Centered root mean squared error

Centered RMSE (cRMSE) is the root mean square difference after removing the mean error from the paired errors.

Usage

crmse(obs, pred, na.rm = TRUE)

Arguments

obs

Numeric observation vector.

pred

Numeric prediction vector paired with obs.

na.rm

Logical; remove incomplete pairs?

Value

One numeric value.

Details

$$\mathrm{cRMSE}=\sqrt{\frac{1}{n}\sum_{i=1}^{n} \left[(obs_i-pred_i)-\frac{1}{n}\sum_{j=1}^{n}(obs_j-pred_j)\right]^2}.$$

cRMSE is non-negative, has the response units, and zero is ideal. It measures disagreement in pattern and spread independently of a constant mean bias. Interpret it with bias() because two models with identical cRMSE can have different systematic errors. Missing-value handling follows bias().

References

Taylor, K. E. (2001). Summarizing multiple aspects of model performance in a single diagram. Journal of Geophysical Research, 106, 7183-7192. doi:10.1029/2000JD900719

Examples

crmse(1:3, c(1, 3, 2))
#> [1] 0.8164966