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1. The data in data(NWOGrants) are outcomes for scientific funding applications for the Netherlands Organization for Scientific Research (NWO) from 2010–2012 (see van der Lee and Ellemers doi:10.1073/pnas.1510159112). These data have a very similar structure to the UCBAdmit data discussed in Chapter 11.
I want you to consider a similar question: What are the total and indirect causal effects of gender on grant awards? Consider a mediation path (a pipe) through discipline. Draw the corresponding DAG and then use one or more binomial GLMs to answer the question.
What is your causal interpretation? If NWO’s goal is to equalize rates of funding between the genders, what type of intervention would be most effective?
2. Suppose that the NWO Grants sample has an unobserved confound that influences both choice of discipline and the probability of an award. One example of such a confound could be the career stage of each applicant. Suppose that in some disciplines, junior scholars apply for most of the grants. In other disciplines, scholars from all career stages compete. As a result, career stage influences discipline as well as the probability of being awarded a grant.
Addthese influencestoyourDAGfromProblem1. Whathappensnowwhenyou condition on discipline? Does it provide an un-confounded estimate of the direct path from gender to an award? Why or why not? Justify your answer with the back-door criterion. Hint: This is structurally a lot like the grandparents-parentschildren-neighborhoods example from a previous week.
If you have trouble thinking this though, try simulating fake data, assuming your DAG is true. Then analyze it using the model from Problem 1. What do you conclude? Is it possible for gender to have a real direct causal influence but for a regression conditioning on both gender and discipline to suggest zero influence?
3. The data in data(Primates301) were first introduced at the end of Chapter 7. In this problem, you will consider how brain size is associated with social learning. There are three parts.
First, model thenumber of observationsof social_learning for eachspecies as afunctionofthelogbrainsize. UseaPoissondistributionforthesocial_learning outcome variable. Interpret the resulting posterior.
Second, some species are studied much more than others. So the number of reported instances of social_learning could be a product of research effort. Use the research_effort variable, specifically its logarithm, as an additional predictor variable. Interpret the coefficient for log research_effort. Does this model disagree with the previous one?
Third, draw a DAG to represent how you think the variables social_learning, brain, and research_effort interact. Justify the DAG with the measured associations in the two models above (and any other models you used).
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