I set up different models: always same dependent variable and dataset, only the independent variable changes. All model assumptions are fullfilled.
Now i do a model selection with the AIC. I look at the model with an independent variable without and with a log transformation. The model with the log transformed dependend variable a has a lower AIC. Then i look at variable b and here the untransformed variable has a lower AIC. In total i look at 14 independend variables and the log transformation shows lower AIC for 6 of them.
My question is if i should use only log transformed or only not transformed data or just decide it for each variable after looking at the AIC?