ace  R Documentation 
Uses the alternating conditional expectations algorithm to find the transformations of y and x that maximise the proportion of variation in y explained by x. When x is a matrix, it is transformed so that its columns are equally weighted when predicting y.
ace(x, y, wt = rep(1, nrow(x)), cat = NULL, mon = NULL, lin = NULL,
circ = NULL, delrsq = 0.01)
x 
a matrix containing the independent variables. 
y 
a vector containing the response variable. 
wt 
an optional vector of weights. 
cat 
an optional integer vector specifying which variables
assume categorical values. Positive values in 
mon 
an optional integer vector specifying which variables are
to be transformed by monotone transformations. Positive values
in 
lin 
an optional integer vector specifying which variables are
to be transformed by linear transformations. Positive values in

circ 
an integer vector specifying which variables assume
circular (periodic) values. Positive values in 
delrsq 
termination threshold. Iteration stops when Rsquared
changes by less than 
A structure with the following components:
x 
the input x matrix. 
y 
the input y vector. 
tx 
the transformed x values. 
ty 
the transformed y values. 
rsq 
the multiple Rsquared value for the transformed values. 
l 
the codes for cat, mon, ... 
m 
not used in this version of ace 
Breiman and Friedman, Journal of the American Statistical Association (September, 1985).
The R code is adapted from S code for avas() by Tibshirani, in the Statlib S archive; the FORTRAN is a doubleprecision version of FORTRAN code by Friedman and Spector in the Statlib general archive.
TWOPI < 8*atan(1)
x < runif(200,0,TWOPI)
y < exp(sin(x)+rnorm(200)/2)
a < ace(x,y)
par(mfrow=c(3,1))
plot(a$y,a$ty) # view the response transformation
plot(a$x,a$tx) # view the carrier transformation
plot(a$tx,a$ty) # examine the linearity of the fitted model
# example when x is a matrix
X1 < 1:10
X2 < X1^2
X < cbind(X1,X2)
Y < 3*X1+X2
a1 < ace(X,Y)
plot(rowSums(a1$tx),a1$y)
(lm(a1$y ~ a1$tx)) # shows that the colums of X are equally weighted
# From D. Wang and M. Murphy (2005), Identifying nonlinear relationships
# regression using the ACE algorithm. Journal of Applied Statistics,
# 32, 243258.
X1 < runif(100)*21
X2 < runif(100)*21
X3 < runif(100)*21
X4 < runif(100)*21
# Original equation of Y:
Y < log(4 + sin(3*X1) + abs(X2) + X3^2 + X4 + .1*rnorm(100))
# Transformed version so that Y, after transformation, is a
# linear function of transforms of the X variables:
# exp(Y) = 4 + sin(3*X1) + abs(X2) + X3^2 + X4
a1 < ace(cbind(X1,X2,X3,X4),Y)
# For each variable, show its transform as a function of
# the original variable and the of the transform that created it,
# showing that the transform is recovered.
par(mfrow=c(2,1))
plot(X1,a1$tx[,1])
plot(sin(3*X1),a1$tx[,1])
plot(X2,a1$tx[,2])
plot(abs(X2),a1$tx[,2])
plot(X3,a1$tx[,3])
plot(X3^2,a1$tx[,3])
plot(X4,a1$tx[,4])
plot(X4,a1$tx[,4])
plot(Y,a1$ty)
plot(exp(Y),a1$ty)
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