# (How) Can I compare the relative importance of coefficients on different population groups in negative binomial regression?

I am trying to determine the relative importance of about 20 different environmental factors on people's behaviour. Behaviour is either exhibited (success) or not (failure). The dataset describing this behaviour is a national census and accordingly people within it are grouped by the area in which they live as well as their sex and age.

For each area, the environmental factors are the same regardless of sex or age (the humidity where I live is the same regardless of how old I am). What I am particularly interested in is examining how these factors affect my subgroups differently (if humidity affects the behaviour, are men more sensitive to it than women?).

Since this is count data with a lot of 'failures' I am using a negative binomial regression to examine how the environmental factors affect each group. I have 6 neg. bin. regression models - three for men (young, middle aged, old) and three for women.

I understand that within a model I can't (easily*) compare the relative importance of the coefficients resulting from a neg. bin. regression, but...

(Q1) if the IVs are always the same for each area and all models always use all of the same IVs, can I compare the relative size of the beta-coefficients between models - namely the relative effect of a coefficient on different populations?

(Q2) if not, is there a way I can compare effects between subgroups (M,F by age) without losing the potential for also comparing effects within each model (*for example by using St. Dev to describe the sensitivity of the model to a 1 S.D. change in the coefficient)?

(Q3) is this approach still valid if I add 5 more IVs that are related to each subgroup (e.g. if I had data on the percentage of each subgroup's population that fall within 1 of 5 possible social class indicators)?

Phew. Happy to expand if not clear. Many thanks in advance. Using SPSS.

• Welcome to CV. Nice question, well posed and thought out. – Mike Hunter Nov 12 '15 at 15:52