# 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.

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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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