I have a Poisson GLM model

    m1 <- glm(count ~ x, data = data, family = "quasipoisson")

The predictor variable x is a cumulative sum of ratios, i.e. real numbers between 0 and 1. (Not important for this question, but if you are interested why the sum is needed, it is because it is a transformation [of a simpler but recursive model](https://stats.stackexchange.com/a/62543/5509)).

##Is it desirable to normalize the predictor variable by logit?

i.e. instead of using cumulative sum of ratios, use cumulative sum of logit of the ratios (`x2`)?

    m2 <- glm(count ~ x2, data = data, family = "quasipoisson")

I tried to look at the q-q plots (`plot(model)`) but they seem to be the same. However I tried to do another plot which is not present in the `plot(model)` output - I don't know if it's actually important or not. So see comparison of the two models on this plot:

![enter image description here][1]

Is this plot actually important for this decision? Does the second plot actually show heteroscedasticity? If yes, then is the original model (without transformation) possibly better according to these plots?


  [1]: https://i.sstatic.net/oOWhx.png