DAGs with multiple levels (and a dichotomous outcome)

[Dan Schober]

I am currently working on a paper that involves a multilevel analysis examining the relationship between perceptions of neighborhood-based violence and leisure-time physical activity across Chicago neighborhoods following the COVID-19 stay-at-home order.

The paper has gone through a few rounds of peer reviews and one of the reviewers is advocating for something I am struggling to address – a Directed Acyclic Graph (DAG) that explores the mediating effects of a level-2 continuous variable called neighborhood safety rate (percentage of adults who report feeling safe within their neighborhood all or most of the time) on the (significant) effects of a level 1 independent variable (neighborhood violence – either “low” or “high”) on the level 1 dependent variable (physical activity in the past month – either “yes” or “no”).

I have not been able to find any clear guidance on whether mediation models/DAGs are possible with multilevel modeling that involves a dichotomous dependent variable (physical activity in the past month – either “yes” or “no”).

Can anyone provide guidance on how such an analysis may be carried out in Stata?

[Tiago Pereira]

Hi, Dan.

It seems your challenge is not related to Stata, but to the structure of the fitted models. Here are some starting points:

https://www.ncbi.nlm.nih.gov/pmc/art...ms-1768737.pdf

https://www.dagitty.net/dags.html

[Erik Ruzek]

I agree with Tiago's suggestions. I view DAGs as conceptual tools that force you to spell out a theory of how your treatment/exposure is related to your outcome. Note that a DAG does not assume your variables are continuous nor does it assume that the relations between variables are linear. You can get from a DAG to a potential regression, SEM, or other statistical model, but there is no way to do so without a strong understanding of DAGs. A tool such as daggity helps.

I have not seen a good illustration or example of a multilevel DAG. There is a nice paper by Kim & Steiner that attempts to draw the DAG implied by random effects and fixed effects models. But most DAG-related work I've seen does not address whether a DAG would be different for multilevel or hierarchical data.