Mean bias fit function — bias • AEME

Calculates the mean difference between modelled and observed values, in the variable's native units:

Usage

bias(obs, sim, na.rm = TRUE)

Arguments

obs: Numeric vector of observed values.
sim: Numeric vector of simulated (modelled) values.
na.rm: Logical; should missing values (NA) in either vector be removed pairwise before computation? Default is TRUE.

Value

numeric; mean(sim - obs), signed, in the same units as obs/sim.

Details

$$\text{Bias} = \frac{1}{n} \sum_{i=1}^n (\text{sim}_i - \text{obs}_i)$$

Positive when the model overestimates on average, negative when it underestimates. Unlike every other function in this file, the raw (signed) value is returned rather than a zero-is-best, non-negative one.

This makes bias() unsafe to drop directly into FUN_list for calibration: since calib_aeme()/run_and_fit() minimise the returned value, minimising a signed bias would push the calibration towards the most negative (maximally under-estimating) solution rather than towards zero bias. Use pbias (or abs(bias(obs, sim))) as a calibration objective; use bias() for diagnosing the direction of a systematic error when inspecting fit after the fact. Like mae/rmse, it stays in the variable's native units and so is not directly comparable across variables with different units or magnitudes.

Examples

obs <- c(1, 2, 3, 4)
sim <- c(1.1, 2.1, 2.9, 4.2)
bias(obs, sim)
#> [1] 0.075