Dimension reduction regression returns a set of up to p orthogonal direction vectors each of length p, the first d of which are estimates a basis of a d dimensional central subspace. The function returns the estimated directions in the original n dimensional space for plotting.
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a dimension reduction regression object created by dr.
select the directions wanted, default is all directions.
If method is
The number of basis vectors to return
select the X matrix, the default is
Dimension reduction regression is used to estimate a basis of the central
subspace or mean central subspace of a regression. If there are p
predictors, the dimension of the central subspace is less than or equal to
p. These two functions,
return vectors that describe the central subspace in various ways.
dr.basis first. If you set
numdir=3, for example, this
method will return a p by 3 matrix whose columns span the estimated
three dimensional central subspace. For all methods except for
this simply returns the first three columns of
ire method, this returns the three vectors determined by a
three-dimensional solution. Call this matrix C. The basis is
determined by back-transforming from centered and scaled predictors to
the scale of the original predictors, and then renormalizing the vectors
to have length one. These vectors are orthogonal in the inner
product determined by Var(X).
dr.direction method return XC, the same space but now a
subspace of the original n-dimensional space. These vectors are
appropriate for plotting.
Both functions return a matrix: for
dr.direction, the matrix has n rows and
numdir columns, and for
dr.basis it has p rows and numdir columns.
Sanford Weisberg <[email protected]>
See R. D. Cook (1998). Regression Graphics. New York: Wiley.
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