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Examining the Dynamic Spread of Marijuana Use in a Social Network with Community Structure

Albert Burgess-Hull

University of Wisconsin – Madison

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May 22, 2017

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Marijuana

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  • The legal status of marijuana is rapidly changing

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  • As of November 2017:

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7 states and the District of Columbia (Washington D.C.) have legalized marijuana for adult (21 yrs)

recreational use

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A majority of the U.S. supports legalization

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    • Future policy shifts are likely to move towards

more legalization -

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Pew Research

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Marijuana Legalization and Public Health

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  • It is commonly believed that marijuana is less harmful than other substances (e.g., alcohol, smoking)

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    • Strong Evidence 🡪 Regular/Chronic Marijuana use is associated with a number of deleterious outcomes:
      • Abnormal Brain Development
      • Increased risk for mental health disorders (e.g., Schizophrenia, depression/anxiety)
      • Diminished Lifestyle Outcomes: school dropout; lower income; unemployment; lower life satisfaction
      • Progression to other illicit Drugs (Gateway Hypothesis)

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Marijuana Legalization and Public Health

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  • It is commonly believed that marijuana is less harmful than other substances (e.g., alcohol, smoking)

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    • Strong Evidence 🡪 Regular/Chronic Marijuana use is associated with a number of deleterious outcomes:
      • Abnormal Brain Development
      • Increased risk for mental health disorders (e.g., Schizophrenia, depression/anxiety)
      • Diminished Lifestyle Outcomes: school dropout; lower income; unemployment; lower life satisfaction
      • Progression to other illicit Drugs (Gateway Hypothesis)

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Especially true for adolescents = increased risk for negative outcomes

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Marijuana Legalization and Public Health

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  • It is commonly believed that marijuana is less harmful than other substances (e.g., alcohol, smoking)

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    • Strong Evidence 🡪 Regular/Chronic Marijuana use is associated with a number of deleterious outcomes:
      • Abnormal Brain Development
      • Increased risk for mental health disorders (e.g., Schizophrenia, depression/anxiety)
      • Diminished Lifestyle Outcomes: school dropout; lower income; unemployment; lower life satisfaction
      • Progression to other illicit Drugs (Gateway Hypothesis)

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Especially true for adolescents = increased risk for negative outcomes

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Marijuana use typically begins in adolescence

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Adolescence and Marijuana Use

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  • A number of factors have been linked to marijuana use:
    • Personality characteristics (e.g., sensation seeking)
    • Biological characteristics (e.g., abnormal brain development)
    • Family environment (e.g., parental monitoring)
    • Environmental context (e.g., drug availability)

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  • Strongest predictors of marijuana use = social context surrounding an individual (Ennett et al., 2006).

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  • Majority of marijuana use during adolescence typically occurs for social reasons (e.g., to be more social) and when others are also using marijuana.

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  • To fully understand the development of marijuana use during adolescence we must take into account the social network

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Social Influence (Social Contagion) and Substance Use

  • Substance use behaviors can spread from person to person within the network
    • Social Influence: The propensity of an individual’s behavior varies with the behavior of a reference group (Manski, 1993).
      • Social connections 🡪 behavior

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Social Contagion – Unanswered Questions

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  • Social Contagion and types of substance use
    • Marijuana use
      • Legal vs. Illegal drug use ---- different social risk

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Social Contagion – Unanswered Questions

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  • Social Contagion and types of behaviors
    • Marijuana use
      • Legal vs. Illegal drug use ---- different social risk

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  • Is Social Contagion stable across the network?
    • The structure of the network influences the

strength/reach of these processes

      • Community structure can affect the spread/diffusion of an epidemic (Stegehuis, van der Hofstad, & van Leeuwaarden, 2016).
        • Different social groups (communities) may have different social norms/values

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Network Communities (Cliques)

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Current Study - Aims

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    • Does community structure influence the strength/reach of contagious processes?

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      • Does the risk of becoming a marijuana user (or transitioning to a chronic marijuana use pattern) when directly connected to marijuana users vary by social community membership?
        • Are different types of marijuana users (e.g., chronic users, moderate users, or non-users) more prevalent in some communities than others?
        • What characteristics differentiate communities that convey higher risk for individuals compared to communities that convey lower risk?

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Methods

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Sample:

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      • PROSPER (PROmoting School-community-university Partnerships to Enhance Resilience)
        • 2 Cohorts of 6th grade students from 28 rural school districts in Iowa and Pennsylvania
          • 5 waves: 6th grade (spring and fall); 7th grade – 9th grade
          • N ≈ 12,000 students per wave
      • Rich dataset: substance use, personality, academic outcomes, mental health, genetic, family environment, …

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        • Network Data: students named up to 7 friends in their grade. Collected using an open name generator

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Methods

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Sample:

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      • 1 School (school 253):
          • 4 waves:
            • 6th grade (2 – waves: spring and fall)
            • 7th grade
            • 8th grade
          • Wave 1: N = 482; 47% Male; 90% White; 40% received free/reduced-price lunch

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Community Detection

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Methods (Community Detection):

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    • Dynamic Latent Space Mixture Models (Sewell & Chen, 2016)

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        • Longitudinal Extension of the Latent Space Mixture model (Handcock, Raftery, & Tantrum, 2007)

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Community Detection: Latent Space

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Methods (Community Detection):

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    • Latent Space Model:
      • Stochastic model of the social network that posits that each network member is located within a multidimensional Latent Social Space.

