I'm working on a multiple regression model. The dependent variable (Y) is an ordered multinomial variable taking these values: A, B, C, D, E and F. The best value is A and the worst is F. In order to run a regression model, one needs to transform the letters (A, B, etc.) into figures.
I hereby ask you: which method between the following three is the best one? Linear transformation, Logistic Transformation and Exponential Transformation (each transformation method can have a logical explanation and a theoretical background)..
Example of figures which can be attributed to the different values of Y:
1. linear transformation : A=6, B=5,C=4.. F=1
2. logistic transformation: A=1, B=0,98, C=0,89, .. F=0.01
3. exponential transformation: A=10, B=8, C=5 .. F=1