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Calculate metrics for model predictive performance evaluation

Source: R/evaluation.R
metrics..Rd

Computes common error metrics that quantify the predictive performance of pharmacometric models by comparing predicted (pred.x) and observed (obs.y) concentration values.

Usage

metrics.(pred.x, obs.y)

Arguments

pred.x

Numeric vector of model-predicted values.

obs.y

Numeric vector of corresponding observed values.

Value

A numeric vector with named elements:

  • APE: absolute prediction error

  • MAE: mean absolute error

  • MAPE: mean absolute percentage error

  • RMSE: root mean squared error

  • rRMSE1: relative RMSE (type 1)

  • rRMSE2: relative RMSE (type 2)

Details

The function stops with an error if pred.x and obs.y have unequal lengths. The following metrics are calculated:

$$APE = \sum |pred.x - obs.y|$$ Absolute prediction error (APE) is the sum of absolute differences.

$$MAE = \frac{1}{n} \sum |pred.x - obs.y|$$ Mean absolute error (MAE) expresses the average absolute deviation.

$$MAPE = \frac{100}{n} \sum \left| \frac{pred.x - obs.y}{obs.y} \right|$$ Mean absolute percentage error (MAPE) normalizes the error by observed values.

$$RMSE = \sqrt{\frac{1}{n} \sum (pred.x - obs.y)^2}$$ Root mean squared error (RMSE) penalizes larger deviations.

$$rRMSE1 = \frac{RMSE}{\bar{obs.y}} \times 100$$ Relative RMSE type 1 is the RMSE normalized by the mean observed value.

$$rRMSE2 = 100 \times \sqrt{\frac{1}{n} \sum \left( \frac{pred.x - obs.y}{(pred.x + obs.y)/2} \right)^2}$$ Relative RMSE type 2 is symmetric and normalizes by the mean of each predicted–observed pair.

Examples


obs.y  <- rnorm(100, mean = 100, sd = 10)
pred.x <- obs.y + rnorm(100, mean = 0, sd = 5)
metrics.(pred.x = pred.x, obs.y = obs.y)
#>    metrics.ape    metrics.mae   metrics.mape   metrics.rmse metrics.rrmse1 
#>     413.924719       4.139247       4.105765       5.071008       4.988664 
#> metrics.rrmse2 
#>       5.067604