  # Re: st: offset variables

 From SamL To statalist@hsphsun2.harvard.edu Subject Re: st: offset variables Date Thu, 4 Jul 2002 04:43:54 -0700 (PDT)

```I cannot provide an exhaustive set of reasons for why one would use the
offset feature rather than enter the exposure as a covariate.  But my
understanding is the following.  By constraining the coefficient of the
exposure variable to equal one you transform the model into a model of
rates (e.g., injuries per unit of exposure instead of the probability
that the person will be injured).  This occurs because the link function
is logistic, and one implication of that is that a positive coefficient of
1, subtracted from both sides of the equation, is equivalent to making the
exposure the denominator of the left-hand side of the equation.

Further, if you estimathe the coefficient (which should be unnecessary if
you know that you want to transform the dependent variable into a rate),
you would obtain a standard error and, as the term is estimated in the
model, the variance-covariance matrix of the estimates will reflect the
association between this estimate and other estimates in the model.  In
other words, the precision of other estimates will be impacted by
estimating this coefficient.  If the reason for including the variable as
an exposure is just to make the model a model of rates, then there is no
need to waste information by estimating the coefficient and thereby
decreasing the precision of other estimates.

At least, that is my understanding.  Hope this helps.

Sam

On Mon, 1 Jul 2002 frone@ria.buffalo.edu wrote:

> I'm reading a matched case-control study that used conditional logistic
> regression (in STATA) to explore the predictors of being injured at work
> during the prior 12 months.  The analysis uses number of days worked
> during the period as an offset variable presumably to adjust for
> differential exposure.  In conditional logistic regression the coefficient
> for the offset is constrained to equal 1.
>
> I don't understand why one would make this constraint, as opposed to using
> number of days worked as another predictor variable.  Is there a reference
> that explains the various uses for offset variables?  I wasn't able to
> find a useful explanation in the STATA archives or through a general
> search of the net.
>
> Thanks in advance for any help.
>
> Mike Frone
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```