Negative binomial regression and substative interpretation of continuous variables

[Faradj Koliev]

Hi everyone,

A quick question: I run negative binomial regression models with binary and continuous variables in it. Ex:

nbreg Y X X1 X2 X3..etc

For continuous variables, I would like calculate how a one standard deviation in X from the mean is associated with a % increase in the frequency of Y.

Any idea how I can calculate this in Stata? Is it the margins command?


Thanks!



UPDATE: As I understand it, I need to standardize the variable to a mean of zero and a standard deviation of 1. This is easily done: egen X_std = std(X). If this is correct, I'll need this standardized version of the variable. But then again, I do I convert the results to percent increases/decreases?

[Matt Warkentin]

Hi Faradj,

As you mention, if you standardize the X variable to be a per SD change in X, then your estimated coefficient (log relative risk) provides you with the information you need. The exp(logRR) will give you the relative risk which can indicate the percent increase or decrease in risk for a 1-SD change in X. For example, if your estimated RR was 2.0, then there is a 100% increase in the outcome for a 1-SD increase in X (100% increase because a RR of 1.0 indicates equal risk for a change in X, and so you subtract off the null effect and you can multiply by 100 to get the percent change in Y). Hope this helps.

Centering to zero won't affect the magnitude of the coefficient, but will change the value of the intercept (constant). Dividing the raw variable by the SD will change the magnitude of the coefficient (so long as SD != 1).

[Faradj Koliev]

Dear Matt: many thanks for this. It was very useful.

[Phil Bromiley]

You can also do this with the margins command producing predicted values for specific values of x. I'm not sure if it applies to nbreg, but in some non-linear models, the effect of a variable changes with the values of the other variables even if there is no interaction term.