car (version 3.0-10)

testTransform: Likelihood-Ratio Tests for Univariate or Multivariate Power Transformations to Normality


testTransform computes likelihood ratio tests for particular values of the power parameter based on powerTransform objects.


testTransform(object, lambda)

# S3 method for powerTransform testTransform(object, lambda=rep(1, dim(object$y)[2]))

# S3 method for lmerModpowerTransform testTransform(object, lambda=1)

# S3 method for bcnPowerTransformlmer testTransform(object, lambda=1)



An object created by a call to powerTransform.


A vector of powers of length equal to the number of variables transformed.


A data frame with one row giving the value of the test statistic, its degrees of freedom, and a p-value. The test is the likelihood ratio test, comparing the value of the log-likelihood at the hypothesized value to the value of the log-likelihood at the maximum likelihood estimate.


The function powerTransform is used to estimate a power transformation for a univariate or multivariate sample or multiple linear regression problem, using the method of Box and Cox (1964). It is usual to round the estimates to nearby convenient values, and this function is use to compulte a likelihood ratio test for values of the transformation parameter other than the ml-type estimate.

For one-parameter families of transformations, namely the Box-Cox power family bcPower and the Yeo-Johnson power family yjPower, this function computes a test based on twice the difference in the log-likelihood between the maximum likelihood-like estimate and the log-likelihood evaluated at the value of lambda specified.

For the bcnPower Box-Cox power with negatives allowed, the test is based on the profile loglikelihood maximizing over the location (or gamma) parameter(s). Thus, gamma is treated as a nusiance parameter.


Box, G. E. P. and Cox, D. R. (1964) An analysis of transformations. Journal of the Royal Statisistical Society, Series B. 26 211-46.

Cook, R. D. and Weisberg, S. (1999) Applied Regression Including Computing and Graphics. Wiley.

Fox, J. and Weisberg, S. (2019) An R Companion to Applied Regression, Third Edition, Sage.

Weisberg, S. (2014) Applied Linear Regression, Fourth Edition, Wiley.

See Also

powerTransform and bcnPower for examples of the use of this function and other tests that might be of interest in some circumstances.


summary(a3 <- powerTransform(cbind(len, adt, trks, sigs1) ~ htype, Highway1))
# test lambda = (0 0 0 -1)
testTransform(a3, c(0, 0, 0, -1))
summary(q1 <- powerTransform(lm(cbind(LoBD$I1L2, LoBD$I1L1) ~ pool, LoBD), family="bcnPower"))
testTransform(q1, c(.3, .8))

# }