Obviously, there is a lot I don't know about the standards of how
Poisson regressions are fitted and reported, but why not try something
like
xi: poisson rate i.score [aw=expos]
or something of that kind? After fitting the regression, you would
have variables _Iscore_2, _Iscore_3 that would show the difference
from the base category 1 (you can tweak the base category around, see
-help xi-), and the approrpiate tests for the differences from that
base category will be the test statstics reported in the output, and
between the estimated categories, through
test _Iscore_2 - _Iscore_3
see if this helps
Stas
On Mon, 18 Oct 2004 11:55:20 -0400, David Harless <[email protected]> wrote:
> Dear Statalisters:
> I am writing to ask for advice on how to calculate (whether there exists?) a
> proper standard error for a mean *difference* in rates from a Poisson
> distributed count. Suggestions or citations would be greatly appreciated.
>
> Here are the details:
> I have counts of the number of failures by groups over time. In each period,
> there is also a score (from 3 to 5) which is claimed as an (ordinal) rating of
> safety of the group in the time period. Example:
>
> . list group period score expos failures in 17/23, sepby(group) noobs
> +----------------------------------------------+
> | group period score expos failures |
> |----------------------------------------------|
> | 7 1 4 10.0092 17 |
> | 7 2 5 15.3863 11 |
> |----------------------------------------------|
> | 8 1 5 143.2803 93 |
> | 8 2 4 32.9646 24 |
> | 8 3 3 31.2676 21 |
> | 8 4 4 89.2825 63 |
> | 8 5 3 26.6402 6 |
> +----------------------------------------------+
>
> My main analysis is poisson regression with fixed effects for the groups
> (xtpoisson, fe) that would include dummy variables for the scores. But I would
> also like to provide a descriptive table that illustrated the change in failure
> rate as the score changed -- and have that table include a correct standard error.
>
> My problem would be straightforward if I simply wanted to present mean failure
> rates by score:
> . gen rate=failures/expos
> . table score [aweight=expos] , c(m rate) format(%9.3f)
> ----------------------
> mean(rate)
> ----------+-----------
> 3 | 0.964
> 4 | 0.847
> 5 | 0.875
> ----------------------
>
> And the proper standard errors may be obtained using -ci- :
>
> . sort score
> . by score: ci failures, exposure(expos) poisson
> -> score = 3
> -- Poisson Exact --
> Variable | Exposure Mean Std. Err. [95% Conf. Interval]
> -------------+---------------------------------------------------------------
> failures | 4684 .9637415 .0143443 .93583 .9922742
>
> And so on.
>
> But I want my table to show the means of the *differences* in failure rates (by
> group) for different scores. Along the lines of:
>
> . tsset group period
> panel variable: group, 1 to 153
> time variable: period, 1 to 7
>
> . gen d_rate=d.rate
> (153 missing values generated)
>
> . gen l_score=l.score
> (153 missing values generated)
>
> . gen sum_expos=expos+l.expos
> (153 missing values generated)
>
> . table l_score score [aweight=sum_expos], c(m d_rate ) f(%9.3f)
> ----------------------------------
> l_score | 3 4 5
> ----------+-----------------------
> 3 | -0.029 -0.069 -0.074
> 4 | -0.026 -0.009 -0.038
> 5 | 0.135 -0.025
> ----------------------------------
>
> I've already made an assumption in weighting by the sum of exposures over the
> two periods in which the difference in rates are calculated. Perhaps there is a
> better way to incorporate this information, but the mean of differences in rates
> must be calculated in a way that reflects different exposures.
>
> So my question is: Can one calculate a proper standard error for a difference
> in rates for a Poisson distributed count, as in the above example?
--
Stas Kolenikov
http://stas.kolenikov.name
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