Predicting Social Influence based on Dynamic Network Structures · 2015. 4. 3. · uence e ect can be a double-edged sword. Promoting the Samsung Note II to increase the adoption

Predicting Social Influence based on Dynamic NetworkStructures

Mantian Hu Chih-Sheng Hsieh Jianmin Jia

Department of Marketing Department of Economics Department of Marketing

Chinese University of Hong Kong

March 13, 2015

M. T. Hu, C. S. Hsieh and J. M. Jia (CUHK) Network Structure and Social Influence March 13, 2015 1 / 16

Network Structure and New Product Diffusion

Figure: Two Networks of the Same Size but Different Structure


Diffusion within the ”String Ball”

Figure: network size = 330, final adopters = 28


Diffusion within the ”Flight Route Map”

Figure: network size = 329, final adopters = 13


Network Structure, Individual Interaction and Social Influence

Network Structure and Human Behaviors

Most human behaviors involve interactions with other people . The interactions

form all kinds of networks.

On the other hand, linked individuals interact with other linked individuals, so the

outcome ultimately depend on the entire network.

Therefore, interactions are shaped by the structure of networks.

Social Influence

Social influence expresses the conformity motive of behaving similar to peers if

there are enough peers doing the same (Young 2009).

Now the existence of social influence has been accepted.(Iyengar et al 2014)

In this paper, we show characteristics of network structure can help with predictions.


Research Framework

Network Identification

Two Layer Snowball Sampling

Identification of Social Influence on Cellphone Adoptions

The Stochastic Actor-Based Dynamic Network Model

Identify Relationships of Network Structure Measures and Social Influence Effect

Meta Analysis

Samsung Phones

Samsung High-end Phones

Samsung Note II

Seeding Strategy Simulation

Compare individual based seeding strategy and network based seeding


Social Influence Identification -

It is hard to distinguish social influence and homophily (Manski 1993, Bramoulle

et al 2009, Hsieh and Lee 2013, Shalizi and Thomas 2011) .

Aral et al. (2009) proposed an approach using dynamic network information and

propensity matching. But it doesn’t fit our purpose.

We propose to use the Stochastic Actor-Oriented Model for Network and Behavior

Dynamics (Snijders 1996, 2001, 2007).

The model estimates the co-evolution of network formation and individual

behaviors using longitudinal network information.


Network Structure Characteristics -

Network size

Network density

Network structure entropy

Std Dev of edge numbers across time

Clustering coefficient

Minimum eigenvalue of adjacency matrix

Epidemic threshold and Assortativity

Ratio of inward and outward network edges

Initial adopter status


Main Findings

Social influence -

Our findings show that 6.0% of approximately 1,000 individual social networks

exhibit social influence for Samsung Note II adoption, 12.3% for Samsung high-end

phone adoption, and 10.2% for Samsung brand adoption.

The effect implies that if all the friends of an individual who has not yet adopted

the cellphone product have already adopted the said product, then social influence

increases the chances of that individual adopting the product by 7.38 times.

Network structure -

Diversity of connection (network structural entropy) and time variation of edge

numbers are the two most important network measures related to the social

influence effect.

Simulations -

Simulation reveals that the social influence effect can be a double-edged sword.

Promoting the Samsung Note II to increase the adoption of it is likely to be difficult

with the existence of social influence, but individuals are more likely to adopt

Samsung branded phones, particularly high-tier ones due to the promotion.


Main Findings

Social influence -







Network structure -



influence effect.

Simulations -






Main Findings

Social influence -







Network structure -



influence effect.

Simulations -






Main Findings

Social influence -







Network structure -



influence effect.

Simulations -






Main Findings

Social influence -







Network structure -



influence effect.

Simulations -






Main Findings

Social influence -







Network structure -



influence effect.

Simulations -






Main Findings

Social influence -







Network structure -



influence effect.

Simulations -






Main Findings

Social influence -







Network structure -



influence effect.

Simulations -






Data Collection

The data for this study were obtained from a major Chinese mobile carrier, which

gave us access to its entire customer base of 1.36 million users in two

medium-sized cities in western China.

The time period we choose is between November 2012 and May 2013, which

corresponds to the release of Samsung Note II.

Through two-layer snowball sampling, we obtain a sample of 26,000 customers

from 1,083 social networks with a mean network size of 110.

We construct seven time-varying monthly network matrices based on the monthly

calling and SMS record of each individual within the network.

In each matrix, an edge is placed between two individuals when they have called or

texted each other within the same month. Thus, network edges are undirected,

and the resulting matrix is symmetric.

We measure network statistics based on the accumulated network, which includes

all edges across sampling periods.


