Ratio of performance to interquartile distance (RPIQ) scales RMSE by the interquartile range of observations.
Details
$$\mathrm{RPIQ}= \frac{Q_{0.75}(obs)-Q_{0.25}(obs)} {\sqrt{n^{-1}\sum_{i=1}^{n}(obs_i-pred_i)^2}}.$$
RPIQ is non-negative and larger values indicate lower error relative to the
middle 50 percent of observed values. It is less influenced by extremes than
rpd(). R uses default type-7 quartiles. For perfect predictions with a
nonzero interquartile range it returns Inf; it returns NA with a warning
for the indeterminate zero-over-zero case. Missing-value handling follows
bias().
References
Bellon-Maurel et al. (2010). See rpd().