# trend.spatial: Builds the Trend Matrix In geoR: Analysis of Geostatistical Data

## Description

Builds the trend matrix in accordance to a specification of the mean provided by the user.

## Usage

 `1` ```trend.spatial(trend, geodata, add.to.trend) ```

## Arguments

 `trend` specifies the mean part of the model. See `DETAILS` below. `geodata` optional. An object of the class `geodata` as described in `as.geodata`. `add.to.trend` optional. Specifies aditional terms to the mean part of the model. See details below.

## Details

The implicity model assumes that there is an underlying process with mean mu(x), where x = (x1, x2) denotes the coordinates of a spatial location. The argument `trend` defines the form of the mean and the following options are allowed:

• `"cte"`the mean is assumed to be constant over the region, in which case mu(x) = mu. This is the default option.

• `"1st"`the mean is assumed to be a first order polynomial on the coordinates:

mu(x) = beta0 + beta1*x1 + beta2*x2.

• `"2nd"`the mean is assumed to be a second order polynomial on the coordinates:

μ(x)= beta0 + beta1*x1 + beta2*x2 + beta3*(x1)^2 + beta4*(x2)^2 + beta5*x1*x2.

• `~ model`a model specification. See `formula` for further details on how to specify a model in R using formulas. Notice that the model term before the `~` is not necessary. Typically used to include covariates (external trend) in the model.

Denote by x_1 and x_2 the spatial coordinates. The following specifications are equivalent:

• `trend = "1st"` and `trend = ~ x1 + x2`

• `trend = "2nd"` and `trend = ~ x1 + x2 + I(x1^2) + I(x2^2) + I(x1*x2)`

Search path for covariates
Typically, functions in the package geoR which calls `trend.spatial` will have the arguments `geodata`, `coords` and `data`.

When the trend is specifed as `trend = ~ model` the terms included in the model will be searched for in the following path sequence (modified in version 1.7-6, no longer attach objects):

1. in the object `geodata` (coerced to data-frame)

2. in the users/session Global environment

3. in the session search path

The argument `add.to.trend` adds terms to what is specified in the argument `trend`. This seems redundant but allow specifications of the type: `trend="2nd", add.trend=~other.covariates`.

## Value

An object of the class `trend.spatial` which is an n x p trend matrix, where n is the number of spatial locations and p is the number of mean parameters in the model.

## Note

This is an auxiliary function typically called by other geoR functions.

## Author(s)

Paulo J. Ribeiro Jr. paulojus@leg.ufpr.br,
Peter J. Diggle p.diggle@lancaster.ac.uk.

## References

Further information on the package geoR can be found at:
http://www.leg.ufpr.br/geoR.

## See Also

The section `DETAILS` in the documentation for `likfit` for more about the underlying model.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```# a first order polynomial trend trend.spatial("1st", sic.100)[1:5,] # a second order polynomial trend trend.spatial("2nd", sic.100)[1:5,] # a trend with a covariate trend.spatial(~altitude, sic.100)[1:5,] # a first degree trend plus a covariate trend.spatial(~coords+altitude, sic.100)[1:5,] # with produces the same as trend.spatial("1st", sic.100, add=~altitude)[1:5,] # and yet another exemple trend.spatial("2nd", sic.100, add=~altitude)[1:5,] ```

### Example output

```--------------------------------------------------------------
Analysis of Geostatistical Data
For an Introduction to geoR go to http://www.leg.ufpr.br/geoR
geoR version 1.7-5.2.1 (built on 2016-05-02) is now loaded
--------------------------------------------------------------

Warning message:
no DISPLAY variable so Tk is not available
[,1]     [,2]      [,3]
[1,]    1 29.52739  80.71854
[2,]    1 33.77939  99.52954
[3,]    1 46.80639 102.58454
[4,]    1 48.71439 121.45354
[5,]    1 49.31639 113.65554
[,1]     [,2]      [,3]      [,4]      [,5]     [,6]
[1,]    1 29.52739  80.71854  871.8668  6515.483 2383.408
[2,]    1 33.77939  99.52954 1141.0473  9906.130 3362.047
[3,]    1 46.80639 102.58454 2190.8382 10523.588 4801.612
[4,]    1 48.71439 121.45354 2373.0919 14750.963 5916.535
[5,]    1 49.31639 113.65554 2432.1064 12917.582 5605.081
[,1] [,2]
[1,]    1  682
[2,]    1  813
[3,]    1  436
[4,]    1  833
[5,]    1  579
[,1]     [,2]      [,3] [,4]
[1,]    1 29.52739  80.71854  682
[2,]    1 33.77939  99.52954  813
[3,]    1 46.80639 102.58454  436
[4,]    1 48.71439 121.45354  833
[5,]    1 49.31639 113.65554  579
[,1]     [,2]      [,3] [,4]
[1,]    1 29.52739  80.71854  682
[2,]    1 33.77939  99.52954  813
[3,]    1 46.80639 102.58454  436
[4,]    1 48.71439 121.45354  833
[5,]    1 49.31639 113.65554  579
[,1]     [,2]      [,3]      [,4]      [,5]     [,6] [,7]
[1,]    1 29.52739  80.71854  871.8668  6515.483 2383.408  682
[2,]    1 33.77939  99.52954 1141.0473  9906.130 3362.047  813
[3,]    1 46.80639 102.58454 2190.8382 10523.588 4801.612  436
[4,]    1 48.71439 121.45354 2373.0919 14750.963 5916.535  833
[5,]    1 49.31639 113.65554 2432.1064 12917.582 5605.081  579
```

geoR documentation built on Feb. 11, 2020, 1:11 a.m.