# Re: st: Offset option in Svylogit and Svyologit

 From Phil Schumm <[email protected]> To [email protected] Subject Re: st: Offset option in Svylogit and Svyologit Date Mon, 31 Jan 2005 13:26:30 -0600

```At 11:52 AM -0500 1/31/05, Carol Carstens wrote:
```
```What does the offset option in svylogit and svyologit calculate?  I can
find no information about how a variable entered as "offset" is handled
by the resulting regression model.
```
```At 11:15 AM -0600 1/31/05, Phil Schumm wrote:
```
An offset refers to a covariate which is included in the model but with a coefficient constrained to be equal to one. For example, this is useful when modeling a dependent variate whose mean is assumed to be directly proportional to a covariate (e.g., total exposure to the risk of some event).
```At 12:40 PM -0500 1/31/05, Carol Carstens wrote:
```
```What is meant by "a mean assumed to be directly proportional to the
covariate"?
```

Carol,

If your interest stems from a particular problem, then I suggest you describe that problem so that we can provide a more specific (and probably more helpful) answer. If you're just curious, then I'd suggest you have a look at pp. 204-8 in McCullagh and Nelder (1989) which describes an example of the use of an offset. In that case, the outcome is the number of wave-related damage incidents to cargo ships. At the most basic level, we might suppose that the number of incidents is proportional to the amount of time at risk (measured in this case in terms of the aggregate months of service):

mean no. of damage incidents = c * (aggregate mos. service)

Note that this is what we mean when we say that the expected number of damage incidents is directly proportional to the period at risk -- in mathematical terms, we are saying that the mean number of damage incidents is equal to the aggregate months of service times a constant (in this case, c). Taking logarithms of both sides then gives:

log(mean no. incidents) = log(c) + log(aggregate mos. service)

which is just a log-linear model with the logarithm of aggregate months of service as an offset (i.e., with a coefficient of one).

At 12:40 PM -0500 1/31/05, Carol Carstens wrote:

How do I test the assumption that the mean of my dep var is directly proportional to a covariate?

Add the variable as a "normal" covariate (i.e., let Stata estimate a coefficient for it), and then use -test- to test the null hypothesis that the underlying value is one. Note that if this test provides evidence that the true value is not one, then you certainly shouldn't be specifying the variable as an offset and probably need to rethink your model. On the other hand, if the test yields a non-significant result, this alone is *not* sufficient justification for constraining the coefficient to equal one. Only a theoretical model can provide such justification (provided that there is no empirical evidence to the contrary).

-- Phil

McCullagh, P. and J. A. Nelder. 1989. Generalized Linear Models, 2nd ed. London: Chapman & Hall.
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