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    • Social Space = multidimensional unobserved characteristic/attribute space (e.g., unmeasured personality/genetic characteristics)

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Community Detection: Latent Space

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Methods (Community Detection):

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    • Latent Space Model:

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    • Social Space = multidimensional unobserved characteristic/attribute space

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      • The probability of a social-tie

between two individuals in

the network increases as the

distance between their latent

positions decreases

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Naturally accounts for transitivity and

reciprocity + homophily on observed covariates

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Community Detection: Latent Space

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Methods (Community Detection):

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  • Latent Space Model:

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  • Extended to identify latent communities (sub-groups) within the network (Handcock, Raftery, & Tantrum, 2007) :
    • To identify communities within the network, it is assumed

that the latent social-space coordinates are drawn from a

finite mixture of G multivariate Gaussian (normal)

distributions

      • Number of mixture components = # of communities within the network

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Community Detection: Latent Space

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Methods (Community Detection):

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  • Latent Space Model:

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  • Latent Space Mixture model extended to model longitudinal social network data (Sewell & Chen, 2016):
    • At each time point, each network member belongs to a specific community
      • Number of Communities fixed over time
        • Community membership is allowed to vary over time (similar to Latent Transition Analysis)
      • To cluster dynamic network data = Hidden Markov model
        • Dependence structure = Markov process: community assignment (and latent positions) only depends on community assignment (or latent positions) at previous time point

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Model Fitting Procedure

  • Dynamic Latent Space Mixture Models (DLSMM) with 1 – 6 latent communities were fit to the 4-waves of network data (4 x 4 x 4 adjacency matrix):
    • Models were fit with the ‘dnc’ package in R (2017).
      • MCMC sampling – package defaults were used for all model specification.
        • Increased # iterations and burn-in samples.
      • dnc: 3-dimensional latent space mixture model

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    • BIC (Schwarz, 1978) was used to select the optimal model

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Model Selection

Model Fit Statistics

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Model

BIC

2 – Community Model

64786.48

3 – Community Model

63087.17

4 – Community Model

61605.09

5 – Community Model

62407.62

6 – Community Model

63300.23

4 – Community model fit data the best

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Results: Visualization and Characteristics

Wave 1:

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Comm. 1

(yellow)

Comm. 2

(red)

Comm. 3

(green)

Comm. 4

(blue)

% of Sample

3%

4%

2%

91%

Boys (%)

0%

11%

0%

57%

Free Lunch (%)

38%

5%

100%

42%

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Results: Visualization and Characteristics

Wave 2 (6th grade):

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Comm. 1

(yellow)

Comm. 2

(red)

Comm. 3

(green)

Comm. 4

(blue)

% of Sample

9%

4%

4%

83%

Boys (%)

2%

0%

100%

61%

Free Lunch (%)

20%

14%

7%

42%

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Results: Visualization and Characteristics

Wave 3 (7th grade):

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Comm. 1

(yellow)

Comm. 2

(red)

Comm. 3

(green)

Comm. 4

(blue)

% of Sample

10%

12%

8%

70%

Boys (%)

20%

0%

100%

62%

Free Lunch (%)

47%

25%

10%

42%

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Results: Visualization and Characteristics

Wave 4 (8th grade):

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Comm. 1

(yellow)

Comm. 2

(red)

Comm. 3

(green)

Comm. 4

(blue)

% of Sample

10%

12%

9%

69%

Boys (%)

22%

2%

100%

61%

Free Lunch (%)

29%

20%

26%

48%

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Results: Marijuana Users

Wave 1 (6th grade):

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All marijuana users were in Community 4 (blue)

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Results: Marijuana Users

Wave 2 (6th grade):

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All marijuana users were in Community 4 (blue)

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Results: Marijuana Users

Wave 3 (7th grade):

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All marijuana users were in Community 4 (blue)

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Results: Marijuana Users

Wave 4 (8th grade):

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All marijuana users were in Community 4 (blue)

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Next Steps

  • Constrain Transition Probabilities
    • Stable latent groups

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  • Run DLSMM on multiple schools

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  • Missing Data

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  • Run Social Influence Models

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Results: Visualization and

Model Fit Statistics

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Quitting Smoking and the Social Network

Are there groups of smokers that are more successful at quitting than other smokers

Classified smokers into groups based on Social Network Characteristics

# of Smokers

# of Drinkers

# of Friends

Stress

Support

Contact

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