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Mean Squared Error (MSE)

Source: R/mse.R
mse.Rd

The MSE is a metric that evaluates the goodness of fit between model simulations and observations (Fisher, 1920). Measured in the squared units of truth and estimate and can vary from \(-\infty\) to \(+\infty\).

Usage

mse(data, ...)

# S3 method for class 'data.frame'
mse(data, truth, estimate, na_rm = TRUE, ...)

mse_vec(truth, estimate, na_rm = TRUE, ...)

Arguments

data

A data.frame containing the columns specified by the truth and estimate arguments.

...

Not currently used.

truth

The column identifier for the true results (that is numeric). This should be an unquoted column name although this argument is passed by expression and supports quasiquotation (you can unquote column names). For _vec() functions, a numeric vector.

estimate

The column identifier for the predicted results (that is also numeric). As with truth this can be specified different ways but the primary method is to use an unquoted variable name. For _vec() functions, a numeric vector.

na_rm

A logical value indicating whether NA values should be stripped before the computation proceeds.

Value

A tibble with columns .metric, .estimator, and .estimate and 1 row of values.

For grouped data frames, the number of rows returned will be the same as the number of groups.

For mse_vec(), a single numeric value (or NA).

Details

The MSE is estimated as follows (Clark et al., 2021): $$ MSE = \frac{1}{n} \sum_{i=1}^{n}{(sim_i - obs_i)^2} $$ where:

  • \(sim\) defines model simulations at time step \(i\)

  • \(obs\) defines model observations at time step \(i\)

References

Fisher, R. A. (1920). Accuracy of observation, a mathematical examination of the methods of determining, by the mean error and by the mean square error. Monthly Notices of the Royal Astronomical Society, 80, 758–770. doi:10.1093/mnras/80.8.758

Clark, M. P., Vogel, R. M., Lamontagne, J. R., Mizukami, N., Knoben, W. J. M., Tang, G., Gharari, S., Freer, J. E., Whitfield, P. H., Shook, K. R., & Papalexiou, S. M. (2021). The Abuse of Popular Performance Metrics in Hydrologic Modeling. Water Resources Research, 57(9), e2020WR029001. doi:10.1029/2020WR029001

See also

Other numeric metrics: kge(), kge2012(), nse(), pbias(), press(), sfe()

Other accuracy metrics: kge(), kge2012(), nse(), pbias(), press(), sfe()

Examples

library(tidyhydro)
data(avacha)

# Supply truth and predictions as bare column names
mse(avacha, obs, sim)
#> # A tibble: 1 × 3
#>   .metric .estimator .estimate
#>   <chr>   <chr>          <dbl>
#> 1 mse     standard        626.

# Or as numeric vectors
mse_vec(avacha$obs, avacha$sim)
#> [1] 625.9438