Coef.qrrvglm-class {VGAM} | R Documentation

## Class “Coef.qrrvglm”

### Description

The most pertinent matrices and other quantities pertaining to a QRR-VGLM (CQO model).

### Objects from the Class

Objects can be created by calls of the form `Coef(object, ...)` where `object` is an object of class `"qrrvglm"` (created by `cqo`).

In this document, R is the rank, M is the number of linear predictors and n is the number of observations.

### Slots

`A`:
  Of class `"matrix"`, A, which are the linear `coefficients' of the matrix of latent variables. It is M by R.
`B1`:
  Of class `"matrix"`, B1. These correspond to terms of the argument `Norrr`.
`C`:
  Of class `"matrix"`, C, the canonical coefficients. It has R columns.
`Constrained`:
  Logical. Whether the model is a constrained ordination model.
`D`:
  Of class `"array"`, `D[,,j]` is an order-`Rank` matrix, for `j` = 1,...,M. Ideally, these are negative-definite in order to make the response curves/surfaces bell-shaped.
`Rank`:
  The rank (dimension, number of latent variables) of the RR-VGLM. Called R.
`lv`:
  n by R matrix of latent variable values.
`lvOrder`:
  Of class `"matrix"`, the permutation returned when the function `order` is applied to each column of `lv`. This enables each column of `lv` to be easily sorted.
`Maximum`:
  Of class `"numeric"`, the M maximum fitted values. That is, the fitted values at the optima for `Norrr = ~ 1` models. If `Norrr` is not `~ 1` then these will be `NA`s.
`NOS`:
  Number of species.
`Optimum`:
  Of class `"matrix"`, the values of the latent variables where the optima are. If the curves are not bell-shaped, then the value will be `NA` or `NaN`.
`OptimumOrder`:
  Of class `"matrix"`, the permutation returned when the function `order` is applied to each column of `Optimum`. This enables each row of `Optimum` to be easily sorted.
`bellshaped`:
  Vector of logicals: is each response curve/surface bell-shaped?
`dispersion`:
  Dispersion parameter(s).
`Dzero`:
  Vector of logicals, is each of the response curves linear in the latent variable(s)? It will be if and only if `D[,,j]` equals O, for `j` = 1,...,M .
`Tolerance`:
  Object of class `"array"`, `Tolerance[,,j]` is an order-`Rank` matrix, for `j` = 1,...,M, being the matrix of tolerances (squared if on the diagonal). These are denoted by T in Yee (2004). Ideally, these are positive-definite in order to make the response curves/surfaces bell-shaped. The tolerance matrices satisfy T_s = -(0.5 D_s^(-1).

### Author(s)

Thomas W. Yee

### References

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

### See Also

`Coef.qrrvglm`, `cqo`, `print.Coef.qrrvglm`.

### Examples

    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)
    y1 = rpois(n, lambda1)
    y2 = rpois(n, lambda2)
    y3 = rpois(n, lambda3)
    yy = cbind(y1,y2,y3)
    p1 = cqo(yy ~ x2 + x3 + x4, fam=poissonff, trace=FALSE)
    ## Not run:
    lvplot(p1, y=TRUE, lcol=1:3, pch=1:3, pcol=1:3)
    ## End(Not run)
    print(Coef(p1), digits=3)

[Package VGAM version 0.7-9 Index]