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From |
David Hoaglin <dchoaglin@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Interpretation GLM coefficients |

Date |
Thu, 19 Jan 2012 07:45:30 -0500 |

Hi, Fabien. Since you are using the log link, the relation between the mean of x1 and the linear predictor is mean(x1) = exp(b1 + b2*ln_x2 + b3*x3 + b4*x4), which you can rewrite as mean(x1) = exp(b1) * [exp(b2)^ln_x2] * [exp(b3)^x3] * [exp(b4)^x4]. Interpretations often use "incidence rate ratios." A change of 1 unit in ln_x2 (not a change of 1 percent in x2) would change the mean of x1 by a factor of exp(b2). A change of 1 unit in x3 would change the mean of x1 by a factor of exp(b3). And changing x4 from 0 to 1 would change the mean of x1 by a factor of exp(b4). For each variable, the interpretation should include the explanation (as applies also in OLS) that the changes are adjusting for the contributions of the other variables in the model. Because the predictor variables generally change together in the data, it is an oversimplification and often misleading to talk in terms of holding the other variables fixed. (Unfortunately, many textbooks do not explain this, but it is an inherent feature of regression-like models.) It may be possible to make predictions that change one variable and hold others fixed, as long as you stay within the region covered by the data. Similarly, a change of 1 unit should not take you (far) outside that region. I hope this discussion is helpful. David Hoaglin On Thu, Jan 19, 2012 at 4:39 AM, Fabien Bertho <fabien.bertho@sciences-po.org> wrote: > Hello, > > I am running glm Poisson regressions and I have some problems in interpreting the coefficients. I am running the following regression: > > - glm x1 ln_x2 x3 x4, robust cluster(distance) family(poisson) link(log) irls - > > Where x1 is an integer, x2 and x3 are continuous variables and x4 is a dummy variable. > > Is the interpretation of glm coefficients different from OLS coefficients? My attempt: > > => A one percent change in x2, generate a b2 unit change in x1 > => A one unit change in x3, generate a b3 unit change in x1 > => The movement of x4 from 0 to 1 produces a b4 unit change in x1 > > Is this correct? > > Thank you. > > Best Regards, > > Fabien BERTHO * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Interpretation GLM coefficients***From:*Fabien Bertho <fabien.bertho@sciences-po.org>

**References**:**st: Interpretation GLM coefficients***From:*Fabien Bertho <fabien.bertho@sciences-po.org>

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