IRMSE: Compute the integrated root mean-square error

In SimDesign: Structure for Organizing Monte Carlo Simulation Designs

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(\theta) = \sqrt{\int [f(\theta, \hat{\psi}) - f(\theta, \psi)]^2 g(\theta, ...)}

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

Value

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

Author(s)

Phil Chalmers [e-mail]

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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/10691898.2016.1246953")}

See Also

RMSE

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 documentation built on Sept. 11, 2024, 8 p.m.