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From |
Stas Kolenikov <skolenik@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Proper standard error for a difference in rates for a Poisson distributed count? |

Date |
Mon, 18 Oct 2004 14:02:35 -0400 |

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 <dwharles@vcu.edu> 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 * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**Re: st: ivreg2 Griliches example instrument validity***From:*"Mark Schaffer" <M.E.Schaffer@hw.ac.uk>

**st: Proper standard error for a difference in rates for a Poisson distributedcount?***From:*David Harless <dwharles@vcu.edu>

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