[R-sig-ME] GEE with gamma family and log link

[Ben Bolker]

   Except for the details of conditional vs marginal effects (discussed 
in a previous thread), the interpretation of fixed effects of a model 
with a log link (GLM(M), GEE, etc.) are not really a 
mixed-model-specific issue, but apply to any model with a log link.

   Your interpretations below sound correct (although you say something 
about "multiplying the arithmetic mean" by exp(beta); this is true, but 
it's also true that you would equivalently be multiplying any sensible 
location parameter (such as the geometric mean) by the same factor

On 11/12/21 8:32 PM, Tahsin Ferdous wrote:
> I am fitting a generalized estimating equation with gamma family and log
> link. I am using GEE (geeglm function) from the R pcakage “geepack” with
> gamma family and log link and unstructured correlation structure.
> 
> Here, response variable or outcome is IFN_gamma_protein_pg_mg . Exposure is
> intervention or probiotic use. Another covariate is Timepoint.
> 
> My code and the output is as mentioned below.
> 
> m8<geeglm(IFN_gamma_protein_pg_mg~Intervention+Timepoint,data=B,family=Gamma(link=log),id=
> Participant_ID,corstr="exchangeable")
> 
> summary(m8)
> 
> * IFN_gamma_protein_pg_mg*
> 
> *Predictors*
> 
> *Estimates*
> 
> *p*
> 
> (Intercept)
> 
> 0.01
> 
> *<0.001*
> 
> Intervention [Probiotics]
> 
> 0.34
> 
> *0.029*
> 
> Timepoint [T2]
> 
> 0.99
> 
> 0.979
> 
> Timepoint [T3]
> 
> 5.30
> 
> 0.059
> 
> Timepoint [T4]
> 
> 0.48
> 
> *0.039*
> 
> Timepoint [T5]
> 
> 0.11
> 
> *<0.001*
> 

> 
> 
> I am trying to interpret the coefficients as follows:
> 
> For every one-unit increase in the probiotic across the population, the log
> average of IFN_gamma_protein increases by 0.34 units.
> 
> The exponentiated coefficient ( exp )= (exp(0.34)=1.41) is the factor by
> which the arithmetic mean outcome on the original scale multiplied, i.e.,
> when intervention is probiotic, for every one-unit increase in the
> probiotic across the population, the average of IFN_gamma_protein on the
> original scale is 1.41 times higher compared to when intervention is
> control within levels of other variable.
> 
> Similarly, for timepoint 2, the average of IFN_gamma_protein on the
> original scale is exp(  )= exp(0.99)= 2.69 times higher compared to
> timepoint 1 within levels of other variable.
> 
> For time point 3, the average of IFN_gamma_protein on the original scale is
> exp(  )= exp(5.30)= 200.34 times higher compared to timepoint 1 within
> levels of other variable.
> 
> Can someone confirm me that I am in the right track in the interpretation
> of parameters?
> 
> I am  posting here as I also want to fit a Gamma GLMM.
> 
> 	[[alternative HTML version deleted]]
> 
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-- 
Dr. Benjamin Bolker
Professor, Mathematics & Statistics and Biology, McMaster University
Director, School of Computational Science and Engineering
(Acting) Graduate chair, Mathematics & Statistics