Response-transformation extensions
The make.tran function creates the needed information to perform
transformations of the response
variable, including inverting the transformation and estimating variances of
back-transformed predictions via the delta method. make.tran is
similar to make.link, but it covers additional transformations.
The result can be used as an environment in which the model is fitted, or as
the tran argument in update.emmGrid (when the given
transformation was already applied in an existing model).
make.tran(type = c("genlog", "power", "boxcox", "sympower", "asin.sqrt",
"bcnPower", "scale"), param = 1, y, ...)type |
The name of the transformation. See Details. |
param |
Numeric parameter needed for the transformation. Optionally, it may be a vector of two numeric values; the second element specifies an alternative base or origin for certain transformations. See Details. |
y, ... |
Used only with |
The functions emmeans, ref_grid, and related ones
automatically detect response transformations that are recognized by
examining the model formula. These are log, log2, log10,
sqrt, logit, probit, cauchit, cloglog; as
well as (for a response variable y) asin(sqrt(y)),
asinh(sqrt(y)), and sqrt(y) + sqrt(y+1). In addition, any
constant multiple of these (e.g., 2*sqrt(y)) is auto-detected and
appropriately scaled (see also the tran.mult argument in
update.emmGrid).
A few additional character strings may be supplied as the tran
argument in update.emmGrid: "identity",
"1/mu^2", "inverse", "reciprocal", "log10", "log2", "asin.sqrt",
and "asinh.sqrt".
More general transformations may be provided as a list of functions and
supplied as the tran argument as documented in
update.emmGrid. The make.tran function returns a
suitable list of functions for several popular transformations. Besides being
usable with update, the user may use this list as an enclosing
environment in fitting the model itself, in which case the transformation is
auto-detected when the special name linkfun (the transformation
itself) is used as the response transformation in the call. See the examples
below.
Most of the transformations available in "make.tran" require a parameter,
specified in param; in the following discussion, we use p to
denote this parameter, and y to denote the response variable.
The type argument specifies the following transformations:
"genlog"Generalized logarithmic transformation: log(y + p), where y > -p
"power"Power transformation: y^p, where y > 0.
When p = 0, "log" is used instead
"boxcox"The Box-Cox transformation (unscaled by the geometric mean): (y^p - 1) / p, where y > 0. When p = 0, log(y) is used.
"sympower"A symmetrized power transformation on the whole real line: abs(y)^p * sign(y). There are no restrictions on y, but we require p > 0 in order for the transformation to be monotone and continuous.
"asin.sqrt"Arcsin-square-root transformation: sin^(-1)(y/p)^{1/2)}. Typically, the parameter p is equal to 1 for a fraction, or 100 for a percentage.
"bcnPower"Box-Cox with negatives allowed, as described for the
bcnPower function in the car package. It is defined as the Box-Cox
transformation (z^p - 1) / p of the variable z = y + (y^2+g^2)^(1/2).
This requires param to have two elements:
the power p and the offset g > 0.
"scale"This one is a little different than the others, in that
param is ignored; instead, param is determined by calling
scale(y, ...). The user should give as y the response variable in the
model to be fitted to its scaled version.
The user may include a second element in param to specify an
alternative origin (other than zero) for the "power", "boxcox",
or "sympower" transformations. For example, type = "power",
param = c(1.5, 4) specifies the transformation (y - 4)^1.5.
In the "genpower" transformation, a second param element may be
used to specify a base other than the default natural logarithm. For example,
type = "genlog", param = c(.5, 10) specifies the log10(y + .5)
transformation. In the "bcnPower" transformation, the second element
is required and must be positive.
For purposes of back-transformation, the sqrt(y) + sqrt(y+1) transformation is treated exactly the same way as 2*sqrt(y), because both are regarded as estimates of 2√μ.
A list having at least the same elements as those returned by
make.link. The linkfun component is the transformation
itself.
The genlog transformation is technically unneeded, because
a response transformation of the form log(y + c) is now auto-detected
by ref_grid.
We modify certain make.link results in transformations
where there is a restriction on valid prediction values, so that reasonable
inverse predictions are obtained, no matter what. For example, if a
sqrt transformation was used but a predicted value is negative, the
inverse transformation is zero rather than the square of the prediction. A
side effect of this is that it is possible for one or both confidence
limits, or even a standard error, to be zero.
# Fit a model using an oddball transformation:
bctran <- make.tran("boxcox", 0.368)
warp.bc <- with(bctran,
lm(linkfun(breaks) ~ wool * tension, data = warpbreaks))
# Obtain back-transformed LS means:
emmeans(warp.bc, ~ tension | wool, type = "response")
### Using a scaled response...
# Case where it is auto-detected:
fib.lm <- lm(scale(strength) ~ diameter + machine, data = fiber)
ref_grid(fib.lm)
# Case where scaling is not auto-detected -- and what to do about it:
fib.aov <- aov(scale(strength) ~ diameter + Error(machine), data = fiber)
fib.rg <- suppressWarnings(ref_grid(fib.aov, at = list(diameter = c(20, 30))))
# Scaling was not retrieved, so we can do:
fib.rg = update(fib.rg, tran = make.tran("scale", y = fiber$strength))
emmeans(fib.rg, "diameter")
## Not run:
### An existing model 'mod' was fitted with a y^(2/3) transformation...
ptran = make.tran("power", 2/3)
emmeans(mod, "treatment", tran = ptran)
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.