# trend.spatial

##### Builds the Trend Matrix

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

- Keywords
- spatial

##### Usage

`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 \(x = (x_1, x_2)\) 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: $$\mu(x)= \beta_0 + \beta_1 x_1 + \beta_2 x_2$$`"2nd"`

the mean is assumed to be a second order polynomial on the coordinates: $$\mu(x)= \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 (x_1)^2 + \beta_4 (x_2)^2 + \beta_5 x_1 * x_2$$`~ 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):

in the object

`geodata`

(coerced to data-frame)in the users/session Global environment

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 \(n \times p\) *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.

##### 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

```
# NOT RUN {
# 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,]
# }
```

*Documentation reproduced from package geoR, version 1.8-1, License: GPL (>= 2)*