SimDesign (version 1.13)

ECR: Compute the empirical coverage rate for Type I errors and Power

Description

Computes the detection rate for determining empirical Type I error and power rates using information from the confidence intervals. Note that using 1 - ECR(CIs, parameter) will provide the empirical detection rate. Also supports computing the average width of the CIs, which may be useful when comparing the efficiency of CI estimators.

Usage

ECR(CIs, parameter, tails = FALSE, CI_width = FALSE, names = NULL)

Arguments

CIs

a numeric vector or matrix of confidence interval values for a given parameter value, where the first element/column indicates the lower confidence interval and the second element/column the upper confidence interval. If a vector of length 2 is passed instead then the returned value will be either a 1 or 0 to indicate whether the parameter value was or was not within the interval, respectively. Otherwise, the input must be a matrix with an even number of columns

parameter

a numeric scalar indicating the fixed parameter value. Alternative, a numeric vector object with length equal to the number of rows as CIs (use to compare sets of parameters at once)

tails

logical; when TRUE returns a vector of length 2 to indicate the proportion of times the parameter was lower or higher than the supplied interval, respectively. This is mainly only useful when the coverage region is not expected to be symmetric, and therefore is generally not required. Note that 1 - sum(ECR(CIs, parameter, tails=TRUE)) == ECR(CIs, parameter)

CI_width

logical; rather than returning the overall coverage rate, return the average width of the CIs instead? Useful when comparing the efficiency of different CI estimators

names

an optional character vector used to name the returned object. Generally useful when more than one CI estimate is investigated at once

References

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

See Also

EDR

Examples

# NOT RUN {
CIs <- matrix(NA, 100, 2)
for(i in 1:100){
   dat <- rnorm(100)
   CIs[i,] <- t.test(dat)$conf.int
}

ECR(CIs, 0)
ECR(CIs, 0, tails = TRUE)

# single vector input
CI <- c(-1, 1)
ECR(CI, 0)
ECR(CI, 2)
ECR(CI, 2, tails = TRUE)

# parameters of the same size as CI
parameters <- 1:10
CIs <- cbind(parameters - runif(10), parameters + runif(10))
parameters <- parameters + rnorm(10)
ECR(CIs, parameters)

# average width of CIs
ECR(CIs, parameters, CI_width=TRUE)

# ECR() for multiple CI estimates in the same object
parameter <- 10
CIs <- data.frame(lowerCI_1=parameter - runif(10),
                  upperCI_1=parameter + runif(10),
                  lowerCI_2=parameter - 2*runif(10),
                  upperCI_2=parameter + 2*runif(10))
head(CIs)
ECR(CIs, parameter)
ECR(CIs, parameter, tails=TRUE)
ECR(CIs, parameter, CI_width=TRUE)

# often a good idea to provide names for the output
ECR(CIs, parameter, names = c('this', 'that'))
ECR(CIs, parameter, CI_width=TRUE, names = c('this', 'that'))
ECR(CIs, parameter, tails=TRUE, names = c('this', 'that'))

# }