Diffusion

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Diffusion Interventions

• Diffusion of innovations
• Behavior change
• Behavior change is short term whereas diffusion
  looks at the long view of how new behaviors spread

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Diffusion of Innovations

• New ideas and practices originate enter
  communities from some external source. These
  external sources can be mass media, labor
  exchanges, cosmopolitan contact, technical shifts
  and so on. Adoption of the new idea or practice
  then flows through interpersonal contact
  networks.

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Diffusion of Innovations

• Rogers wrote consecutive texts on this topic
• 1962 1st Edition
• 1971 2nd Edition (with Shoemaker)
• 1983 3rd Edition
• 1995 4th Edition
• 2003 5th Edition
• Synthesized, elaborated, codified, explained
  diffusion of innovations

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ELEMENTS OF THE DIFFUSION OF INNOVATIONS

• 1) The rate of diffusion is influenced by the
  perceived characteristics of the innovation such
  as relative advantage, compatibility,
  observability, trialability and complexity,
  radicalness, and cost.
• 2) Diffusion occurs over time such that the rate
  of adoption often yields a cumulative adoption
  S-shaped pattern.
• 3) Individuals can be classified as early or late
  adopters.
• 4) Individuals pass through stages during the
  adoption process typically classified as (1)
  knowledge, (2) persuasion, (3) decision, (4)
  implementation or trial, and (5) confirmation.

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Characteristics of an Innovation

• Relative advantage
• Compatibility
• Complexity
• Trialability
• Observability
• Cost
• Radicalness

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4 Elements according to Rogers

• Innovation An idea or practice perceived as new
• Perceived attributes relative advantage,
  compatibility, complexity, trialability,
  observability
• Communication channels
• Homophily vs. heterophily
• Time at the individual macro levels
• Social system

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Hypothetical Cumulative and Incidence Adoption
Curves for DiffusionHomogenous Mixing
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Behavior Change Stages in Four Models
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Diffusion

• Takes time
• Is difficult even when something is seemingly
  worthwhile
• Is guided and influenced by many factors, some
  obvious, some not so obvious
• Provides a macro micro perspective on behavior
  change

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Diffusion

• Process by which an innovation is communicated
  through certain channels over time among the
  members of a social system
• Communication is special in that it attempts to
  reduce uncertainty about the innovation
• Diffusion vs. Dissemination vs. Technology
  Transfer

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Hypothetical Diffusion When Adopters Persuade
Non-adopters at a Rate of One Percent(Homogenous
Mixing)
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Hypothetical Cumulative and Incidence Adoption
Curves for DiffusionHomogenous Mixing
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The Diffusion of Knowledge, Attitudes and
Practices (KAP)
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Example of Diffusion
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The Two-Step Flow Hypothesis of Mass Media
Influence
Friends
Family
Mass Media
Opinion Leaders
Coworkers
Others
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Mathematical Models Used to Derive Diffusion Rate
Parameters
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History

• Early pre-paradigmatic research by
  Anthropologists, Economists, Sociologists
  interested in cultural change (1903-1940)
• In 1943, Ryan Gross published a study farmers
  adoption of hybrid seed creating the paradigm
• By 1962 Rogers published Diffusion of
  Innovations which solidified the paradigm
• Coleman, Katz Menzels (1966) study of Medical
  Innovation solidified the theory on diffusion
  networks

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Ryan Gross

• Studied the diffusion of hybrid seed corn,
  retrospectively 1928-1941
• 2 communities in Iowa, 255 of 257 farmers adopted
• Contrasted economic and social variables
• Established diffusion paradigm

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Number of Diffusion Publications Over Time
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Diffusion Publications and Research
InnovationsRatio of Innovations to Publications
Remained Constant
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Reasons for Decline

• It was perceived as fallow intellectually (15 of
  18 variables used by Ryan Gross)
• Political climate was against cultural
  imperialism. It was politically incorrect
  associated with technological hegemony
• Environment suffered from the spread of
  technological innovations (pesticides,
  herbicides)
• Social scientists not trained in matrix methods
  to investigate network reasons for diffusion

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Research on Innovation Diffusion in Many Fields

