Compute the (normalized) root mean square error

Computes the average deviation (root mean square error; also known as the root mean square deviation) of a sample estimate from the parameter value. Accepts estimate and parameter values, as well as estimate values which are in deviation form.

RMSE(
  estimate,
  parameter = NULL,
  type = "RMSE",
  MSE = FALSE,
  percent = FALSE,
  unname = FALSE
)

RMSD(
  estimate,
  parameter = NULL,
  type = "RMSE",
  MSE = FALSE,
  percent = FALSE,
  unname = FALSE
)

Arguments

estimate

a numeric vector, matrix/data.frame, or list of parameter estimates. If a vector, the length is equal to the number of replications. If a matrix/data.frame, the number of rows must equal the number of replications. list objects will be looped over using the same rules after above after first translating the information into one-dimensional vectors and re-creating the structure upon return

parameter

a numeric scalar/vector indicating the fixed parameter values. If a single value is supplied and estimate is a matrix/data.frame then the value will be recycled for each column; otherwise, each element will be associated with each respective column in the estimate input. If NULL then it will be assumed that the estimate input is in a deviation form (therefore sqrt(mean(estimate^2)) will be returned)

type

type of deviation to compute. Can be 'RMSE' (default) for the root mean square-error, 'NRMSE' for the normalized RMSE (RMSE / (max(estimate) - min(estimate))), 'SRMSE' for the standardized RMSE (RMSE / sd(estimate)), 'CV' for the coefficient of variation, or 'RMSLE' for the root mean-square log-error

MSE

logical; return the mean square error equivalent of the results instead of the root mean-square error (in other words, the result is squared)? Default is FALSE

percent

logical; change returned result to percentage by multiplying by 100? Default is FALSE

unname

logical; apply unname to the results to remove any variable names?

Value

returns a numeric vector indicating the overall average deviation in the estimates

References

Chalmers, R. P., & Adkins, M. C. (2020). Writing Effective and Reliable Monte Carlo Simulations with the SimDesign Package. The Quantitative Methods for Psychology, 16(4), 248-280. doi:10.20982/tqmp.16.4.p248

Sigal, M. J., & Chalmers, R. P. (2016). Play it again: Teaching statistics with Monte Carlo simulation. Journal of Statistics Education, 24(3), 136-156. doi:10.1080/10691898.2016.1246953

See also

bias

MAE

Author

Phil Chalmers rphilip.chalmers@gmail.com

Examples

pop <- 1
samp <- rnorm(100, 1, sd = 0.5)
RMSE(samp, pop)
#> [1] 0.5054696

dev <- samp - pop
RMSE(dev)
#> [1] 0.5054696

RMSE(samp, pop, type = 'NRMSE')
#> [1] 0.2173464
RMSE(dev, type = 'NRMSE')
#> [1] 0.2173464
RMSE(dev, pop, type = 'SRMSE')
#> [1] 2.204096
RMSE(samp, pop, type = 'CV')
#> [1] 0.5050305
RMSE(samp, pop, type = 'RMSLE')
#> [1] 0.2724405

# percentage reported
RMSE(samp, pop, type = 'NRMSE')
#> [1] 0.2173464
RMSE(samp, pop, type = 'NRMSE', percent = TRUE)
#> [1] 21.73464

# matrix input
mat <- cbind(M1=rnorm(100, 2, sd = 0.5), M2 = rnorm(100, 2, sd = 1))
RMSE(mat, parameter = 2)
#>        M1        M2 
#> 0.4792211 1.0632404 
RMSE(mat, parameter = c(2, 3))
#>        M1        M2 
#> 0.4792211 1.5376152 

# different parameter associated with each column
mat <- cbind(M1=rnorm(1000, 2, sd = 0.25), M2 = rnorm(1000, 3, sd = .25))
RMSE(mat, parameter = c(2,3))
#>        M1        M2 
#> 0.2514461 0.2531606 

# same, but with data.frame
df <- data.frame(M1=rnorm(100, 2, sd = 0.5), M2 = rnorm(100, 2, sd = 1))
RMSE(df, parameter = c(2,2))
#>        M1        M2 
#> 0.4382088 1.0450931 

# parameters of the same size
parameters <- 1:10
estimates <- parameters + rnorm(10)
RMSE(estimates, parameters)
#> [1] 1.381805