Problem

Say we want to understand how individual-level characteristics (e.g., how long ago the person migrated from the rural area to the urban area) influence the probability of consuming wild meat in the Brazilian Amazon region. Ideally, we would just survey people and they would honestly answer our questions regarding wild meat consumption. However, because consuming wild meat is illegal in this region, people might be reluctant to speak truthfully about this behavior.

As I mentioned before, there are several survey methods, collectively known as indirect questioning methods, that have been developed that enables us to understand the determinants of a sensitive behavior without requiring people to disclose if they themselves have such a behavior. As a result, it is expected that these survey methods will generate more reliable information. Here is a really nice review on these methods (Nuno and St. John 2015).

We will use a indirect questioning technique called “unrelated question design”. This is how this approach works. We randomly divide our participants into two sets:

1. Set one: for these participants, we directly ask about the consumption of a non-sensitive item (e.g., pizza). We will assume that they respond truthfully given that this is a non-sensitive item.

2. Set two: for these participants, we first ask them to roll a dice. Without having participants show the dice outcome to the interviewer, we tell them that:

• if they get 1-2, they should answer our question as though we were asking about the non-sensitive item (i.e., pizza).
• if they get 3-6, they should answer the question as though we were asking about the sensitive item (e.g., wild meat).

The question that we ask is “Do you consume this item in your house?”

Because we do not see the dice outcome from the second set of participants, we can’t tell if participants are answering about pizza or wild meat. As a result, they are not disclosing information about their individual behavior and are expected to answer truthfully. Nevertheless, statistical discrepancies between the patterns between the first and second set of participants should tell us something about consumption of wild meat.

Analysis steps

Say that our binary response variable for the i-th interviewee is \(y_i\). Furthermore, say that our covariate \(x_i\) is how long ago the person migrated from the rural area to the urban area. Assuming that \(x_i\) is the number of years since the person migrated to the urban area, please simulate this variable from a Poisson distribution with \(\lambda=4\).

Based on these settings, I would like you to:

1. Come up with a generative model for the first set of participants

2. Come up with a generative model for the second set of participants

3. Based on these generative models, simulate some fake data.

4. Create JAGS code to fit these models.

5. Does your JAGS model work when you run it on the fake data?

Comments?

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