mat.sar2 {dae} R Documentation

## Forms an sar2 correlation matrix

### Description

Form the correlation matrix of order order whose correlations follow the sar2 pattern, a pattern used in crop competition models. The resulting matrix is banded and is a constrained AR3 matrix.

### Usage

mat.sar2(gamma, order, print = NULL)

### Arguments

 gamma A numeric containing the two values of gamma, being parameters linked with spatial dependence and competition. order The order of the matrix to be formed. print A character giving the object to be printed. Currently, only the claculated values of the ar3parameters can be printed. If NULL, nothing is printed.

### Details

The values of the AR3 parameters, phi, are calculated from the gammas as follows:
phi[1] = gamma[1] + 2 * gamma[2]; phi[2] = -gamma[2] * (2*gamma[2] + gamma[1]);
phi[3] = gamma[1] * gamma[2] * gamma[2].

Then the correlations in the correlation matrix, corr say, are calculated from the correlation parameters, phi. Let omega = 1 - phi[2] - phi[3] * (phi[1] + phi[3]). Then the values in

• the diagonal of corr (k = 1) are one;

• the first subdiagonal band (k = 2) of corr are equal to (phi[1] + phi[2]*phi[3]) / omega;

• the second subdiagonal band (k = 3) of corr are equal to
(phi[1] * (phi[1] + phi[3]) + phi[2] * (1 - phi[2])) / omega;

• the subsequent subdiagonal bands, (k = 4:order), of corr are equal to
phi[1]*corr[k-1] + phi[2]*corr[k-2] + phi[3]*corr[k-3].

### Value

A banded correlation matrix whose elements follow an sar2 pattern.

Chris Brien

### Examples

corr <- mat.sar2(gamma = c(-0.4, 0.2), order = 4)
corr <- mat.sar2(gamma = c(-0.4, 0.2), order = 4, print = "ar3")

[Package dae version 3.2.28 Index]