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Compute the robust effect size index estimate from t statistic (default)

Source: R/t2S.R
t2S.Rd

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.

Usage

t2S(t, rdf, n, unbiased = TRUE)

Arguments

t

The t statistic for the parameter of interest.

rdf

Model residual degrees of freedom/degrees of freedom of the t statistic.

n

Number of independent samples.

unbiased

Logical, whether to use unbiased or alternative estimator. See details.

Value

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

Details

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

The formula for the unbiased conversion is:

\(S = (t * \sqrt(2) * \Gamma(rdf/2)) / (\sqrt(n * rdf) * \Gamma((rdf - 1)/2))\)

The formula for the alternative estimator is derived by squaring the t statistic and using the f2S formula. This estimator may be appealing for its intuitive relationship to the F statistic; the absolute value of RESI estimates using this formula will be equal to a RESI estimate using an F 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:

\( \sqrt(max(0, (t^2 * (rdf - 2)/rdf - 1)/rdf))\)

Examples

# to obtain t values, first fit a lm
mod = lm(charges ~ region * age + bmi + sex, data = RESI::insurance)
# run lmtest::coeftest to get t values, using a robust variance-covariance formula
ts = lmtest::coeftest(mod, vcov. = sandwich::vcovHC)[,'t value']

# get RESI estimates using unbiased estimator
t2S(ts, n = nrow(RESI::insurance), rdf = mod$df.residual)
#>         (Intercept)     regionnorthwest     regionsoutheast     regionsouthwest 
#>        -0.067297337        -0.026687397        -0.033398602        -0.002467535 
#>                 age                 bmi             sexmale regionnorthwest:age 
#>         0.149720414         0.152301107         0.058360820         0.016662071 
#> regionsoutheast:age regionsouthwest:age 
#>         0.036086004        -0.014963251 

# get RESI estimates using alternative estimator
t2S(ts, n = nrow(RESI::insurance), rdf = mod$df.residual, unbiased = FALSE)
#>         (Intercept)     regionnorthwest     regionsoutheast     regionsouthwest 
#>         -0.06148040          0.00000000         -0.01917451          0.00000000 
#>                 age                 bmi             sexmale regionnorthwest:age 
#>          0.14717461          0.14979819          0.05154917          0.00000000 
#> regionsoutheast:age regionsouthwest:age 
#>          0.02354410          0.00000000