# Opt: Optimums In VGAM: Vector Generalized Linear and Additive Models

## Description

Generic function for the optimums (or optima) of a model.

## Usage

 `1` ```Opt(object, ...) ```

## Arguments

 `object` An object for which the computation or extraction of an optimum (or optimums) is meaningful. `...` Other arguments fed into the specific methods function of the model. Sometimes they are fed into the methods function for `Coef`.

## Details

Different models can define an optimum in different ways. Many models have no such notion or definition.

Optimums occur in quadratic and additive ordination, e.g., CQO or CAO. For these models the optimum is the value of the latent variable where the maximum occurs, i.e., where the fitted value achieves its highest value. For quadratic ordination models there is a formula for the optimum but for additive ordination models the optimum must be searched for numerically. If it occurs on the boundary, then the optimum is undefined. At an optimum, the fitted value of the response is called the maximum.

## Value

The value returned depends specifically on the methods function invoked.

## Note

In ordination, the optimum of a species is sometimes called the species score.

Thomas W. Yee

## 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.

`Opt.qrrvglm`, `Max`, `Tol`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```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, family = poissonff, data = hspider, Crow1positive = FALSE) Opt(p1) ## Not run: clr <- (1:(ncol(depvar(p1))+1))[-7] # Omits yellow persp(p1, col = clr, las = 1, main = "Vertical lines at the optimums") abline(v = Opt(p1), lty = 2, col = clr) ## End(Not run) ```