VGAM (version 0.8-2)

Tol: Tolerances

Description

Generic function for the tolerances of a model.

Usage

Tol(object, ...)

Arguments

object

An object for which the computation or extraction of a tolerance or tolerances is meaningful.

...

Other arguments fed into the specific methods function of the model. Sometimes they are fed into the methods function for Coef.

Value

• The value returned depends specifically on the methods function invoked.

Warning

There is a direct inverse relationship between the scaling of the latent variables (site scores) and the tolerances. One normalization is for the latent variables to have unit variance. Another normalization is for all the tolerances to be unit. These two normalization cannot simultaneously hold in general. For rank-R>1 models it becomes more complicated because the latent variables are also uncorrelated. An important argument when fitting quadratic ordination models is whether EqualTolerances is TRUE or FALSE. See Yee (2004) for details.

Details

Different models can define an optimum in different ways. Many models have no such notion or definition.

Tolerances occur in quadratic ordination, i.e., CQO or UQO. They have ecological meaning because a high tolerance for a species means the species can survive over a large environmental range (stenoecous species), whereas a small tolerance means the species' niche is small (eurycous species). Mathematically, the tolerance is like the variance of a normal distribution.

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.

See Also

Tol.qrrvglm. Max, Opt.

Examples

set.seed(111)  # This leads to the global solution
hspider[,1:6] = scale(hspider[,1:6]) # Standardized environmental vars
# vvv p1 = cqo(cbind(Alopacce, Alopcune, Alopfabr, Arctlute, Arctperi,
# vvv                Auloalbi, Pardlugu, Pardmont, Pardnigr, Pardpull,
# vvv                Trocterr, Zoraspin) ~
# vvv          WaterCon + BareSand + FallTwig + CoveMoss + CoveHerb + ReflLux,
# vvv          Bestof = 2,
# vvv          fam = quasipoissonff, data = hspider, Crow1positive=FALSE)
# vvv 
# vvv Tol(p1)