• In Demography and fertility transition studies
• In Sociology by re-newed attention on diffusion
  networks
• In Communication as a tool to evaluate
  communication campaigns
• In Organizations as a means to understand and
  plan change

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Diffusion Networks

• A specific branch and approach to diffusion study
• Some might argue that diffusion is only diffusion
  when one looks at networks and that other
  diffusion studies are behavior or social change
• Diffusion networks has been historically the
  branch of networks focused on behavior change

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Lineage of Diffusion Network Models From Valente
(2006)

• Type (1) Social integration
• Social Factors are important - Ryan Gross 1943
• Social Integration - Coleman Katz Menzel 1966
• Opinion Leaders - Rogers 1964
• Norms - Becker 1970
• Rogers Kincaid 1981
• Type (2) Bridges Structure
• Weak Ties - Granovetter 1973
• Burt 1987 1992
• Watts (2002)

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Lineage (cont.)

• Type (3) Critical levels
• Schelling 1972
• Thresholds - Granovetter 1978
• Critical Mass - Marwell, Oliver et al. 1988
  Markus 1988
• Network Thresholds - Valente 1995/1996
• Type (4) Dynamics
• Marsden Polodny 1990
• Spatial Temporal Heterogeneity Strang Tuma,
  1995
• Valente 1995 2005

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(1) Social Integration/ Opinion Leaders

• Integration can be measured many ways
• Behavior is a function of being embedded within
  a/the community
• Usually operationalized as receiving ties

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Coleman Katz Menzel 1966

• Actually 1957 was first paper
• Data collected 1955-1956
• Interviewed all MDs in 4 Illinois cities Peoria,
  Bloomington, Galesburg, Quincy
• Sampled prescription records first 3 days of each
  month to measure Time of Tetracycline Adoption

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Diffusion of Tetracycline for Marginal versus
Integrated Doctors
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Diffusion Network Simulation w/ 3 Initial
Adopter Conditions (Valente Davis, 1999)
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Diffusion Network Game

• Distribute red, white blue chips
• Give
• Red to OLs
• Blue to Randoms and
• White
• Allow them to give chips to those people who
  nominated them

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Diffusion Network Game

• Distribute Red, White Blue Chips to different
  initial starts
• Red awareness
• White attitude
• Blue behavior
• Can only receive a white chip if have red one
  only receive a blue one if have red white

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(2) Structural

• Structural models require data from the entire
  network
• Can use sociometric data to identify bridges
• Can also use to measure structural equivalence
  and constraint

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Granovetter, Strength of Weak Ties (1973), AJS

• Seminal article
• Cited thousands of times
• Granovetter was Whites student
• First faculty appointment at JHU
• Left JHU for Stonybrook, now at Stanford

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Granovetter, Strength of Weak Ties (cont.)

• Cognitive balance inclines friends of friends to
  know friends - transitivity. Granovetter shows
  Figure 1 which is the forbidden triad, i.e., this
  type of network configuration rarely occurs.

C
The Forbidden Triad
A
B
C
If A B are linked and A C are linked then
it implies that C B are linked
A
B
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SWT Bridges created shorter paths

• Bridges - individuals who link otherwise
  disconnected sub-groups. Individuals who act as
  bridges have weak ties. So a bridge is composed
  of weak ties, but not all weak ties are bridges.

I
H
G
D
J
F
C
A
B
K
E
L
Weak Tie
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(3) Critical Levels

• Tipping points
• Macro vs. micro tipping points, critical mass vs.
  thresholds
• Most CM/threshold models were not explicitly
  social network explanations

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(4) Dynamics

• Can model how ideas/behaviors spread through a
  network
• Simplest model assumes static (fixed) network and
  the idea spreads on that network
• Start with initial adopters and let the behavior
  percolate through the network

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Network Exposure
Non User
User
Exposure33
Exposure66
Exposure100
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Exposure Equation
where E is the exposure matrix, S is the social
network, A is the adoption matrix, n is the
number of respondents, n indicates the sum of
each row, and t is the time period. The exposure
equation is a very general model in which the
social network can be direct relations,
positional relations, narrowly focused, or
broadly focused.
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Computing Network Weighted Scores Such as Network
Exposure
Nx1 Vector of Row Totals
Nx1 Vector of Scores
Nx1 Vector of Network Weighted Scores
1 2 3 4 ....N
1 2 3 4 ..N
N x N Adjacency Matrix (or weight matrix)
X



