# ace

0th

Percentile

##### 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 the x 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 the x 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 the x 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 the x matrix and zero to the response variable.
delrsq
termination threshold. Iteration stops when R-squared 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 double-precision version of FORTRAN code by Friedman and Spector in the Statlib general archive.

• ace
##### 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, 243-258. X1 <- runif(100)*2-1 X2 <- runif(100)*2-1 X3 <- runif(100)*2-1 X4 <- runif(100)*2-1 # 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) 
Documentation reproduced from package acepack, version 1.4.1, License: MIT + file LICENSE

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