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)?