Package 'acepack' reference manual

Title:	ACE and AVAS for Selecting Multiple Regression Transformations
Description:	Two nonparametric methods for multiple regression transform selection are provided. The first, Alternative Conditional Expectations (ACE), is an algorithm to find the fixed point of maximal correlation, i.e. it finds a set of transformed response variables that maximizes R^2 using smoothing functions [see Breiman, L., and J.H. Friedman. 1985. "Estimating Optimal Transformations for Multiple Regression and Correlation". Journal of the American Statistical Association. 80:580-598. <doi:10.1080/01621459.1985.10478157>]. Also included is the Additivity Variance Stabilization (AVAS) method which works better than ACE when correlation is low [see Tibshirani, R.. 1986. "Estimating Transformations for Regression via Additivity and Variance Stabilization". Journal of the American Statistical Association. 83:394-405. <doi:10.1080/01621459.1988.10478610>]. A good introduction to these two methods is in chapter 16 of Frank Harrel's "Regression Modeling Strategies" in the Springer Series in Statistics.
Authors:	Phil Spector [aut], Jerome Friedman [aut], Robert Tibshirani [aut], Thomas Lumley [aut], Shawn Garbett [cre, aut] , Jonathan Baron [aut]
Maintainer:	Shawn Garbett <[email protected]>
License:	MIT + file LICENSE
Version:	1.5.2
Built:	2025-01-27 23:32:19 UTC
Source:	CRAN

Alternating Conditional Expectations

Description

Uses the alternating conditional expectations algorithm to find the transformations of y and x that maximize 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.

Usage

ace(
  x,
  y,
  wt = rep(1, nrow(x)),
  cat = NULL,
  mon = NULL,
  lin = NULL,
  circ = NULL,
  delrsq = 0.01,
  control = NULL
)
ace(
  x,
  y,
  wt = rep(1, nrow(x)),
  cat = NULL,
  mon = NULL,
  lin = NULL,
  circ = NULL,
  delrsq = 0.01,
  control = NULL
)

Arguments

`x`	matrix; A matrix containing the independent variables.
`y`	numeric; A vector containing the response variable.
`wt`	numeric; An optional vector of weights.
`cat`	integer; 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`	integer; 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`	integer; 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`	integer; 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`	numeric(1); termination threshold. Iteration stops when R-squared changes by less than `delrsq` in 3 consecutive iterations (default 0.01).
`control`	named list; control parameters to set. Documented at `set_control`.

Value

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 R-squared value for the transformed values.
`l`	the codes for cat, mon, ...

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.

Examples


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)

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)

Additivity and variance stabilization for regression

Description

Estimate transformations of x and y such that the regression of y on x is approximately linear with constant variance

Usage

avas(
  x,
  y,
  wt = rep(1, nrow(x)),
  cat = NULL,
  mon = NULL,
  lin = NULL,
  circ = NULL,
  delrsq = 0.01,
  yspan = 0,
  control = NULL
)
avas(
  x,
  y,
  wt = rep(1, nrow(x)),
  cat = NULL,
  mon = NULL,
  lin = NULL,
  circ = NULL,
  delrsq = 0.01,
  yspan = 0,
  control = NULL
)

Arguments

`x`	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
`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`	numeric(1); Termination threshold for iteration. Stops when R-squared changes by less than `delrsq` in 3 consecutive iterations (default 0.01).
`yspan`	yspan Optional window size parameter for smoothing the variance. Range is $[0,1]$ . Default is 0 (cross validated choice). .5 is a reasonable alternative to try.
`control`	named list; control parameters to set. Documented at `set_control`.

Value

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 R-squared value for the transformed values.
`l`	the codes for cat, mon, ...
`m`	not used in this version of avas
`yspan`	span used for smoothing the variance
`iters`	iteration number and rsq for that iteration
`niters`	number of iterations used

References

Rob Tibshirani (1987), “Estimating optimal transformations for regression”. Journal of the American Statistical Association 83, 394ff.

