mat.sar2 {dae}

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.

Author(s)

Chris Brien

See Also

mat.I, mat.J, mat.cor, mat.corg, mat.banded, mat.exp, mat.gau, mat.ar1, mat.ar2, mat.ar3, mat.sar, mat.ma1, mat.ma2, mat.arma

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")