I am beginning a project that will employ regression/covariate adjustment to estimate the average effect of treatment on the treated (ATT) and I realize that I have two questions concerning how one estimates the ATT in such a setting and how one interprets the regression output when using GLMs.
First, I am slightly confused on the specification of a desired treatment effect under a regression adjustment framework. For example, in alternative strategies, such as matching or weighting, syntax for executing these methods typically supports an explicit argument where one specifies the desired treatment effect:
effect = ate,
qoi = att, something along these lines. However, in a standard regression formula in R
y ~ x1 + x2 + ..., data = data I do not know how to effectively specify the argument for the treatment effect that I want to estimate. By default, does regression adjustment estimate the ATE? If so, how does one modify this?
Second, after reading papers by Mood 2010, Hanmer and Kalkan 2012, and Norton and Dowd 2018, it is apparent to me that, when modeling non-continuous outcomes, regression coefficients, odds ratios, IRRs, hazard ratios, etc. may prove problematic in interpretation. One solution is to estimate average marginal effects (AMEs). This leads me to my second question. Suppose that I estimate the ATT for a treatment on a count outcome. I then estimate the AME. Can I effectively interpret this AME as the ATT, or are they fundamentally different quantities of interest?