interpretation of glm fam(gaussian) link(log)

[Umama Afr]

Dear stata team,
I have been looking for a way to model my skewed data and I read that using glm family(gaussian) link(log) could be a reasonable approach. I am not sure however about the interpretation. if I add eform, will the interpretation be the geometric mean ratio? if not, then what be a code for modelling the geometric mean ratio?

thank you very much

[Joseph Coveney]

using glm family(gaussian) link(log) . . .. if I add eform, will the interpretation be the geometric mean ratio? if not, then what be a code for modelling the geometric mean ratio?

See below.

.ÿ
.ÿclearÿ*

.ÿ
.ÿsetÿseedÿ1416634

.ÿquietlyÿsetÿobsÿ500

.ÿ
.ÿgenerateÿbyteÿxÿ=ÿmod(_n,ÿ2)

.ÿgenerateÿdoubleÿyÿ=ÿruniform()

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.ÿ*ÿAnswerÿtoÿfirstÿquestion
.ÿ*
.ÿquietlyÿameansÿyÿifÿ!x

.ÿtempnameÿmean0

.ÿscalarÿdefineÿ`mean0'ÿ=ÿr(mean_g)

.ÿquietlyÿameansÿyÿifÿx

.ÿdisplayÿinÿsmclÿasÿtextÿ"Geometricÿmeanÿratioÿ=ÿ"ÿasÿresultÿr(mean_g)ÿ/ÿ`mean0'
Geometricÿmeanÿratioÿ=ÿ1.1562465

.ÿ
.ÿglmÿyÿi.x,ÿfamily(gaussian)ÿlink(log)ÿeformÿnolog

GeneralizedÿlinearÿmodelsÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNo.ÿofÿobsÿÿÿÿÿÿ=ÿÿÿÿÿÿÿÿ500
Optimizationÿÿÿÿÿ:ÿMLÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿResidualÿdfÿÿÿÿÿ=ÿÿÿÿÿÿÿÿ498
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿScaleÿparameterÿ=ÿÿÿ.0829651
Devianceÿÿÿÿÿÿÿÿÿ=ÿÿ41.31661402ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ(1/df)ÿDevianceÿ=ÿÿÿ.0829651
Pearsonÿÿÿÿÿÿÿÿÿÿ=ÿÿ41.31661402ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ(1/df)ÿPearsonÿÿ=ÿÿÿ.0829651

Varianceÿfunction:ÿV(u)ÿ=ÿ1ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ[Gaussian]
Linkÿfunctionÿÿÿÿ:ÿg(u)ÿ=ÿln(u)ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ[Log]

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿAICÿÿÿÿÿÿÿÿÿÿÿÿÿ=ÿÿÿ.3525337
Logÿlikelihoodÿÿÿ=ÿ-86.13341589ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿBICÿÿÿÿÿÿÿÿÿÿÿÿÿ=ÿÿ-3053.558

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿOIM
ÿÿÿÿÿÿÿÿÿÿÿyÿ|ÿÿÿÿÿexp(b)ÿÿÿStd.ÿErr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿ1.xÿ|ÿÿÿ1.094607ÿÿÿ.0570213ÿÿÿÿÿ1.74ÿÿÿ0.083ÿÿÿÿÿ.9883629ÿÿÿÿ1.212271
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ.4736638ÿÿÿÿ.018217ÿÿÿ-19.43ÿÿÿ0.000ÿÿÿÿÿ.4392716ÿÿÿÿ.5107487
------------------------------------------------------------------------------

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.ÿ*
.ÿgenerateÿdoubleÿln_yÿ=ÿln(y)

.ÿquietlyÿregressÿln_yÿi.xÿ/*ÿotherÿpredictorsÿ*/

.ÿnlcomÿGMR:ÿexp(_b[1.x])

ÿÿÿÿÿÿÿÿÿGMR:ÿÿexp(_b[1.x])

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿln_yÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿGMRÿ|ÿÿÿ1.156246ÿÿÿ.1069653ÿÿÿÿ10.81ÿÿÿ0.000ÿÿÿÿÿ.9465984ÿÿÿÿ1.365895
------------------------------------------------------------------------------

.ÿ
.ÿ//ÿYouÿcanÿdoÿsmearingÿifÿyouÿwant,ÿbutÿitÿwon'tÿmatterÿifÿyouÿcanÿassumeÿhomoscedasticity
.ÿpredictÿdoubleÿmu,ÿxb

.ÿpredictÿdoubleÿre,ÿresiduals

.ÿgenerateÿdoubleÿereÿ=ÿexp(re)

.ÿsummarizeÿere,ÿmeanonly

.ÿgenerateÿdoubleÿmereÿ=ÿr(mean)

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.ÿscalarÿdefineÿ`mean0'ÿ=ÿr(mean)

.ÿsummarizeÿsmearÿifÿx,ÿmeanonly

.ÿdisplayÿinÿsmclÿasÿtextÿ"Geometricÿmeanÿratioÿ=ÿ"ÿasÿresultÿr(mean)ÿ/ÿ`mean0'
Geometricÿmeanÿratioÿ=ÿ1.1562465

.ÿ
.ÿexit

endÿofÿdo-file


.

Question for you: why do you want a geometric mean ratio instead of the generalized linear model fit?

[Marcos Almeida]

Also, (quite) generally speaking, as a ‘way to model skewed data’, the gamma family or the use power is something to think about.

[John Mullahy]

I agree with Marcos that you might consider a gamma family assumption. Since the model in levels is

y = exp(xb)*u

gamma is actually a natural baseline GLM family assumption since it specifies the conditional variance as proportional to the square of the conditional mean. You would still probably want to do robust covariance estimation in case the assumption is incorrect, but that would be true in any event.