Additivity and Variance Stabilization for Regression

DESCRIPTION:

Computes a form of nonlinear regression which transforms both the dependent and independent variables to produce an additive model with constant residual variance.

USAGE:

avas(x, y, wt=<<see below>>, monotone=NULL, linear=NULL,  
      categorical=NULL, circular=NULL, tolerance=0.01, span.var="cv") 

REQUIRED ARGUMENTS:

x
vector or matrix containing the explanatory variables. Columns represent variables and rows represent observations. Missing values are not accepted.
y
vector containing the response variable. This must have the same number of observations as x. Missing values are not accepted.

OPTIONAL ARGUMENTS:

wt
vector of weights. The length of wt should be the same as the length of y. By default an unweighted regression is carried out (all weights are unity).
monotone
integer vector specifying which variables are to be transformed by monotone transformations. Values in monotone refer to the columns of the x matrix.
linear
integer vector specifying which variables are to be transformed by linear transformations. Positive values in linear refer to columns of the x matrix and a zero value refers to the y variable.
categorical
integer vector specifying which variables assume categorical values. Values in categorical refer to columns of the x matrix.
circular
integer vector specifying which variables assume circular (periodic) values. Values in circular refer to columns of the x matrix. A variable specified as circular that has values outside the range [0, 1] will be transformed using the default (general ordered) transformation.
tolerance
termination threshold. Iteration stops when the multiple R-squared changes by less than tolerance in 3 consecutive iterations.
span.var
fraction of the data used for smoothing the variance, span.var must lie between 0 and 1, or can be set to the character string "cv" for cross validation.

VALUE:

a list with the following components:
tx
vector or matrix of the transformed x values. This is a vector when there is only one x variable.
ty
vector like y of the transformed y values.
rsq
the multiple R-squared value for the transformed values.
iterations
iteration number.
span.var
actual span used for smoothing the variance.

DETAILS:

The y variable can only be transformed using the linear or general ordered (the default) transformations.

REFERENCES:

Tibshirani, R. (1988). Estimating transformations for regression via additivity and variance stabilization. Journal of the American Statistical Association 83, 394-405.

The chapter "Regression and Smoothing for Continous Response Data" in the S-PLUS Guide to Statistical and Mathematical Analysis.

SEE ALSO:

, , .

EXAMPLES:

x <- runif(200, 0, 2*pi);  y <- exp(sin(x)+rnorm(200)/2) 
a <- avas(x, y) 
plot(y, a$ty) # view the response transformation 
plot(x, a$tx) # view the carrier transformation 
plot(a$tx, a$ty) # examine the linearity of the fitted model