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I am trying to fit a glm using the Gamma family and the "identity" link. As I am analyzing nutrient concentrations in coastal waters (that can not be negative and are unlikely to be zero) I assume the Gamma distribution would be suitable. There are no zeros and no negative values in the data. If I have more than one independent variable (year, site, dist, season) and interactions in the model

m1<-glm(din~year*site*dist*season,family="Gamma"(link="identity"),data=mydata)

I get this error :

Error: no valid set of coefficients has been found:
  please supply starting values
        In addition: Warning message:
        In log(ifelse(y == 0, 1, y/mu)) : NaNs produced

I do understand, that using the identity link and therefore a linear predictor may produce negative values. As Gamma can not handle negative values it produces the error.

Can I add a shift (eg. add +4 to all data) to avoid this error? If yes, how would you choose the shift?

If I use the log-link, the results are diverted by the transformation (significant differences between the smaller values but non in in the higher values).

Thank you for your ideas!

Here I posted my data:
Ancova: How to proceed when residuals are not normal distrubuted but transformation changes meaning of results

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