dataTrans: Scale invariant Box-Cox transformation

In fdaMixed: Functional Data Analysis in a Mixed Model Framework

Scale invariant Box-Cox transformation

Description

Performs forward and backward Box-Cox power transformation including the invariance scaling based on the geometric mean.

Usage

dataTrans(y, mu, direction = "backward", geoMean = NULL)

Arguments

y	The numeric variable object to be transformed.
mu	The power parameter, where zero corresponds to the logarithmic transformation.
direction	A character variable. If the lower case of the first letter equals "b" (default), then the backward transformation is performed. If the lower case of the first letter equals "f", then the forward transformation is performed.
geoMean	If a numeric is stated, then this is taken as the geometric mean of the untransformed observations. If NULL (default), then the geometric mean is computed from the observation y. The latter is only available for the forward transformation.

Value

The transformed variable.

Note

This function is intended to be used in conjunction with fdaLm to achieve estimates on the orginal scale. Thus, the geometric mean of the original observations should be kept in order to have the correct backtransformation.

Author(s)

Bo Markussen <[e-mail]>

Examples

# ----------------------------------------------------
# Make 3 samples with the following characteristics:
#   1) length N=500
#   2) sinusoid form + linear fixed effect + noise
#   3) exponential transformed
# ----------------------------------------------------

N <- 500
sample.time <- seq(0,2*pi,length.out=N)
z <- c("a","b","c")
x0 <- c(0,10,20)
x1 <- rep(x0,each=N)
y <- c(sin(sample.time),sin(sample.time),sin(sample.time))+x1+rnorm(3*N)

# Make exponential-Box-Cox-backtransformation
# Scaling with geometric mean requires that we solve the Whiteker function
geoMean <- mean(y)
geoMean <- uniroot(function(x){x*log(x)-geoMean},c(exp(-1),(1+geoMean)^2))$root
y <- dataTrans(y,0,"b",geoMean)

# ----------------------------------------------------
# Do fda's with global and marginal fixed effects
# Also seek to find Box-Cox transformation with mu=0
# ----------------------------------------------------

est0 <- fdaLm(y|z~x0,boxcox=1)
est1 <- fdaLm(y|z~x1,boxcox=1)

# -----------------------------------------------------
# Display results
# -----------------------------------------------------

# Panel 1
plot(sample.time,dataTrans(est0$betaHat[,"(Intercept)"]+est0$betaHat[,"x0"],
                           est0$boxcoxHat,"b",geoMean)/
                 dataTrans(est0$betaHat[,"(Intercept)"],est0$boxcoxHat,"b",geoMean),
     main="Effect of x (true=1.2)",xlab="time",
     ylab="response ratio")
abline(h=dataTrans(est1$betaHat["(Intercept)"]+est1$betaHat["x1"],
                   est1$boxcoxHat,"b",geoMean)/
         dataTrans(est1$betaHat["(Intercept)"],est1$boxcoxHat,"b",geoMean),col=2)
legend("topleft",c("marginal","global"),pch=c(1,NA),lty=c(NA,1),col=1:2)

# Panel 2
plot(sample.time,dataTrans(est0$betaHat[,"(Intercept)"]+est0$betaHat[,"x0"],
                           est0$boxcoxHat,"b",geoMean)-
                 dataTrans(est0$betaHat[,"(Intercept)"],est0$boxcoxHat,"b",geoMean),
     main="Effect of x (true=1)",xlab="time",
     ylab="response difference")
abline(h=dataTrans(est1$betaHat["(Intercept)"]+est1$betaHat["x1"],
                   est1$boxcoxHat,"b",geoMean)-
         dataTrans(est1$betaHat["(Intercept)"],est1$boxcoxHat,"b",geoMean),col=2)
legend("bottomleft",c("marginal","global"),pch=c(1,NA),lty=c(NA,1),col=1:2)

# Panel 3
plot(sample.time,est0$xBLUP[,1,1],type="l",
     main="Marginal ANOVA",xlab="time",ylab="x BLUP")

# Panel 4
plot(sample.time,est1$xBLUP[,1,1],type="l",
     main="Global ANOVA",xlab="time",ylab="x BLUP")
     

fdaMixed documentation built on Sept. 14, 2023, 1:09 a.m.