ace(x, y, wt=<<see below>>, monotone=NULL, linear=NULL, categorical=NULL, circular=NULL, tolerance=0.01, n.solution=1)
wt
should be the same as the length of
y
.
By default an unweighted regression is carried out (all weights unity).
Missing values are not accepted.
monotone
refer to the columns of the
x
matrix,
0
refers
to
y
.
linear
refer to columns of the
x
matrix and
0
refers to the
y
variable.
categorical
refer to columns of the
x
matrix,
0
to
y
.
circular
refer to columns of the
x
matrix,
0
to
y
.
All values of a circular variable must lie in the range [0, 1]; if
this is not true, a general ordered (default) transformation will be performed.
tolerance
in 3 consecutive iterations.
x
or a list of length
n.solution
of objects like
x
(if
n.solution
is greater than
1
) containing the transformed
x
values.
n.solution
of vectors
(if
n.solution
is greater than
1
) containing the transformed
y
values.
ace
stands for Alternating Conditional Expectation.
Transformations are iteratively found using Super Smoother
until the correlation fails to increase.
The default transformation assumes (for purposes of smoothing) that values
of the variable imply an ordering of the variable but no restriction is placed
on the transformation.
The data are passed into the Fortran routine in single precision, but key
calculations are performed in double precision.
If the first and second solutions have approximately equal (and large)
rsq
, then any linear combination of the two transformations will have
a large
rsq
as well.
Such an occurrence may be due to clustering in the
x
variables so that
an approximate step function is optimal.
Breiman, L. and Friedman, J. H. (1985).
Estimating optimal transformations for multiple regression and correlation.
(with discussion).
Journal of the American Statistical Association
80, 580-619.
The chapter "Regression and Smoothing for Continuous Response Data" in the S-PLUS Guide to Statistical and Mathematical Analysis.
x <- runif(200,0,2*pi) y <- exp(sin(x)+rnorm(200)/2) exace <- ace(x,y)