# Re: st: Interpreting a log-level specification with a rate

 From "Clive Nicholas" To statalist@hsphsun2.harvard.edu Subject Re: st: Interpreting a log-level specification with a rate Date Sun, 9 Mar 2008 08:45:36 +0000

```Stefan Duke wrote:

>  I have a statistics related question, not directly stata. But maybe
>  still somebody can help me as I am puzzeled.
>  I ran a regression
>  log(y) = c + b*m
>
>  where m is the migration rate per 1000 residents. I want to know how
>  to interpret the coefficient b. In text books the usual interpretation
>  for log-level specification is
>  % delta y =  (100 b) delta m
>
>  So delta m is taken as 1 and an increase by 1 unit in the independent
>  leads to a b*100 percentage increase in y.
>  But I have a rate per thousand as the independent variable. Hence an
>  increase by 1 unit would mean 1000 emigrants per 1000 resident which
>  doesn't make much sense. Has anybody any thoughts?

Divide _m_ by 10 to make it a percentage variable, take its log and
then regress on _y_ on _m_. After fitting your model, say, with -glm-
plus the -fam(bin)-, link(logit)- and -robust- options, _m_ should
then have a percentage interpretation (i.e., a 1-unit increase in the
_m_ parameter = a 100% increase in the _m_ variable). Exponentiate it
with -eform- for an odds-ratio interpretation.

--
Clive Nicholas

[Please DO NOT mail me personally here, but at
<clivenicholas@hotmail.com>. Thanks!]

"Courage is going from failure to failure without losing enthusiasm."
-- Winston Churchill
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```