[SOLVED] Using BCNPower Transform (car) and emmeans

Using BCNPower Transform (car) and emmeans

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

Solution

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.