# Coef.qrrvglm-class: Class "Coef.qrrvglm" In VGAM: Vector Generalized Linear and Additive Models

## 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.

`latvar`:

n by R matrix of latent variable values.

`latvar.order`:

Of class `"matrix"`, the permutation returned when the function `order` is applied to each column of `latvar`. This enables each column of `latvar` to be easily sorted.

`Maximum`:

Of class `"numeric"`, the M maximum fitted values. That is, the fitted values at the optimums 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 optimums are. If the curves are not bell-shaped, then the value will be `NA` or `NaN`.

`Optimum.order`:

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).

Thomas W. Yee

## References

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

`Coef.qrrvglm`, `cqo`, `print.Coef.qrrvglm`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```x2 <- rnorm(n <- 100) x3 <- rnorm(n) x4 <- rnorm(n) latvar1 <- 0 + x3 - 2*x4 lambda1 <- exp(3 - 0.5 * ( latvar1-0)^2) lambda2 <- exp(2 - 0.5 * ( latvar1-1)^2) lambda3 <- exp(2 - 0.5 * ((latvar1+4)/2)^2) y1 <- rpois(n, lambda1) y2 <- rpois(n, lambda2) y3 <- rpois(n, lambda3) yy <- cbind(y1, y2, y3) # vvv 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) # vvv print(Coef(p1), digits = 3) ```