skewPower {car} | R Documentation |
Transform the elements of a vector using, the skew power transformations.
skewPower(U, lambda, jacobian.adjusted=FALSE, gamma) ## S3 method for class 'skewpowerTransform' contour(x, ksds = 4, levels = c(0.5, 0.95, 0.99, 0.999), main = "Skew Power Log-likelihood", ...) ## S3 method for class 'skewpowerTransformlmer' contour(x, ksds = 4, levels = c(0.5, 0.95, 0.99, 0.999), main = "Skew Power Log-likelihood", ...)
U |
A vector, matrix or data.frame of values to be transformed |
lambda |
The one-dimensional transformation parameter, usually in
the range from -2 to 2, or if |
jacobian.adjusted |
If |
gamma |
The skew power family has two parameters, the power lambda, and the start gamma, which can be any positive value. |
x |
An object created by a call to |
ksds |
Contour plotting of the log-likelihood surface will cover plus of minus |
levels |
Contours will be drawn at the values of levels. For example, |
main |
Title for the contour plot |
... |
Additional arguments passed to the generic contour function. |
The skewPower
family is a modification of the Box-Cox power family, see bcPower
that allows the untransformed response to include negative values. Ignoring the Jacobian, correction, the Box-Cox family is defined to be (U^(lambda)-1)/lambda
for lambda not equal to zero, and
log(U) if lambda = 0. The skewPower family
is the Box-Cox transformation of z = .5 * (U + (U^2 + γ^2)^{1/2}). Zero or negative values for \code{U} are permitted if gamma is positive.
If jacobian.adjusted
is TRUE
, then the transformed values are scaled to have Jacobian equal to 1, as suggested by Box and Cox (1964). This simplifies computing the maximum likelihood-like estimates of the transformation parameters.
Missing values are permitted, and return NA
where ever U
is equal to NA
.
The contour method allows drawing a contour plot for the two-dimensional log-likelihood for the skew power parameters with a univariate response.
Returns a vector or matrix of transformed values. The contour method is used for the side-effect of drawing a contour plot.
Sanford Weisberg, <sandy@umn.edu>
Fox, J. and Weisberg, S. (2011) An R Companion to Applied Regression, Second Edition, Sage.
Hawkins, D. and Weisberg, S. (2016) Combining the Box-Cox Power and Generalized Log Transformations to Accomodate Negative Responses In Linear and Mixed-Effects Linear Models, submitted for publication.
Weisberg, S. (2014) Applied Linear Regression, Fourth Edition, Wiley Wiley, Chapter 7.
powerTransform
, bcPower
, boxCox
# Univariate Example, from Hawkins and Weisberg (2016) m1 <- lm(I1L1 ~ pool, LoBD) p1 <- powerTransform(m1, family="skewPower") summary(p1) # summary prints estimate, se and conf.ints for both parameters # helper functions c(p1$lambda, p1$gamma, LogLik=p1$llik) vcov(p1) # Estimated covarinace from inverse Hessian # tests are for lambda, maximizing over gamma (profile log-likelihoods testTransform(p1, lambda=0.5) # Contour plot of the log-likelihood contour(p1, main="", levels=c(.5, .95, .99)) # the boxCox function can provide profile log-likelihoods for each of the two parameters: boxCox(m1, family="skewPower", param="lambda", lambda=seq(0.25, 1.1, length=100)) boxCox(m1, family="skewPower", param="gamma", gamma=seq(3, 80, length=100)) # Fit with fixed gamma, in this case fixed at the estimate from p1 p2 <- powerTransform(m1, family="skewPower", gamma=p1$gamma) # summary gives different tests because gamma is fixed rather than maximized over summary(p2) # Multivariate Response p3 <- powerTransform(update(m1, as.matrix(cbind(LoBD$I1L2, LoBD$I1L1)) ~ .), family="skewPower") summary(p3) # gamma fixed p4 <- powerTransform(update(m1, as.matrix(cbind(LoBD$I1L2, LoBD$I1L1)) ~ .), family="skewPower", gamma=p3$gamma) summary(p4) # mixed models fit with lmer - requires lmer and nloptr packages ## Not run: data <- reshape(LoBD[1:20,], varying=names(LoBD)[-1], direction="long", v.names="y") names(data) <- c("pool", "assay", "y", "id") data$assay <- factor(data$assay) require(lme4) m2 <- lmer(y ~ pool + (1|assay), data) f1 <- powerTransform(m2, family="skewPower") summary(f1) f2 <- powerTransform(m2, family="skewPower", gamma= 10) summary(f2) ## End(Not run)