Coef.qrrvglm: Returns Important Matrices etc. of a QO Object

Description

This methods function returns important matrices etc. of a QO object.

Usage

Coef.qrrvglm(object, varlvI = FALSE, reference = NULL, ...)

Arguments

object

A CQO or UQO object. The former has class "qrrvglm".

varlvI

Logical indicating whether to scale the site scores (latent variables) to have variance-covariance matrix equal to the rank-$R$ identity matrix. All models have uncorrelated site scores (latent variables), and this option stretches or shrinks the or

reference

Integer or character. Specifies the reference species. By default, the reference species is found by searching sequentially starting from the first species until a positive-definite tolerance matrix is found. Then this tolerance m

...

Currently unused.

Value

The A, B1, C, T, D matrices/arrays are returned, along with other slots. For UQO, C is undefined. The returned object has class "Coef.qrrvglm" (see Coef.qrrvglm-class).

Details

If ITolerances=TRUE or EqualTolerances=TRUE (and its estimated tolerance matrix is positive-definite) then all species' tolerances are unity by transformation or by definition, and the spread of the site scores can be compared to them. Vice versa, if one wishes to compare the tolerances with the sites score variability then setting varlvI=TRUE is more appropriate.

For rank-2 QRR-VGLMs, one of the species can be chosen so that the angle of its major axis and minor axis is zero, i.e., parallel to the ordination axes. This means the effect on the latent vars is independent on that species, and that its tolerance matrix is diagonal. The argument reference allows one to choose which is the reference species, which must have a positive-definite tolerance matrix, i.e., is bell-shaped. If reference is not specified, then the code will try to choose some reference species starting from the first species. Although the reference argument could possibly be offered as an option when fitting the model, it is currently available after fitting the model, e.g., in the functions Coef.qrrvglm and lvplot.qrrvglm.

References

Yee, T. W. (2004) A new technique for maximum-likelihood canonical Gaussian ordination. Ecological Monographs, 74, 685--701.

Yee, T. W. (2006) Constrained additive ordination. Ecology, 87, 203--213.

Examples

Run this code

set.seed(123)
x2 = rnorm(n <- 100)
x3 = rnorm(n)
x4 = rnorm(n)
lv1 = 0 + x3 - 2*x4
lambda1 = exp(3 - 0.5 * (lv1-0)^2)
lambda2 = exp(2 - 0.5 * (lv1-1)^2)
lambda3 = exp(2 - 0.5 * ((lv1+4)/2)^2) # Unequal tolerances
y1 = rpois(n, lambda1)
y2 = rpois(n, lambda2)
y3 = rpois(n, lambda3)
set.seed(111)
p1 = cqo(cbind(y1,y2,y3) ~ x2 + x3 + x4, poissonff, trace=FALSE)
lvplot(p1, y=TRUE, lcol=1:3, pch=1:3, pcol=1:3)
Coef(p1)
print(Coef(p1), digits=3)

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