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

 From "Weichle, Thomas" To Subject Re: st: Interpreting coefficients for a gamma regression with log link (Stata 11) Date Mon, 19 Sep 2011 10:17:53 -0500

```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).

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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```