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Computing Network Weighted Scores Such as Network
Exposure
Nx1 Vector of Row Totals
Nx1 Vector of Scores
Nx1 Vector of Network Weighted Scores
1 2 3 4 ....N
1 2 3 4 ..N
0 1 0 1 0 . 1 0 1 0 0 . 0 1 0 1 1 . 1 0 0 0
1 . 1 0 0 1 0 . . .
1 0 1 1 0 . .
2 2 3 2 2 . .
.5 1.0 .33 .5 1.0 . .
X



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NxT Matrix of Exposure Scores
1 2 3 4 ...T
1 2 3 4 ..N
0.00 0.25 0.50 0.50 ... 0.00 0.00 0.00 0.00
. 0.00 0.00 0.00 0.00 . 0.25 0.25 0.25 0.25
. 0.33 0.33 0.66 1.00 . . .
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4. Personal network exposure

• Personal network exposure is the degree an
  individual is exposed to an innovation through
  his/her personal network.
• Network exposure provides
• 1. awareness information
• 2. influence/persuasion
• 3. detailed information on how to get the
  innovation, possible problems, updates, refills,
  enhancements, novel uses
• 4. something to talk about

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Network Exposure (cont.)

• 5. social support needed to face opposition
• 6. reinforcement and a sense of belonging
• 7. relay experiences
• Exposure computed on direct ties and on ties of
  ties by using the geodesic and weighing the ties
  by its inverse.
• Every network has a different maximum geodesic
  measure so we need to approximate the influence
  of any one point on any other point. Luckily the
  flow matrix has been created which does precisely
  that.

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Three Studies with Data on Time-of-adoption
Social Networks
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Datasets

• Provide static view of network
• 1 based on observational data on adoption (but it
  is sampled)
• 2 based on recall- though recall is probably
  pretty good
• They are varied and the network data are pretty
  good

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Two of these Datasets Have Received the Most
Attention

• Medical innovation by Coleman, Katz Menzel
  (1966)
• Burt, 1987 Marsden Podolny 1990 Strang and
  Tuma, 1993 Valente, 1995 1996 Van den Bulte
  Lilien, 2001
• Korean family planning by Rogers Kincaid
  (1981)
• Dozier, 1977 Montgomery, 1994 Valente,
  1995 1996.

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Regression on Time to Adoption by Network
Exposure External Contacts
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Maximum Likelihood Logistic Regression on
Adoption by Time, Ties Sent/Received Network
Exposure.
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Exposure Adoption?

• Represents a challenge to the diffusion and
  other behavior change models
• Could be a function of location on the diffusion
  curve more likely after critical mass
• Very disappointing from a replication perspective
• What model can explain this?

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Network Threshold
Non User
User
PN Threshold33
PN Threshold66
PN Threshold100
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Graph of KFP Communication Network Rogers
Kincaid, 1981
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Graph of Time of Adoption by Network Threshold
for One Korean Family Planning Community
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Threshold
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Time
1973
1963
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Table Adjusted Odds Ratios for the Likelihood of
Low and High-threshold Adoption.

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Network Structure

• Network structure is partly defined by
  centrality.
• Central members, popular students for example,
  both influence and are influenced by group norms
• Central members can also contribute
  disproportionately to peer influence at micro
  level

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Agent Based Models

• Advent of computing has enabled scientists to
  generate hypothetical scenarios and model how
  people interact
• Fundamental issue is
• Do assumptions match reality
• Are the processes reasonable

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First Contact Diffusion (Rumor)/Random Seeds
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Rate of Diffusion

• Network Structure
• Real Rnd Cent Clustered
• Seeds Leaders 0.16 0.42 0.41 0.27
• Random 0.18 0.43 0.41 0.27
• Between 0.20 0.45 0.47 0.27
• Marginals 0.20 0.44 0.45 0.27

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Simulated Network Structural Properties