

3000

4000

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Number of followers

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5000

6000

7000

8000

9000

10000

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Time

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Fig. 5. Number of followers over time

Table 2 summarizes the parameter estimates for the ETAS model. Simulated data with the

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corresponding ETAS point process model are shown in Fig. 6. Table 2. Specification of the self-exciting point process model (2) used for simulation

Value







p

c

m0

0.01376837

2.1254544

1.157623

0.01343711

0.3

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Parameter

0.5886

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Fig. 6. Simulated conditional intensity function for model #2

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Our hypothesis is that the greater the number of followers per event, the greater the influence. Therefore incorporating the number of followers into our predictive model as another dimension presumably provides better results. Fig. 6 reveals that the ETAS model is much more able to capture jumps and leaps of the process compared to our dataset. Utilizing statistical tests such as the K-S goodness-of-fit test and AIC test allows us to test whether the number of followers impacts the model. Table 3 summarizes the results for a two sample K-S test demonstrating how well both models perform in terms of the original data. It contains the p-values and the values of the K-S test statistic (D) corresponding to each model.

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ACCEPTED MANUSCRIPT Table 3. The K-S goodness-of-fit test output

ETAS model (Model #2)

D = 0.3993, p-value = 0.03135

D = 0.1223, p-value = 0.02216

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Self-exciting Hawkes process (Model #1)

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These results support our hypothesis that incorporating the number of followers into the

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predictive models provides a better simulation for understanding such phenomena.

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Since the ETAS model has more parameters in comparison to the self-exciting Hawkes process, AIC values are used to analyze parsimony, complexity and accuracy of the models. The

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homogeneous Poisson model is also often used as a reference model for comparison of

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Table 4. AIC test results

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competing point process models. Table 4 summarizes the AIC values for candidate models.

Time series model Homogeneous

Self-exciting

Hawkes ETAS model (Model

(ARIMA (3,1,3))

Poisson model

process (Model #1)

#2)

9787.670

5401.592

4473.017

4012.011

The AIC values show that the ETAS model is the one with the minimum AIC value. Therefore, the ETAS model provides a better fit than a homogeneous Poisson model or selfexciting Hawkes process or the benchmark ARIMA time series model.

29

ACCEPTED MANUSCRIPT We next estimate the self-exciting Hawkes process model, ETAS model, the benchmark Poisson process model and the benchmark ARIMA model and compare their goodness of fit by

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computing their average AIC values across all datasets.

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Table 5. Models’ comparative average AIC values

Self-exciting

Hawkes ETAS model (Model

(ARMIA (p,q,r))

Poisson model

process (Model #1)

13398.661

9047.397

7143.110

#2)

6415.187

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Time series model Homogeneous

According to Table 5, the ETAS model has the lowest average AIC value. The proposed

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ETAS model outperforms the three benchmarks, which indicates that it can capture the influence

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network better than other models. The benchmark homogeneous Poisson process and the

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benchmark ARIMA time series model seem to fare much lower than the ETAS and the selfexciting Hawkes process. The Poisson process model fails to capture any exciting effects among user activities to make the prediction. Also, the ARIMA time series model appears to fail to capture the dependency between the current event and the past events on the time line. Recall that, in the online content popularity context where the occurrence of an event increases the likelihood of subsequent events, whether slightly or greatly, it is imperative to account for exciting effects among users’ activities. Our result implies that the impact of the number of followers on brand post popularity is an important issue in OSNs. It is necessary to consider the event occurrence time and the number of followers as two major factors in modeling of online social dynamics.

30

ACCEPTED MANUSCRIPT We found that ETAS model provides much more accuracy to predict popularity of brand posts. It allows us to consider the role of the influential users in amplifying the brand post

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popularity and secondarily proposing the brand to their friends and followers networks. It implies

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that influential users with a high number of followers can have a significant influence in

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spreading the content of the brand post to others.

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5. Discussion and Limitations

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We have adapted a powerful approach for modeling the content popularity in OSNs. In contrast to the previous studies that focused on a one-dimensional function of time, the model

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recommended in this paper allows us to characterize and quantify the content popularity as a

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joint probability function of time and the number of followers. The self-exciting Hawkes process

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and ETAS models have been calibrated to simulate popularity growth patterns of brand post contents on Twitter and as expected, the ETAS model outperforms the other models to capture bursts of activity over time.

This model can enable brand marketing managers to observe how often their fans respond to their posts within OSNs, and gauge the response for different types of content such as news, contests, applications, video, pictures, product information, brand’s history, testimonials, etc. They will also have the ability to see how these brand posts move through the Internet. These predictive models can help companies decide how often and when a new brand post should be posted, and how many times the same piece of content can be shared in order to engage more fans and followers. Certainly there is no magic number for the ideal number of posts within OSNs; it is important for brands to post enough content while refraining from posting too much 31

ACCEPTED MANUSCRIPT at the same time. The mathematical configuration of ETAS model also confirms that if the time difference between two consecutive events is big enough, most likely the brand post will become

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obsolete and suggests that it is time to post a new content to keep a connection opened with fans.

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As another managerial implication of this study, the mathematical formulation of the ETAS model reveals that the greater the number of followers per event, the greater the influence. This

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means that a high number of followers improve activity in posting tweets and being more often

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retweeted. It highlights the role of influential users who significantly affect the engagement of a brand post, even if they are involved later. Thus, if companies identify and increase the number

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of influential users within their online social networks, they should experience an increase of brand recommendations and awareness. Engaging more users that are influential during the early

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life of the brand post could cause viral effects, which is likely to influence potential consumers for a longer period. Many approaches have been proposed to find influential users within OSNs.

