Problem log(0) practical solution?

[Icke]

Hello everyone,

I want to model the association of a score (range 0-125) and age with an exponential approach because my scatterplot show an exponential progression.

My approach is:
I do log(score)
-> do a linear regression with age as covariate
-> do exp(regression coefficients)

The problem is: log(0) does not exist.

Just that it works I did log(score+0.01), but that is mathematically not correct.
Another Idea is to shift the score values systematically to the range 1-126. But this is also not a clean way.

Are there other possibilities or ideas to model an exponential fit to the data despite 0 values?

I would be very happy for every comment on this topic

Thanx in advance.

Best wishes
Icke

 

[Dason]

I'm guessing the response is integers? Does it appear like the variance increase as the mean increases?

 

[Icke]

Yes the score is 0,1,2,3,...
And yes, at the beginning the variance increases with increasing mean, but in the middle and the end of the mean this is no more the case.

 

[Dason]

I'm not sure what you mean by "but in the middle and the end of the mean this is no more the case"

It sounds like possibly a generalized linear model with a Log link and either a Poisson or Negative Binomial response distribution would be appropriate.

 

[Icke]

ok, I forgot to mention that I don`t conduct a classical linear regression but a Linear Quantile Regression with a Mixed Model approach...