Solved – Standardised mean absolute error (SMAE) and how to calculate it

I am using the mean absolute error

mean(abs(obs - pred)) 

as one of the measures assessing the fit of my model. I would also like to have a standardised measure ranging 0 – 1 to compliment this. Given that there is MSE and SMSE, how does one go about to get a standardised MAE?

thank you.

If you can deduce the worst possible MAE in your particular situation, you can divide the MAE you actually get by this, which will scale your MAE to the interval [0,1], with a perfect fit mapped to 0 and the worst possible MAE mapped to 1.

However, often there is no upper bound to the MAE. Fits can often in principle be unboundedly bad. In such a situation, you cannot scale your MAE to any predetermined interval linearly. Of course you could non-linearly scale it by

$$ text{MAE} mapsto frac{2}{pi}arctan(text{MAE}), $$

which does map any MAE to [0,1], but I would rather doubt that this would be very enlightening.

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