Mean Squared Error (MSE) — MSE • metrica

It estimates the MSE for a continuous predicted-observed dataset.

Usage

MSE(data = NULL, obs, pred, tidy = FALSE, na.rm = TRUE)

Arguments

data: (Optional) argument to call an existing data frame containing the data.
obs: Vector with observed values (numeric).
pred: Vector with predicted values (numeric).
tidy: Logical operator (TRUE/FALSE) to decide the type of return. TRUE returns a data.frame, FALSE returns a list; Default : FALSE.
na.rm: Logic argument to remove rows with missing values (NA). Default is na.rm = TRUE.

Value

an object of class numeric within a list (if tidy = FALSE) or within a data frame (if tidy = TRUE).

Details

The MSE, also known as MSD, measures general agreement, as includes both variance (lack of precision) and bias (lack of accuracy). The MSE of predictions could be decomposed following a variety of approaches (e.g. Willmott et al. 1981; Correndo et al. 2021). Its calculation is simple, the sum of squared differences between predictions and observations divided by the sample size (n). The greater the value the worse the predicted performance. Unfortunately, the units of MSE do not have a direct interpretation. For a more direct interpretation, the square root of MSE (RMSE) has the same units as the variable of interest. For the formula and more details, see online-documentation

References

Willmott (1981). On the validation of models. Phys. Geogr. 2, 184–194. doi:10.1080/02723646.1981.10642213

Correndo et al. (2021). Revisiting linear regression to test agreement in continuous predicted-observed datasets. Agric. Syst. 192, 103194. doi:10.1016/j.agsy.2021.103194

Examples

# \donttest{
set.seed(1)
X <- rnorm(n = 100, mean = 0, sd = 10)
Y <- rnorm(n = 100, mean = 0, sd = 9)
MSE(obs = X, pred = Y)
#> $MSE
#> [1] 155.6413
#> 
# }