ace
From acepack v1.4.1
by Shawn Garbett
Alternating Conditional Expectations
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.
 Keywords
 models
Usage
ace(x, y, wt = rep(1, nrow(x)), cat = NULL, mon = NULL, lin = NULL, circ = NULL, delrsq = 0.01)
Arguments
 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
cat
refer to columns of thex
matrix and zero to the response variable. Variables must be numeric, so a character variable should first be transformed with as.numeric() and then specified as categorical.  mon
 an optional integer vector specifying which variables are
to be transformed by monotone transformations. Positive values
in
mon
refer to columns of thex
matrix and zero to the response variable.  lin
 an optional integer vector specifying which variables are
to be transformed by linear transformations. Positive values in
lin
refer to columns of thex
matrix and zero to the response variable.  circ
 an integer vector specifying which variables assume
circular (periodic) values. Positive values in
circ
refer to columns of thex
matrix and zero to the response variable.  delrsq
 termination threshold. Iteration stops when Rsquared
changes by less than
delrsq
in 3 consecutive iterations (default 0.01).
Value

A structure with the following components:
References
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.
Examples
library(acepack)
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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