z2S function

Compute the robust effect size index estimate from Z statistic

This function computes the robust effect size index from Vandekar, Tao, & Blume (2020). Vector arguments are accepted. If different length arguments are passed they are dealt with in the usual way of R.

z2S(z, n, unbiased = TRUE)

Arguments

• z: The Z statistic for the parameter of interest.
• n: Number of independent samples.
• unbiased: Logical, whether to use unbiased or alternative estimator. See details.

Returns

Returns a scalar or vector argument of the robust effect size index estimate.

Details

This function computes S, the RESI, from a Z statistic. The formula for the unbiased estimator (default) is derived by solving the expected value of the Z statistic for S. It is unbiased and consistent.

The formula for the unbiased conversion is:

$S = Z/\sqrt(n)$

The formula for the alternative estimator is derived by squaring the Z statistic and using the chisq2S formula. This estimator may be appealing for its intuitive relationship to the Chi-square statistic; the absolute value of RESI estimates using this formula will be equal to a RESI estimate using a Chi-square statistic for the same model. However, this estimator does have finite sample bias, which is an important consideration for the coverage of the bootstrapping that resi uses.

The formula for the alternative conversion is:

$\sqrt(max(0, (Z^2 - 1)/n)) * sign(Z)$

Examples

# to obtain example z values, first fit a glm
mod = glm(charges ~ region * age + bmi + sex, data = RESI::insurance)
# run coeftest to get z values using a robust variance-covariance function
zs = lmtest::coeftest(mod, vcov. = sandwich::vcovHC)[,'z value']

# get RESI estimates using unbiased estimator
z2S(zs, n = nrow(RESI::insurance))

# get RESI estimates usng alternative estimator
z2S(zs, n = nrow(RESI::insurance), unbiased = FALSE)