Using BCNPower Transform (car) and emmeans

Question

The car package in R implements Box-Cox with non-positives (BCN). This is not a standard Box-Cox transformation, although it builds on it.

The emmeans package can handled transformed data. It can back transform if the proper functions are defined. There are built-in transformations under make.tran. This is the interface emmeans uses.

make.tran returns a list containing the transformation, its inverse, the jacobian, and a function to test the domain.

How can you add the BCN transformation to the built-in ones?

Is it a matter of simply creating a new list with the proper content (like specified by make.tran) and using this within the environment calling emmeans?

Thanks

Answer 1

Here is something that works. You need to set global variables lambda and gamma equal to the corresponding parameter values as documented for car::bcnPower().

tran = list (
   linkfun = function(mu) {
       s = sqrt(mu^2 + gamma^2)
       if (abs(lambda) < 1e-10) log(.5*(mu + s))
       else ((0.5 * (mu + s))^lambda - 1) / lambda  },
   linkinv = function(eta) {
       q = if (abs(lambda) < 1e-10) 2 * exp(eta)
       else 2 * (lambda * eta + 1) ^ (1/lambda)
       (q^2 - gamma^2) / (2 * q) },
   mu.eta = function(eta) {
       if (abs(lambda) < 1e-10) { q = 2 * exp(eta); dq = q }
       else { q = 2 * (lambda * eta + 1) ^ (1/lambda)
       dq = 2 * (lambda * eta + 1)^(1/lambda - 1) }
       0.5 * (1 + (gamma/q)^2) * dq },
   valideta = function(eta) all(eta > 0),
   param = c(lambda, gamma),
   name = paste0("bcnPower(", signif(lambda,3), ", ", signif(gamma,3), ")")
)

Then use tran as if you had created it via make.tran().

This will be available by way of make.tran("bcnPower, c(lambda, gamma)) after a month or more, when the next release is uploaded to CRAN.