# Class ``Coef.qrrvglm'' The most pertinent matrices and other quantities pertaining to a QRR-VGLM (CQO model). class ## 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 $T_s = -(0.5 D_s^(-1)$. ## References Yee, T. W. (2004). A new technique for maximum-likelihood canonical Gaussian ordination. **Ecological Monographs**, 74 , 685--701. ## Author(s) Thomas W. Yee ## See Also `Coef.qrrvglm`, `cqo`, `print.Coef.qrrvglm`. ## Examples ```r 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) ```

Coef.qrrvglm-class function