Examples


TWOPI <- 8*atan(1)
x <- runif(200,0,TWOPI)
y <- exp(sin(x)+rnorm(200)/2)
a <- avas(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

# From D. Wang and M. Murphy (2005), Identifying nonlinear relationships
# regression using the ACE algorithm.  Journal of Applied Statistics,
# 32, 243-258, adapted for avas.
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 <- avas(cbind(X1,X2,X3,X4),Y)

par(mfrow=c(2,1))

# 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.
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)

TWOPI <- 8*atan(1)
x <- runif(200,0,TWOPI)
y <- exp(sin(x)+rnorm(200)/2)
a <- avas(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

# From D. Wang and M. Murphy (2005), Identifying nonlinear relationships
# regression using the ACE algorithm.  Journal of Applied Statistics,
# 32, 243-258, adapted for avas.
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 <- avas(cbind(X1,X2,X3,X4),Y)

par(mfrow=c(2,1))

# 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.
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)

Set internal parameters that control ACE and AVAS algorithms

Description

These parameters are used in the smoothing routines of ACE and AVAS. ACE and AVAS both have their own smoothing implementations. This sets them globally for the package.

The default values are good for the vast majority of cases. This routine is included to provide complete control to the user, but is rarely needed.

Usage

set_control(
  alpha = NULL,
  big = NULL,
  span = NULL,
  sml = NULL,
  eps = NULL,
  spans = NULL,
  maxit = NULL,
  nterm = NULL
)
set_control(
  alpha = NULL,
  big = NULL,
  span = NULL,
  sml = NULL,
  eps = NULL,
  spans = NULL,
  maxit = NULL,
  nterm = NULL
)

Arguments

`alpha`	numeric(1); AVAS; Controls high frequency (small span) penalty used with automatic span selection (base tone control). An alpha < 0.0 or alpha > 10.0 results in no effect. Default is 5.0.
`big`	numeric(1); ACE and AVAS; a large floating point number. Default is 1.0e30.
`span`	numeric(1); ACE and AVAS; Span to use in smoothing represents the fraction of observations in smoothing window. Automatic span selection is performed if set to 0.0. Default is 0.0 (automatic). For small samples (n < 40) or if there are substantial serial correlations between observations close in x - value, then a specified fixed span smoother (span > 0) should be used. Reasonable span values are 0.3 to 0.5.
`sml`	numeric(1); AVAS; A small number. Should be set so that '(sml)**(10.0)' does not cause floating point underflow. Default is 1e-30.
`eps`	numeric(1); AVAS; Used to numerically stabilize slope calculations for running linear fits.
`spans`	numeric(3); AVAS; span values for the three running linear smoothers. "spans(1)" Tweeter span. Default is 0.05. "spans(2)" Midrange span. Default is 0.2. "spans(3)" Woofer span. Default is 0.5. Warning: These span values should be changed only with great care.
`maxit`	integer(1); ACE and AVAS; Maximum number of iterations. Default is 20.
`nterm`	integer(1); ACE and AVAS; Number of consecutive iterations for which rsq must change less than delcor for convergence. Default is 3.

Examples

set_control(maxit=40)
set_control(maxit=20)
set_control(alpha=5.0)
set_control(big=1e30, sml=1e-30)
set_control(eps=1e-3)
set_control(span=0.0, spans=c(0.05, 0.2, 0.5))
set_control(maxit=20, nterm=3)
set_control(maxit=40)
set_control(maxit=20)
set_control(alpha=5.0)
set_control(big=1e30, sml=1e-30)
set_control(eps=1e-3)
set_control(span=0.0, spans=c(0.05, 0.2, 0.5))
set_control(maxit=20, nterm=3)

Package 'acepack'

Help Index

Alternating Conditional Expectations

Description

Usage

Arguments

Value

References

Examples

Additivity and variance stabilization for regression

Description

Usage

Arguments

Value

References

Examples

Set internal parameters that control ACE and AVAS algorithms

Description

Usage

Arguments

Examples