R help - Oct 2008 - back transforming output from negative binomial

Dear all,

I used the glm.nb with the default values from the MASS package to run a 
negative binomial regression. Here is a simple example:


    set.seed(123)
    y <- c( rep(0, 30), rpois(70, lambda=2) )
    smoke  <- factor( sample( c("NO", "YES"), 100,
replace=T ) )
    height <- c( rnorm(30, mean=100, sd=20), rnorm(70, mean=150, sd=20) )

    fit <- glm.nb( y ~ smoke + height )
    coef(summary(fit))
                   Estimate  Std. Error    z value     Pr(>|z|)
    (Intercept) -2.34907191 0.537610710 -4.3694664 1.245505e-05
    smokeYES    -0.03479730 0.197627539 -0.1760751 8.602349e-01
    height       0.01942373 0.003527538  5.5063142 3.664243e-08


The question now is how do I report the results, say, for height? Do I 
simply take the anti logs. i.e. 1.019613 = exp(0.019423) ?

I have seen one paper where they report using anti log base 10 instead 
of natural base but they use STATA though.

Please kindly advise. Thank you.

Regards, Adai

Adaikalavan Ramasamy <a.ramasamy <at> imperial.ac.uk> writes:
> 
> Dear all,
> 
> I used the glm.nb with the default values from the MASS package to run a 
> negative binomial regression. Here is a simple example:
[snip -- thanks for the example!]
> The question now is how do I report the results, say, for height? Do I 
> simply take the anti logs. i.e. 1.019613 = exp(0.019423) ?
> 
> I have seen one paper where they report using anti log base 10 instead 
> of natural base but they use STATA though.
> 
  Yes, exactly. If you look at ?glm.nb you
will see that it uses a log link function, and therefore
you should exponentiate (anti-log) to back-transform.
Natural, not base-10 logs, are used.
Don't forget that back-transforming standard errors
by themselves is meaningless, you have to back-transform
lower and upper confidence limits ...

  Ben Bolker