R: Sufficient Dimension Reduction for a Point Pattern on a...

sdr.lpp {spatstat.linnet} | R Documentation

## Sufficient Dimension Reduction for a Point Pattern on a Linear Network

### Description

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

### Usage

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

### Arguments

`X` | A point pattern on a linear network (object of class `"lpp"`).
`covariates` | A list of pixel images (objects of class `"im"` or `"linim"`) 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.
`...` | Extra arguments are ignored.

### Details

This is the method for `sdr` for the class `"lpp"` of point patterns on a linear network.

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)

Based on a Matlab original, for two-dimensional point patterns, by Yongtao Guan. Adapted to R, and to linear networks, 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

    #   sdr(bei, bei.extra)

       xim <- as.linim(function(x,y) { x }, simplenet)
       yim <- as.linim(function(x,y) { y }, simplenet)
       X <- runiflpp(30, simplenet)
       sdr(X, list(x=xim, y=yim))

[Package spatstat.linnet version 2.3-1 Index]