trend.spatial: Builds the Trend Matrix

Description

Builds the trend matrix according to the specification of the mean part of the model provided by the user.

Usage

trend.spatial(trend, geodata)

Arguments

trend

specifies the mean part of the model. See DETAILS below.

geodata

an object of the class geodata as described in as.geodata.

Value

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.

itemize

trend = "1st"andtrend = ~ x1 + x2
trend = "2nd"andtrend = ~ x1 + x2 + x1^2 + x2^2 + x1*x2

bold

Search path for covariates

cr

Typically, functions in the package geoR which calls trend.spatial will have the arguments goedata, coords and data.

When the trend is specifed as trend = ~ model the terms included in the model will be searched for in the following loactions (in this order):

as elements of the listgeodata
as columns in the data-framegeodata$covariates
as columns in the data-framegeodata$data

Details

The implicty 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 with the following options:

"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 degree 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 degree polynomial on the coordinates: $$\mu(x)= \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_1 (x_1)^2 + \beta_2 (x_2)^2 + \beta_1 x_1 * \beta_2 x_2$$} ~ model{a model specification. See formula for further details on how to specify a model using formulas. Notice that the model term before ~ is not necessary. Tipically used to include covariates (external trend) in the model.}

References

Further information about geoR can be found at: http://www.maths.lancs.ac.uk/~ribeiro/geoR.