Introduction

Author

Thomas W. Valente

Published

December 5, 2024

Modified

December 5, 2024

Outline

  • Introduction to the network diffusion model and the motivation for netdiffuseR

  • The classic datasets (MI, BF & KFP)

  • Simulating diffusion with netdiffuseR

  • Data management features

  • The FCTC study – multiple networks both static and dynamic

Acknowledgements

NetDiffuseR was created with the support of grant R01 CA157577 from the National Cancer Institute/National Institutes of Health.  

It has benefited from input provided by participants of the Center for Applied Network Analysis at the University of Southern California

Motivation for NetdifusseR

Build a platform in which:

  • network exposure terms can be easily calculated and compared;

  • other diffusion network terms can be created (e.g., Moran’s I, infectiousness, susceptibility);

  • multiple dynamic and static networks can be analyzed simultaneously;

  • Graphical displays of diffusion processes can be made;

  • Statistical tests both conventional and new can be conducted;

  • Integrate network diffusion models with other analytic approaches;

  • and more.

Diffusion Networks

  • Unique set of studies that combine social network data with behavioral data

    • Typically have data from zero or low prevalence to saturation or high prevalence.

    • Multiple time points presents unique opportunities and challenges.

    • Data often do not include dis-adoption but the model accounts for it.

  • Network data may be static or dynamic.

  • Can have one or multiple networks

  • Model multiple behaviors simultaneously (e.g., tobacco & alcohol, awareness & adoption, VHS & Betamax)

  • Because we combine networks and behavior

    • Can have people in the network with no adoption data

    • People with adoption data but not in the network

Diffusion of Innovations

  • Explains how new ideas and practices spread within and between communities.

  • One of the oldest and richest social science theories.

  • Many factors influence diffusion

    • Spatial

    • Economic

    • Cultural

    • Developmental

    • Biological

    • Etc.

  • One of the most significant is social networks

Diffusion Networks

Structural Equivalence is Associated with Influence

Burt, R. (1987) Social contagion and innovation: Cohesion versus structural equivalence. American Journal of Sociology, 92, 1287-1335.

My article discovered network thresholds

Graph of Time of Adoption by Network Threshold for One Korean Family Planning Community

Indirect Exposures Matter

Alter Attributes May Affect Influence

Centrality Weighted Exposures

  • Node A: Threshold=3/5, Susceptibility=1, Susc_Normed=1/3
  • Node E: Impact 3/5, Infectiousness=1, Infect_Normed=1/3

Other Features: Extending Exposure

  • Thresholds

  • Indirect exposures

  • Attribute weighted

  • Network weighted (i.e., centrality)

  • Infectiousness

  • Susceptibility

  • Ego-alter table

  • Graphing!

1995 Reported on the 3 Classic Studies

  • 3 classic diffusion network datasets

  • MI: Medical Innovation

  • BF: Brazilian Farmers

  • KFP: Korean Family Planning

Diffusion Curves for Classic Studies

6 Diffusion Network Studies 3 Early Studies Lost

  • Rogers’ dissertation on 2-4D Weed Spray

  • Rogers’ work in Colombia

  • Becker’s study of public health officers in New York, Ohio, and Michigan (compared 2 innovations)

3 Classic Diffusion Network Studies

Medical Innovation Korean Family Planning Brazilian Farmers
Country USA Korean Brazil
# Respondents 125 Doctors 1,047 Women 692 Farmers
# Communities 4 25 11
Innovation Tetracycline Family Planning Hybrid Corn Seed
Time for Diffusion 18 Months 11 Years 20 Years
Year Data Collected 1955 1973 1966
Ave. Time to 50% 6 7 16
Highest Saturation 89% 83% 98%
Lowest Saturation 81% 44% 29%
Citation Coleman et al (1996) Rogers & Kincaid (1981) Rogers et al (1970)

Reconfigure to Event History Data

Medical Innovation (Coleman, Katz, & Menzel, 1966),

Data collected from physicians in the 4 cities in Illinois in 1955 (Galesburg, Bloomington, Quincy, & Peoria). 125 MDs interviewed about the medical practice characteristics:

  • 3 network questions: advice, discussion, and friends.

  • Adoption data collected by analyzing the prescription records of local pharmacies on the first 3 days of each month.

Brazilian Farmers (Rogers, Ascroft, & Röling, 1970)

As part of the USAID funded 3-country study, farmers in selected villages in India, Nigeria, and Brazil were interviewed about their farming practices, use of media, and other personal characteristics. Networks were measured by asking:

  • their three best friends, (2) the three most influential people in their community, (3) the three most influential people regarding various farm innovations, and (4) the best person to organize a cooperative project.

  • Adoption data were collected by asking farmers when they first planted hybrid seed corn

Korean Family Planning (Rogers & Kincaid, 1981)

Scholars at Seoul National University's School of Public Health collected data on the adoption of family planning methods among all married women of child-bearing age in 25 Korean villages in 1973 (N=1,047). Networks Network data were obtained by asking respondents to name five people from whom

  • they sought advice about (1) family planning, (2) general information,
  1. abortion, (4) health, (5) the purchase of consumer goods, and (6) children's education.
  • Adoption data were obtained by asking respondents to state the year they first used a modern family planning method.

Exposure results

Term MI KFP BF
Detail Agents 1.27
Science Orientation 0.60**
Journals Subs. 1.63*
# Sons 1.43**
Media Camp. Exp. 1.10**
Income 1.18**
Visits to City 1.00
Out Degree 0.96 1.05 0.98
In Degree 1.04 1.06** 1.02*
Exposure (Cohesion) 0.94 1.16 2.16**

Simulating diffusion

  • Seeds:
    • Type (central, bridging, marginal, random, etc.)
    • Size (e.g., 5%, 10%, 15%)
  • Network structure:
    • Random
    • Small world
    • Empirical
    • Scale-free (centralized)
    • Attribute-based (e.g., homophily)
  • Threshold distribution:
    • Uniform
    • Normal (varying variance)
    • Skewed
    • Beta
  • Mechanism:
    • Cohesion
    • Structural equivalence
    • Indirect ties
    • Attribute-based (e.g., homophilous more persuasive)
  • Adoption behavior:
    • No-disadoption
    • Disadoption
    • Conflicting behaviors (perhaps coded as -1,0, 1)
    • Incorporate uncertainty

Reading Data Challenges

  • Merging attribute and network data

    • Nominated but no attribute data

    • Attribute data no network data

  • Data file formats

    • Single flat file

    • 2 files: edgelist and attribute file (flat)

    • Cohort studies: 1 file separate waves of data

Formats

  • Survey Data (static & dynamic)

  • Edge-list and Attribute data

  • Panel Data

  • STATNET, Igraph, ….

Input Types: Single Flat File

  • Flat File with IDs, Nodelist, and Time of Adoption
  • Typically a retrospective study
  • Examples, Medical Innovation, Korean Family Planning; Brazilian Farmers

Input Types: Double Files

  • Files will have mostly matching IDs
  • One or both files may contain time information
  • Edgelist may also, potentially, contain values or spell information

Input Types: Classic Cohort/Longitudinal

  • IDs and Nodelist Network data
  • Behavior is typically binary (e.g., ever smoked) or potentially valued (e.g., # of cigarettes
  • Examples SNS