Data Collection
















Data Collection
















Data Collection
















Data Collection
















Data Collection
















8 152

377 564

760 936

1083

1486 1630

1919 2135

2351 2615

3840

5011 5211

5563 5796

6067

6432 6678

Nov '12 Dec '12 Jan '13 Feb '13 Mar '13 Apr '13 May '13

Samsung Note II Samsung High-end Samsung

Figure: The monthly number of adopters for each level


The Stochastic Actor-Oriented Model for Network and Behavior Dynamics -Assumptions

It is a continuous time model.

We observe network (g) and several behavioral outcomes (y1, y2, · · · , yH)at two or

more discrete points in time (say t1 < t2 < · · · < tM). We treat them as snapshots

from a continuous process.

Between any two discrete time points, tm and tm+1, there are “micro” steps at

stochastically determined moments that individuals have chances to change their

network ties or behaviors.

Changes of state variables, z = (g , y1, · · · , yH), are assumed to follow a continuous

Markov process.

The changes of network tie and behavior made by an individual are conditionally

independent of each other, given the current state of the process.

Moreover, one and only one individual can make decision at a time.


Results - Scatter Plots of Estimated Social Influence and Homophily

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−2 0 2 4 6 8

24

68

10

Estimate of coefficient

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NoteII

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−4 0 2 4 6

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−4 −2 0 2 4

24

68


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Brand

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Results - Meta Regression of Social Influence – Collection of Results fromSeparated Regressions

Samsung NoteII Samsung HighEnd Samsung Brand

significance magnitude significance magnitude significance magnitude

Clustering −0.175 0.222 2.171∗∗ 1.258∗∗ 3.994∗∗∗ 2.168∗∗∗coefficient (−0.23, 0.247) (0.28, 0.049) (3.25, 0.276) (3.79, 0.202) (5.29, 0.337) (7.37, 0.236)

Minimum 0.0212 −0.0074 0.0212 0.0054 −0.0132 −0.0031eigenvalue (1.01, 0.249)(−0.50, 0.049) (1.28, 0.261) (0.65, 0.187)(−0.66, 0.284)(−0.35, 0.184)

Epidemic −7.437∗∗ −5.872∗∗∗ −18.74∗∗∗ −6.488∗∗∗ −8.581∗∗∗ −5.546∗∗∗threshold (−3.22, 0.263)(−3.42, 0.094)(−5.08, 0.286)(−5.40, 0.254)(−4.57, 0.312)(−5.26, 0.239)

Assortativity 0.542 0.646 1.457∗∗∗ 0.860∗∗ 1.579∗∗∗ 1.258∗∗∗(1.12, 0.250) (1.24, 0.055) (3.81, 0.282) (2.92, 0.206) (4.12, 0.312) (4.63, 0.227)

Log in-out edge 0.0130 0.0453 0.0319 0.0772 0.0481 0.0299ratio (0.12, 0.243) (0.39, 0.049) (0.39, 0.258) (1.16, 0.190) (0.60, 0.285) (0.51, 0.189)

Degc. 13.04∗∗∗ 8.326∗ 13.24∗∗∗ 7.230∗∗∗ 10.29∗∗∗ 7.269∗∗∗diversity (3.78, 0.294) (2.50, 0.073) (4.66, 0.300) (3.70, 0.218) (3.95, 0.313) (4.10, 0.217)

Eigc. 5.117∗∗ 2.683∗ 3.149∗∗ 1.816∗∗ 2.055 0.562diversity (3.05, 0.275) (2.07, 0.059) (2.65, 0.270) (2.94, 0.196) (1.64, 0.288) (1.00, 0.184)

Initial adopters’ 0.0113+ 0.00478 0.0302∗∗∗ 0.00593 0.0251∗∗ 0.00941degc. (1.89, 0.257) (1.04, 0.053) (3.82, 0.282) (1.24, 0.190) (2.86, 0.297) (1.60, 0.189)

Initial adopters’ −0.417 −0.349 −0.727 −0.681+ −2.080∗∗ −1.556∗∗eigc. (−1.07, 0.250)(−0.96, 0.052)(−1.60, 0.263)(−1.92, 0.195)(−3.07, 0.299)(−3.17, 0.204)

Sd of edge 0.00213∗∗∗ 0.0023∗∗∗ 0.000475 0.0012∗∗∗ 0.000509 0.0012∗∗∗number (3.61, 0.286) (5.03, 0.105) (1.10, 0.260) (4.93, 0.213) (1.03, 0.285) (3.67, 0.197)

Observations 410 715 791


Simulation Results


Managerial Implications and Future Work

A new perspective on company targeting strategies - network based targeting.

Network structure information significantly complements individual demographic

and local position information.

The right networks must be selected based on a general network structure prior to

selecting the right seeds based on personal characteristics and network positions.

For future research, we will also examine a competitive scenario (e.g., Samsung

versus Apple) and investigate the relationship between their network structures and

adoption behaviors under competition.


Documents

Predicting Social Influence based on Dynamic Network Structures · 2015. 4. 3. · uence e ect can be a double-edged sword. Promoting the Samsung Note II to increase the adoption