In a count model, how do I predict the change in y--for each observation--if one of my independent variables changes?

[Mark Samms]

I am using Stata 13.1.

I am using a count model--a negative binomial regression. My dependent variable is count data (number of individual customers at each company in the industry). Since at most companies there are no customers, and a small number of companies account for most customers, I need to use a count model like negative binomial. My independent variables include company characteristics (NOT individual customer characteristics) and sales and marketing efforts targeted at those companies. Relatively few of the companies in the industry currently supply any customers, and relatively few are currently targeted for any marketing efforts (around 200 out of 2,000 are marketed to and around 200 supply customers). I am trying to estimate how many more customers would likely materialize at each company (each observation) if sales and marketing efforts were increased at that company. I have a single numerical variable that represents sales/marketing efforts and can range from zero to 4. So if marketing went from zero to 4 or from 2 to 4, how many more customers would materialize at that company? My negative binomial regression converges and gives plausible coefficients. But I don't want marginal effects at the mean, or predicted values at current levels of sales and marketing. I want the difference in predicted values for each observation if only one of my independent variables changed and everything else remained constant. I think there should be a way to do this using margins and predictions, but I'm not sure how. Please advise. The goal is to advise the company on whether to increase sales and marketing efforts and how best to target them. Thank you very much!

[Clyde Schechter]

Well, if you have entered your sales/marketing efforts variable as a categorical variable with factor variable notation you can use

margins sales_marketing, pwcompare

[Richard Williams]

You want a prediction for each case, right? I think you could do something like

clonevar xx = x
nbreg y i.xx
predict p
replace xx = 1
predict p1
replace xx = 2
predict p2
gen diff21 = p2 - p1

[Phil Bromiley]

With a lot of zeros, you might consider a zero inflated negative binomial estimator.

I'm not sure whether this applies for negative binomial but with some non-linear estimators the effect of a change in x depends on the values of all the other variables. I'm sure Richard or Clyde can tell you whether this is an issue in negative binomial or not, but you could also test it by changing some values for other ivs (as Richard indicates) and doing the predictions.