SimDesign: IRMSE – R documentation

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IRMSE

Compute the integrated root mean-square error

Description

Computes the average/cumulative deviation given two continuous functions and an optional function representing the probability density function. Only one-dimensional integration is supported.

Usage

IRMSE(
  estimate,
  parameter,
  fn,
  density = function(theta, ...) 1,
  lower = -Inf,
  upper = Inf,
  ...
)

Arguments

`estimate`	a vector of parameter estimates
`parameter`	a vector of population parameters
`fn`	a continuous function where the first argument is to be integrated and the second argument is a vector of parameters or parameter estimates. This function represents a implied continuous function which uses the sample estimates or population parameters
`density`	(optional) a density function used to marginalize (i.e., average), where the first argument is to be integrated, and must be of the form `density(theta, ...)` or `density(theta, param1, param2)`, where `param1` is a placeholder name for the hyper-parameters associated with the probability density function. If omitted then the cumulative different between the respective functions will be computed instead
`lower`	lower bound to begin numerical integration from
`upper`	upper bound to finish numerical integration to
`...`	additional parameters to pass to `fnest`, `fnparam`, `density`, and `integrate`,

Details

The integrated root mean-square error (IRMSE) is of the form

IRMSE(θ) = √{\int [f(θ, \hat{ψ}) - f(θ, ψ)]^2 g(θ, ...)}

where g(θ, ...) is the density function used to marginalize the continuous sample (f(θ, \hat{ψ})) and population (f(θ, ψ)) functions.

Value

returns a single numeric term indicating the average/cumulative deviation given the supplied continuous functions

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

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

Examples

# logistic regression function with one slope and intercept
fn <- function(theta, param) 1 / (1 + exp(-(param[1] + param[2] * theta)))

# sample and population sets
est <- c(-0.4951, 1.1253)
pop <- c(-0.5, 1)

theta <- seq(-10,10,length.out=1000)
plot(theta, fn(theta, pop), type = 'l', col='red', ylim = c(0,1))
lines(theta, fn(theta, est), col='blue', lty=2)

# cumulative result (i.e., standard integral)
IRMSE(est, pop, fn)

# integrated RMSE result by marginalizing over a N(0,1) distribution
den <- function(theta, mean, sd) dnorm(theta, mean=mean, sd=sd)

IRMSE(est, pop, fn, den, mean=0, sd=1)

# this specification is equivalent to the above
den2 <- function(theta, ...) dnorm(theta, ...)

IRMSE(est, pop, fn, den2, mean=0, sd=1)

SimDesign

Structure for Organizing Monte Carlo Simulation Designs

v2.3

GPL (>= 2)

Authors

Phil Chalmers [aut, cre] (<https://orcid.org/0000-0001-5332-2810>), Matthew Sigal [ctb], Ogreden Oguzhan [ctb]

Initial release