dr.slices.RdDivides a vector into slices of approximately equal size.
dr.slices(y, nslices)
dr.slices.arc(y, nslices)a vector of length \(n\) or an \(n \times p\) matrix
the number of slices, no larger than \(n\), or a vector of \(p\) numbers giving the number of slices in each direction. If \(y\) has \(p\) columns and nslices is a number, then the number of slices in each direction is the smallest integer greater than the p-th root of nslices.
If \(y\) is an n-vector, order \(y\). The goal for the number of observations per slice
is \(m\), the smallest integer in nslices/n. Allocate the first \(m\) observations to
slice 1. If there are duplicates in \(y\), keep adding observations to the first
slice until the next value of \(y\) is not equal to the largest value in the
first slice. Allocate the next \(m\) values to the next slice, and again check
for ties. Continue until all values are allocated to a slice. This does not
guarantee that nslices will be obtained, nor does it guarantee an equal number
of observations per slice. This method of choosing slices is invariant under
rescaling, but not under multiplication by \(-1\), so the slices of \(y\) will not
be the same as the slices of \(-y\). This function was rewritten for Version 2.0.4 of
this package, and will no longer give exactly the same results as the program Arc. If you
want to duplicate Arc, use the function dr.slice.arc, as illustrated in the
example below.
If \(y\) is a matrix of p columns, slice the first column as described above. Then, within each of the slices determined for the first column, slice based on the second column, so that each of the “cells” has approximately the same number of observations. Continue through all the columns. This method is not invariant under reordering of the columns, or under multiplication by \(-1\).
Returns a named list with three elements as follows:
ordered eigenvectors that describe the estimates of the dimension reduction subspace
Gives the actual number of slices produced, which may be smaller than the number requested.
The number of observations in each slice.
R. D. Cook and S. Weisberg (1999), Applied Regression Including Computing and Graphics, New York: Wiley.
data(ais)
summary(s1 <- dr(LBM~log(SSF)+log(Wt)+log(Hg)+log(Ht)+log(WCC)+log(RCC)+
log(Hc)+log(Ferr), data=ais,method="sir",nslices=8))
#>
#> Call:
#> dr(formula = LBM ~ log(SSF) + log(Wt) + log(Hg) + log(Ht) + log(WCC) +
#> log(RCC) + log(Hc) + log(Ferr), data = ais, method = "sir",
#> nslices = 8)
#>
#> Method:
#> sir with 8 slices, n = 202.
#>
#> Slice Sizes:
#> 25 25 25 25 27 27 30 18
#>
#> Estimated Basis Vectors for Central Subspace:
#> Dir1 Dir2 Dir3 Dir4
#> log(SSF) 0.155356 0.045363 -0.08080 0.007174
#> log(Wt) -0.969123 0.006309 0.28789 0.249082
#> log(Hg) -0.157412 -0.456823 -0.00915 -0.045435
#> log(Ht) -0.054094 0.315217 -0.68876 -0.542777
#> log(WCC) 0.005472 0.007850 -0.01038 -0.061888
#> log(RCC) -0.006035 -0.419167 0.08569 0.566282
#> log(Hc) 0.094247 0.716934 -0.65463 -0.555732
#> log(Ferr) -0.003480 0.009819 0.01067 -0.088837
#>
#> Dir1 Dir2 Dir3 Dir4
#> Eigenvalues 0.9391 0.2220 0.09066 0.06427
#> R^2(OLS|dr) 0.9991 0.9991 0.99925 0.99926
#>
#> Large-sample Marginal Dimension Tests:
#> Stat df p.value
#> 0D vs >= 1D 269.35 56 0.0000000
#> 1D vs >= 2D 79.66 42 0.0004021
#> 2D vs >= 3D 34.82 30 0.2492051
#> 3D vs >= 4D 16.51 20 0.6847223
# To make this idential to ARC, need to modify slices to match.
summary(s2 <- update(s1,slice.info=dr.slices.arc(ais$LBM,8)))
#>
#> Call:
#> dr(formula = LBM ~ log(SSF) + log(Wt) + log(Hg) + log(Ht) + log(WCC) +
#> log(RCC) + log(Hc) + log(Ferr), data = ais, method = "sir",
#> nslices = 8, slice.info = dr.slices.arc(ais$LBM, 8))
#>
#> Method:
#> sir with 8 slices, n = 202.
#>
#> Slice Sizes:
#> 25 25 25 25 27 27 30 18
#>
#> Estimated Basis Vectors for Central Subspace:
#> Dir1 Dir2 Dir3 Dir4
#> log(SSF) 0.155356 0.045363 -0.08080 0.007174
#> log(Wt) -0.969123 0.006309 0.28789 0.249082
#> log(Hg) -0.157412 -0.456823 -0.00915 -0.045435
#> log(Ht) -0.054094 0.315217 -0.68876 -0.542777
#> log(WCC) 0.005472 0.007850 -0.01038 -0.061888
#> log(RCC) -0.006035 -0.419167 0.08569 0.566282
#> log(Hc) 0.094247 0.716934 -0.65463 -0.555732
#> log(Ferr) -0.003480 0.009819 0.01067 -0.088837
#>
#> Dir1 Dir2 Dir3 Dir4
#> Eigenvalues 0.9391 0.2220 0.09066 0.06427
#> R^2(OLS|dr) 0.9991 0.9991 0.99925 0.99926
#>
#> Large-sample Marginal Dimension Tests:
#> Stat df p.value
#> 0D vs >= 1D 269.35 56 0.0000000
#> 1D vs >= 2D 79.66 42 0.0004021
#> 2D vs >= 3D 34.82 30 0.2492051
#> 3D vs >= 4D 16.51 20 0.6847223