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The simplest approach is to count the number of followers, but there are other efficient techniques based on mining link structure along with the temporal order of information adoption (Lee, Kwak et al. 2010).

Also, since fans’ reactions and response time to different types of the brand post content are dissimilar, it is important for brands to look carefully at the performance of their various brand post contents and see which of them during their lifecycle have similar looking stationary/nonstationary background rates. If they do not follow the same growth pattern, each category needs an individual point process to represent it. Our work proposes a mechanism for capturing the evolution of the online content popularity posted by brands on Twitter. It facilitates the early prediction of a tweet behavior on Twitter and the simulation of the rhythm and timing of the most engaging postings. Through the simulation 32

ACCEPTED MANUSCRIPT and the early prediction of a brand’s tweet, brands have a better view of timing promotions to foster relationship with customers.

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Our research can be extended to determine a peak release time for products of consumer interest on the market through analyzing aggregative/collective brand posts from OSNs. If brand

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posts are not propagating further on OSNs, it could indicate that the brand is losing its fans’

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awareness and popularity, so improvement actions should be taken.

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Several limitations of our study deserve mention. First, we assume that all users follow the same response time distribution for their own activities. However, individual activity burst shows

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a sequence of discrete events. This is unlikely to be a single distribution for the purposes of fitting exponential or Pareto distributions to the long term dependency. Another limitation is that

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the various types of events are aggregated. Multivariate self and mutual exciting point process models should be developed to deal with different streams of information and measure cross

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interactions and mutual information between one sequence of events and another. Furthermore, even though we chose a small time increment, i.e. t  1min for the bin width in order to control the amount of data through parameter t, we cannot determine if events occurring in the same minute are correlated with one another. This means that the events recorded on the same minute are assumed to be statistically independent. While we consider the same importance for fan’s response times, we can track down brand’s most engaging minutes, hours and days of the week to determine real effective time windows that should be taken into computation in order to provide a better prediction. In summary, our analysis indicates that a stationary Poisson process for the background rate of spontaneous events is a rather unlikely assumption in many social systems. The ETAS model and self-exciting point process can be considered a more reliable underlying process. 33

ACCEPTED MANUSCRIPT 6. Conclusion and directions for future research This paper adapts a stochastic point process framework for analysis of the dynamic

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microstructure of online social networks (OSNs). Especially, we investigate the possibility of

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using crowdsourcing on OSNs as a marketing mechanism to enhance brand awareness and

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popularity. Such crowdsourcing activities help brands spur innovation and drive brand awareness across OSNs platforms. We describe such dynamics in terms of the stochastic occurrence times

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and number of followers. One-dimensional and two-dimensional self-exciting point process

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models are adjusted to simulate popularity growth patterns of brand post contents on Twitter. Our findings indicate that point models are able to describe the cascade of influencers on the

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online social networks. Our results suggest that incorporating the number of followers into

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predictive models as another dimension of input provides a better understanding of the content popularity. Our future work focuses on applying a full package of multivariate point processes to

7. References

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different streams of events within OSNs.

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[56] Rybski, D., S. V. Buldyrev, et al. (2012). "Communication activity in a social network: relation between long-term correlations and inter-event clustering." Sci. Rep. 2.

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[57] SAS Harvard Business Review Analytic Services. (2010). “The New Conversation: TakingSocial Media from Talk to Action”. Harvard Business School Publishing.

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[58] Sashi, C. M. (2012). "Customer engagement, buyer-seller relationships, and social media." Management Decision 50(2): 253-272.

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[59] Szabo, G. and B. A. Huberman (2010). "Predicting the popularity of online content." Commun. ACM 53(8): 80-88. [60] Veen, A. and F. P. Schoenberg (2008). "Estimation of Space–Time Branching Process Models in Seismology Using an EM–Type Algorithm." Journal of the American Statistical Association 103(482): 614-624. [61] Wang, T., M. Bebbington, et al. (2012). "Markov-modulated Hawkes process with stepwise decay." Annals of the Institute of Statistical Mathematics 64(3): 521-544. [62] Willinger, W., R. Rejaie, et al. (2010). "Research on online social networks: time to face the real challenges." SIGMETRICS Perform. Eval. Rev. 37(3): 49-54.

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ACCEPTED MANUSCRIPT Amir Hassan Zadeh is a PhD student in the Management Science and Information Systems Department within the Spears School of Business at

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Oklahoma State University. He received his master’s in Industrial and Systems Engineering from Amirkabir University of Technology, Tehran, Iran. He has been

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published in the Journal of Production Planning and Control, Annals of Information Systems, Advances

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in Intelligent and Soft Computing, and also conference proceedings of IEEE, and DSI. His current

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media analytics for marketing and healthcare.

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research interests include decision support systems, big data analytics for complex networks, and social

Ramesh Sharda is the interim Vice Dean of the Watson Graduate School of Management, Watson/ConocoPhillips Chair and a Regents Professor of

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Management Science and Information Systems in the Spears School of Business at Oklahoma State University. He also serves as the Executive

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Director of the PhD in Business for Executives Program. He has coauthored two textbooks (Business Intelligence and Analytics: Systems for Decision

Support, 10th edition, Prentice Hall and Business Intelligence: A Managerial Perspective on Analytics, 3rd Edition, Prentice Hall). His research has been published in major journals in management science and information systems including Management Science, Operations Research, Information Systems Research, Decision Support Systems, Interfaces, INFORMS Journal on Computing, and many others. He is a member of the editorial boards of journals such as the Decision Support Systems and Information Systems Frontiers. He is currently serving as the Executive Director of Teradata University Network and received the 2013 INFORMS HG Computing Society Lifetime Service Award.

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