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# Re: st: Interpreting coefficients for a gamma regression with log link (Stata 11)

 From Hitesh Chandwani To statalist@hsphsun2.harvard.edu Subject Re: st: Interpreting coefficients for a gamma regression with log link (Stata 11) Date Tue, 20 Sep 2011 08:37:19 -0500

```Thank you Thomas for the comments and help. I really appreciate it!

-Hitesh

On Mon, Sep 19, 2011 at 10:17 AM, Weichle, Thomas <Thomas.Weichle@va.gov> wrote:
> Hi Hitesh,
> As you know may know, the output being displayed is different depending
> on whether you specify the eform option or not.  The resulting model is
> the same but the interpretation of the coefficients is slightly
> different.  Suppose x is a 1/0 variable.  Then, b =
> ln(E(y|x=1))/ln(E(y|x=0)) is the unexponentiated coefficient for x and
> e(b) = e^[ln(E(y|x=1))/ln(E(y|x=0))] = e^[ln(E(y|x=1))]/[e^ln(E(y|x=0))]
> = E(y|x=1)/E(y|x=0) is the exponentiated coefficient for x.  When
> dealing with cost as an outcome, Blough (2000) states that the ratio
> directly interpreted from the exposure variable may be preferable to
> point estimates (unexponentiated coefficient).
>
> Returning to your specific questions:
> 1) You are correct in stating that the exponentiated coefficient of
> 1.031383 represents the arithmetic mean ratio in the dependent variable
> between HIV+ and HIV- patients [specifically mean(hiv=1)/mean(hiv=0)].
>
> 2) Since 'insurance_3' is the reference category, the exponentiated
> coefficient for 'insurance_1' is interpreted as the following ratio:
> [mean(insurance_1)/mean(insurance_3)].
>
> Tom Weichle
> Math Statistician
> Center for Management of Complex Chronic Care (CMC3)
> Hines VA Hospital, Bldg 1, C202
> 708-202-8387 ext. 24261
> Thomas.Weichle@va.gov
>
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>

--
Hitesh S. Chandwani
University of Texas at Austin

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```