Combining List Experiments and the Network Scale Up Method

Gustavo Díaz
Northwestern University

Verónica Pérez Bentancur
Universidad de la República

Ines Fynn
Universidad Católica del Uruguay

Lucía Tiscornia
University College Dublin

 

Paper and slides: gustavodiaz.org/talk

List experiment

Now I am going to read you things that make people angry or upset

List experiment

After I read them all, tell me HOW MANY of them upset you

List experiment

I don’t want to know which ones, just tell me HOW MANY

Control group

  1. The federal government increasing tax on gasoline
  2. Professional athletes getting million dollar contracts
  3. Large corporations polluting the environment

List experiment

I don’t want to know which ones, just tell me HOW MANY

Treatment group

  1. The federal government increasing tax on gasoline
  2. Professional athletes getting million dollar contracts
  3. Large corporations polluting the environment

List experiment

I don’t want to know which ones, just tell me HOW MANY

Treatment group

  1. The federal government increasing tax on gasoline
  2. Professional athletes getting million dollar contracts
  3. Large corporations polluting the environment
  4. A black family moving next door

Reduces bias but increase variance

Reduces bias but increase variance

Reduces bias but increase variance

Reduces bias but increase variance

Solutions

Ways to reduce variance in list experiment estimates:

Solutions

Ways to reduce variance in list experiment estimates:

Combined estimator

  • Logic: You don’t need a list experiment for those who admit to the sensitive item in the direct question

\[ \hat{\mu} = \overline{Y} + (1 - \overline{Y}) (\overline{V}_{1,0} - \overline{V}_{0,0}) \]

  • \(\overline{Y}\): Proportion confess in direct question

  • \((\overline{V}_{1,0} - \overline{V}_{0,0})\): List experiment estimate among those not confessing

Combined estimator

  • Logic: You don’t need a list experiment for those who admit to the sensitive item in the direct question

\[ \hat{\mu} = \underbrace{\overline{Y} + (1 - \overline{Y}) (\overline{V}_{1,0} - \overline{V}_{0,0})}_{\text{Weighted average of prevalence rates}} \]

Problem

  • Can’t always include direct questions

  • Need an indirect questioning technique that lets us infer individual responses to sensitive item

  • But most rely on anonymity

  • Can’t combine without extra modeling assumptions or altered designs

Network Scale-Up Method (NSUM)

How many people do you know,

Network Scale-Up Method (NSUM)

How many people do you know, who also know you,

Network Scale-Up Method (NSUM)

How many people do you know, who also know you, with whom you have interacted in the last year

Network Scale-Up Method (NSUM)

How many people do you know, who also know you, with whom you have interacted in the last year in person, by phone, or any other channel.

  • Named Michael
  • Named Christina
  • Gave birth in the past 12 months
  • Commercial pilots
  • Have tested positive for HIV

Why NSUM?

  • Can infer individual responses to sensitive item

Assumption: Symmetrical exposure

If someone knows an unusually large number of people with the sensitive item, then they are likely to hold the sensitive item too.

  • If true, can use NSUM responses instead of direct questions
  • Goal: Find individuals with large sensitive network relative to personal network

Hierarchical model

\[ \begin{align*} y_{ik} \sim \text{negative-binomial}( & \text{mean} = e^{\alpha_i + \beta_k},\\ & \text{overdispersion} = \omega_k) \end{align*} \]

  • \(y_{ik}\): Degree of group \(k\) for person \(i\)

  • \(\alpha_i\): Expected degree of person \(i\) (logged)

  • \(\beta_k\): Expected degrees of group \(k\) (logged)

  • \(\omega_k\): Controls variance in propensity to know someone from group \(k\)

Hierarchical model

  • Fit via MLE to estimate parameters

  • Focus on standardized residuals:

\[ r_{ik} = \sqrt{y_{ik}} - \sqrt{e \alpha_i + \beta_k} \]

  • High residual: \(i\) knows a disproportionately high number of people in sensitive group \(k\) (given personal network and overall group size)

Application

Survey

  • Online sample in Montevideo, Uruguay (N = 2688)

  • Four criminal governance tools

Negative

  • Threaten neighbors
  • Evict neighbors

Positive

  • Make donations to neighbors
  • Offer jobs to neighbors

Survey

  • Online sample in Montevideo, Uruguay (N = 2688)

  • Four criminal governance tools

Negative

  • Threaten neighbors
  • Evict neighbors

Positive

  • Make donations to neighbors
  • Offer jobs to neighbors

Direct question

During the last six months, in your neighborhood, have you seen gangs…

  • Threaten neighbors
  • Evict neighbors
  • Make donations to neighbors
  • Offering jobs neighbors
  • Blackmail neighbors
  • Blackmail businesses
  • Pay a neighbor’s phone or electricity bills

List experiments

Things people have experienced in the last six months:

List A List B
Saw people doing sports Saw people playing soccer
Visited friends Chatted with friends
Activities by feminist groups Activities by LGBTQ groups
Went to church Went to charity events

List experiments

Things people have experienced in the last six months:

List A List B
Saw people doing sports Saw people playing soccer
Visited friends Chatted with friends
Activities by feminist groups Activities by LGBTQ groups
Went to church Went to charity events
Did not drink mate Gangs threatening neighbors

List experiments

Things people have experienced in the last six months:

List A List B
Saw people doing sports Saw people playing soccer
Visited friends Chatted with friends
Activities by feminist groups Activities by LGBTQ groups
Went to church Went to charity events
Gangs threatening neighbors Did not drink mate

NSUM

How many people do you know, who also know you, with whom you have interacted in the last year in person, by phone, or any other channel

  • 15 reference groups + sensitive item (range 0-10+)
  • Recode

\[ Y_i^{\prime} = \begin{cases} 1, &\text{ if } r_{ik} > Mean(r_{ik}) + SD(r_{ik})\\ 0, &\text{ otherwise} \end{cases} \]

Combined estimates

Combined estimates

More generally

  • NSUM informative if direct question informative

  • NSUM can be informative if direct question uninformative

  • Variance reduction equal or higher with NSUM

Summary

  • Direct questions can help improve statistical precision list experiments

  • Concern using direct questions to begin with

  • Can use NSUM in the same way

  • Only in applications where symmetrical exposure is plausible

  • Logic applies to other strategies to improve precision, other indirect questioning techniques

NSUM groups

From Las Piedras
Male 25-29
Police officers
University students
Had a kid last year
Passed away last year
Married last year
Female 45-49

Public employees
Welfare card holders
Registered with party
With kids in public school
Did not vote in last election
Currently in jail
Recently unemployed [Sensitive item]