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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.

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  • $\begingroup$ Welcome to CV. Nice question, well posed and thought out. $\endgroup$ – Mike Hunter Nov 12 '15 at 15:52
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Relative variable importance is an area that has seen a reasonable amount of study in the statistical literature. Solutions range from easily derived heuristics to rigorous and CPU-intensive multivariate solutions. On the easier side of this spectrum, "quick and dirty" metrics include ranking the absolute values of the t-statistics associated with the model parameters, the magnitude of that metric is an indicator of that variable's importance. Beta coefficients aren't appropriate since, unless the inputs have been standardized, they are expressing the change in Y for each unit change in X and, therefore, would not be comparable across predictors of differing scale and variance.

Ulrike Gromping has papers and an R module (RELAIMPO) that reviews many of the solutions that have been proposed over the years. She is probably the expert in this area right now.

http://prof.beuth-hochschule.de/groemping/relaimpo/

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  • $\begingroup$ thanks for the welcome and the direction towards more information. Will have a look and see if I can find the answer in some of her work - couldn't with an initial scan, but will post it back here if I do. $\endgroup$ – Nick G Nov 12 '15 at 21:21
  • $\begingroup$ Bear in mind that her work isn't focused on the NBD. I would be very surprised if you found any reference to variable importance specifically wrt the NBD model. You will need to generalize and plug it in as appropriate. $\endgroup$ – Mike Hunter Nov 12 '15 at 21:28

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