I am new to datamethods forum. I apologize if my post here is not appropriate. Please let me know if there are sets of rules which I should follow (other than what is stated on FAQs).
I am currently working with count data with overdispersion. A count data outcome (Length of Hospital Stay) and sets of explanatory variables (both continuous and categorical). I am trying to interpret the post estimate adjusted marginal effect (Average adjusted marginal/partial effect, AME) after a negative binomial regression.
I understand the AME for a binary variable X is the incremental effect of 1.X compared to 0.X (reference). However, I am not sure if the AME (average marginal or partial effects) can be compared across covariates in a single model. I had read articles such as Norton et al. and Williams, but was not able to find explanation. It might also be most likely that I have not fully understood the concept of marginal effect.
For illustrative purpose, I present a fictitious case.
For example, let’s say, for an overdispersed count outcome variable (e.g., count of LOS) and 4 independent variables (age, race[black/ white], gender [man/woman], presence of comorbidity [0 , 1 , 2+]), I conduct negative binomial regression using Stata (simple analysis)
nbreg LOS age i.race i.gender i.comorbidity, irr
margins, dydx(race gender)
lets say the AME for race (white vs black) is 4.1 days with 95%CI (3.8-4.3) and the AME for gender (woman vs man) is 6 days with 95% CI(5.8-6.1).
Can I state that the AME of gender on LOS is greater than that of race?
Thank you for your kind advice.