Consider the following case: I am analyzing a the effect of (among other variables) the age of a firm on a specific binary event. Theoretically my perception is that age matters, but not linearly. That is, I don't believe that the age of firms e.g. 300 years matter 15 times more than a firm 20 years old. Can a transformation be used in such case?
Mathematically a log transformation has the properties that i look for as it evens out the weight of very high vs. low values. Below is a visual example. The transformed value chart demonstrates roughly the effect I want to model on the DV in the logistic regression.
To me, intuitively it makes perfect sense, however it is difficult for me to find any examples of this particular case as all sources I have been through covers transformation for normality and linearity in OLS regression, assumptions that do not apply to logistic regression.
I hope anyone can help with this most likely simple question.
y axis: value, x: axis (hypothetical observation, not relevant)
Edit: how can the best transformation be identified when the DV is binary?
When attempting to find the best transformation for a continuous IV in relation to a binary DV, how is this best done? For a continuous DV in e.g. OLS regression, this is possible visually, but when attempting this for a binary variable, it obviously becomes difficult (see below).