# sdr

##### Sufficient Dimension Reduction

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.

- Keywords
- multivariate, spatial

##### Usage

```
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.

##### Details

Given a point pattern \(X\) and predictor variables \(Z_1, \dots, Z_p\), 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 \(Z_1, \dots, Z_p\). 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 |
`method="DR"` |

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.

##### 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.

##### Examples

```
# NOT RUN {
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))
# }
```

*Documentation reproduced from package spatstat, version 1.55-1, License: GPL (>= 2)*