ccoef {VGAM} | R Documentation

## Extract Model Constrained/Canonical Coefficients

### Description

`ccoef` is a generic function which extracts the constrained (canonical) coefficients from objects returned by certain modelling functions.

### Usage

    ccoef(object, ...)

### Arguments

`object` | An object for which the extraction of canonical coefficients is meaningful.
`...` | Other arguments fed into the specific methods function of the model.

### Details

For constrained quadratic and ordination models, canonical coefficients are the elements of the C matrix used to form the latent variables. They are highly interpretable in ecology, and are looked at as weights or loadings.

They are also applicable for reduced-rank VGLMs.

### Value

The value returned depends specifically on the methods function invoked.

### Warning

For QO models, 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 species' tolerances to be unit (provided `EqualTolerances` is `TRUE`). These two normalizations cannot simultaneously hold in general. For rank R models with R>1 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.

### Author(s)

Thomas W. Yee

### References

Yee, T. W. and Hastie, T. J. (2003) Reduced-rank vector generalized linear models. Statistical Modelling, 3, 15–41.

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

`ccoef-method`, `ccoef.qrrvglm`, `ccoef.cao`, `coef`.

### Examples

    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,
             fam = quasipoissonff, data = hspider, Crow1positive=FALSE)
    ccoef(p1)

[Package VGAM version 0.7-9 Index]