R: Sufficient Dimension Reduction

sdr {spatstat.core} | R Documentation

## Sufficient Dimension Reduction

### Description

Given a point pattern and a set of predictors, find a minimal set of new predictors, each constructed as a linear combination of the original predictors.

### Usage

    sdr(X, covariates, ...)

    ## S3 method for class 'ppp'
    sdr(X, covariates,
                      method = c("DR", "NNIR", "SAVE", "SIR", "TSE"),
                      Dim1 = 1, Dim2 = 1, predict=FALSE, ...)

### Arguments

`X` | A point pattern (object of class `"ppp"`).
`covariates` | A list of pixel images (objects of class `"im"`) to serve as predictor variables.
`method` | Character string indicating which method to use. See Details.
`Dim1` | Dimension of the first order Central Intensity Subspace (applicable when `method` is `"DR"`, `"NNIR"`, `"SAVE"` or `"TSE"`).
`Dim2` | Dimension of the second order Central Intensity Subspace (applicable when `method="TSE"`).
`predict` | Logical value indicating whether to compute the new predictors as well.
`...` | Additional arguments (ignored by `sdr.ppp`).

### Details

Given a point pattern X and predictor variables Z[1], ..., Z[p], Sufficient Dimension Reduction methods (Guan and Wang, 2010) attempt to find a minimal set of new predictor variables, each constructed by taking a linear combination of the original predictors, which explain the dependence of X on Z[1], ..., Z[p]. The methods do not assume any particular form of dependence of the point pattern on the predictors. The predictors are assumed to be Gaussian random fields.

Available methods are:

`method="DR"` | directional regression
`method="NNIR"` | nearest neighbour inverse regression
`method="SAVE"` | sliced average variance estimation
`method="SIR"` | sliced inverse regression
`method="TSE"` | two-step estimation

The result includes a matrix `B` whose columns are estimates of the basis vectors of the space of new predictors. That is, the `j`th column of `B` expresses the `j`th new predictor as a linear combination of the original predictors.

If `predict=TRUE`, the new predictors are also evaluated. They can also be evaluated using `sdrPredict`.

### Value

A list with components `B, M` or `B, M1, M2` where `B` is a matrix whose columns are estimates of the basis vectors for the space, and `M` or `M1,M2` are matrices containing estimates of the kernel.

If `predict=TRUE`, the result also includes a component `Y` which is a list of pixel images giving the values of the new predictors.

### Author(s)

Matlab original by Yongtao Guan, translated to R by Suman Rakshit.

### References

Guan, Y. and Wang, H. (2010) Sufficient dimension reduction for spatial point processes directed by Gaussian random fields. Journal of the Royal Statistical Society, Series B, 72, 367–387.

### See Also

`sdrPredict` to compute the new predictors from the coefficient matrix.

`dimhat` to estimate the subspace dimension.

`subspaceDistance`

### Examples

       A <- sdr(bei, bei.extra, predict=TRUE)
       A
       Y1 <- A$Y[[1]]
       plot(Y1)
       points(bei, pch=".", cex=2)
       # investigate likely form of dependence
       plot(rhohat(bei, Y1))

[Package spatstat.core version 2.3-1 Index]