Compute the relative standard error ratio

Source: R/summary_functions.R

Computes the relative standard error ratio given the set of estimated standard errors (SE) and the deviation across the R simulation replications (SD). The ratio is formed by finding the expectation of the SE terms, and compares this expectation to the general variability of their respective parameter estimates across the R replications (ratio should equal 1). This is used to roughly evaluate whether the SEs being advertised by a given estimation method matches the sampling variability of the respective estimates across samples.

RSE(SE, ests, unname = FALSE)

Arguments

SE

a numeric matrix of SE estimates across the replications (extracted from the results object in the Summarise step). Alternatively, can be a vector containing the mean of the SE estimates across the R simulation replications

ests

a numeric matrix object containing the parameter estimates under investigation found within the Summarise function. This input is used to compute the standard deviation/variance estimates for each column to evaluate how well the expected SE matches the standard deviation

unname

logical; apply unname to the results to remove any variable names?

Value

returns vector of variance ratios, (RSV = SE^2/SD^2)

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


R <- 10000
par_ests <- cbind(rnorm(R), rnorm(R, sd=1/10),
                  rnorm(R, sd=1/15))
colnames(par_ests) <- paste0("par", 1:3)
(SDs <- colSDs(par_ests))
#>       par1       par2       par3 
#> 1.00233527 0.09950858 0.06682729 

SEs <- cbind(1 + rnorm(R, sd=.01),
             1/10 + + rnorm(R, sd=.01),
             1/15 + rnorm(R, sd=.01))
(E_SEs <- colMeans(SEs))
#> [1] 1.00018554 0.10001727 0.06673456
RSE(SEs, par_ests)
#>      par1      par2      par3 
#> 0.9978553 1.0051120 0.9986124 

# equivalent to the form
colMeans(SEs) / SDs
#>      par1      par2      par3 
#> 0.9978553 1.0051120 0.9986124