VGAM (version 1.1-14)

Tol: Tolerances

Description

Generic function for the tolerances of a model.

Usage

Tol(object, ...)

Value

The value returned depends specifically on the methods function invoked. For a cqo binomial or Poisson fit, this function returns a

\(R \times R \times S\) array, where \(R\) is the rank and \(S\) is the number of species. Each tolerance matrix ought to be positive-definite, and for a rank-1 fit, taking the square root of each tolerance matrix results in each species' tolerance (like a standard deviation).

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 and 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, cqo, rcim for UQO.

Examples

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

Tol(p1)
}