MAE: Compute the mean absolute error

Description

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", percent = FALSE, unname = FALSE)

Arguments

estimate

a numeric vector or matrix/data.frame 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

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 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))

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. 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. 10.1080/10691898.2016.1246953

Examples

Run this code

# NOT RUN {
pop <- 1
samp <- rnorm(100, 1, sd = 0.5)
MAE(samp, pop)

dev <- samp - pop
MAE(dev)
MAE(samp, pop, type = 'NMAE')
MAE(samp, pop, type = 'SMAE')

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

# 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))

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

# }