# Can MAD (median absolute deviation) or MAE (mean absolute error) be used to calculate prediction intervals?

From my understanding, RMSE (root mean square error) estimated through cross-validation can be used to calculate the prediction interval of a mixed-effect linear model with gaussian error. In my case, the response variable is log10-transformed, so I calculate

10^(RMSE * sigma level)

To estimate the prediction error in terms of orders of magnitude considering a given sigma level (e.g. 1.96 for 95% interval). Can you please confirm this is correct?

Now, I would like to know if I can apply the same calculation to calculate the prediction interval using MAD (median absolute deviation) or MAE (mean absolute error). If not, is there any way to interpret MAE or MAD given a certain level of confidence (e.g. % of times the error is within a given interval)?

Thanks

• In mixed models, you can calculate two types of prediction intervals, one conditional on the random effects, and one from the marginal model that has the random effects integrated out. It is not clear which one are you looking for. – Dimitris Rizopoulos Jun 21 '19 at 8:56
• I'm referring to the one considering fixed effects only – Oritteropus Jun 21 '19 at 14:06

## 1 Answer

You can transform (an estimate of) the MAE into (an estimate of) the standard deviation (which the RMSE is another estimate of):

$$\hat{\sigma} = \sqrt{\frac{\pi}{2}}\hat{\text{MAE}}.$$

• Very helpful, thanks! – Oritteropus Jun 26 '19 at 7:14