[R] back transforming output from negative binomial

Ben Bolker bolker at ufl.edu
Thu Oct 2 19:25:25 CEST 2008

Adaikalavan Ramasamy wrote:
> Ben, fantastic. Thank you for confirming it.
> One more question. What do you call the back transformed variable?
> In my domain, people use something called the ratio of mean but I am not
> sure if it is the same. I am not what the "ratio" is between.

  It depends.  For the intercept, the back-transformed parameter
is essentially the geometric mean of the baseline group (assuming
you're using treatment contrasts).  For factors, the back-transf
parameters are the ratios between the means of observations at one
factor level and the mean at the baseline level.  For continuous
covariates, it's the proportional increase per unit of increase
in the covariate.

> Regards, Adai
> Ben Bolker wrote:
>> 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
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