avas  R Documentation 
Estimate transformations of x
and y
such that
the regression of y
on x
is approximately linear with
constant variance
avas(x, y, wt = rep(1, nrow(x)), cat = NULL, mon = NULL,
lin = NULL, circ = NULL, delrsq = 0.01, yspan = 0)
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 
yspan 
Optional window size parameter for smoothing the
variance. Range is 
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 avas 
yspan 
span used for smoothing the variance 
iters 
iteration number and rsq for that iteration 
niters 
number of iterations used 
Rob Tibshirani (1987), “Estimating optimal transformations for regression”. Journal of the American Statistical Association 83, 394ff.
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, 243258, adapted for avas.
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 < 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)
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