Compute the mean absolute error

Computes the average absolute deviation of a sample estimate from the parameter value. Accepts estimate and parameter values, as well as estimate values which are in deviation form.

Usage

MAE(
  estimate,
  parameter = NULL,
  type = "MAE",
  center = mean,
  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 or matrix 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 mean(abs(estimate)) will be returned)
type: type of deviation to compute. Can be 'MAE' (default) for the mean absolute error, 'NMSE' for the normalized MAE (MAE / (max(estimate) - min(estimate))), or 'SMSE' for the standardized MAE (MAE / sd(estimate))
center: function to compute the central tendency. Default uses mean, reflecting the canonical \(mean((\hat{p}_i - p)^2)\) difference, but other options can be supplied to provide more robust central tendency estimates, such as median (i.e., median-squared error) or \(x) mean(x, trim = 0.1)
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 mean absolute error 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

Author

Phil Chalmers rphilip.chalmers@gmail.com

Examples


pop <- 1
samp <- rnorm(100, 1, sd = 0.5)
MAE(samp, pop)
#> [1] 0.3545376

dev <- samp - pop
MAE(dev)
#> [1] 0.3545376
MAE(samp, pop, type = 'NMAE')
#> [1] 0.1193529
MAE(samp, pop, type = 'SMAE')
#> [1] 0.7859817

# matrix input
mat <- cbind(M1=rnorm(100, 2, sd = 0.5), M2 = rnorm(100, 2, sd = 1))
MAE(mat, parameter = 2)
#>        M1        M2 
#> 0.4552233 0.8681354 

# same, but with data.frame
df <- data.frame(M1=rnorm(100, 2, sd = 0.5), M2 = rnorm(100, 2, sd = 1))
MAE(df, parameter = c(2,2))
#>        M1        M2 
#> 0.4040587 0.7386515 

# parameters of the same size
parameters <- 1:10
estimates <- parameters + rnorm(10)
MAE(estimates, parameters)
#> [1] 0.8352983