y
as a sum of
nonparametric functions of projections of the
x
variables.
ppreg(x, y, min.term, max.term=min.term, wt=rep(1, nrow(x)), rwt=rep(1, ncol(y)), xpred=NULL, optlevel=2, bass=0, span="cv")
ppreg
function is not very useful if
x
contains only one column.
ppreg
will return complete results only for this minimum number of terms.
x
.
Missing values are not accepted.
y
.
Missing values are not accepted.
xpred
is omitted, then the original
x
data will be regressed on,
and the residuals will be returned in
ypred
.
Missing values are not accepted.
0
to
3
which determines the throughness of an optimization
routine in
ppreg
.
A higher number means more optimization.
supsmu
); the range of values is
0
to
10
, with
increasing values resulting in increased smoothing.
supsmu
).
The default is
"cv"
, which results in automatic span selection
by local cross validation.
span
can also take a value from 0 < span <= 1.
xpred
.
If
xpred
was not input,
then
ypred
contains the residuals for the model fit.
minterm
by
ncol(x)
matrix of the direction vectors,
alpha[m,j]
contains the j-th component of the direction in the m-th term.
minterm
by
ncol
(y) matrix of term weights,
beta[m,k]
contains the value of the term weight for the
m-th term and the k-th response variable.
zhat
.
z[i,m]
contains the z value of the i-th observation in the
m-th model term, i.e.,
z
equals x %*% t(alpha).
The columns of
z
have been sorted.
zhat[i,m]
is the smoothed ordinate value (phi) of the i-th
observation in the m-th model term evaluated at
z[i,m]
.
minterm
.
minterm
.
esq[M]
contains the fraction of unexplained variance
for the solution consisting of M terms.
Values are zero for M less than
minterm
.
ncol(y)
by
maxterm
containing the fraction of unexplained
variance for each response.
esqrsp[k,M]
is for
the k-th response variable for the solution consisting of M terms, for
M ranging from
min.term
to
max.term
.
Other columns are zero.
The
z
component of the result is sorted, thus it can not be compared
with the original data.
Friedman, J. H. and Stuetzle, W. (1981).
Projection pursuit regression.
Journal of the American Statistical Association
76, 817-823.
The chapter "Regression and Smoothing for Continuous Response Data" in the S-PLUS Guide to Statistical and Mathematical Analysis.
x1 <- rnorm(100) ; x2 <- rnorm(100) ; eps <- rnorm(100, 0, .1) x <- matrix(c(x1, x2), 100, 2) y <- x1*x2 + eps # Set up a matrix of predictor values. xpred <- matrix(c(0, 0, 0, 1, 1, 0, 1, 1), 4, 2, byrow=T) # Use ppreg with unit weights for both the observations and # the response, and a 2 term regression model (picked from 3 terms). a <- ppreg(x, y, 2, 3, xpred=xpred) # Plot the function values versus their abscissas, to look for structure. matplot(a$z, a$zhat)