trend.spatial {geoR} | R Documentation

## Builds the Trend Matrix

### Description

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

### 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 = (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 (in this order):

1. in the users/session Global environment
2. in the session search path
3. as elements of the list `geodata`
4. as columns in a data-frame `geodata$covariates`
5. as columns in a data-frame `geodata$data`
6. in remainder of 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. Paulo.Ribeiro@est.ufpr.br,
Peter J. Diggle p.diggle@lancaster.ac.uk.

### References

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

### See Also

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

### Examples

    data(SIC)
    # 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,]

[Package geoR version 1.5-7 Index]