persp.qrrvglm {VGAM} | R Documentation

## Perspective plot for QRR-VGLMs

### Description

Produces a perspective plot for a CQO model (QRR-VGLM). It is only applicable for rank-1 or rank-2 models with argument `Norrr = ~ 1`.

### Usage

    persp.qrrvglm(x, varlvI = FALSE, reference = NULL, plot.it = TRUE,
                  xlim=NULL, ylim=NULL, zlim=NULL,
                  gridlength=if(Rank==1) 301 else c(51,51),
                  whichSpecies = NULL,
                  xlab = if(Rank==1) "Latent Variable" else "Latent Variable 1",
                  ylab = if(Rank==1) "Expected Value" else "Latent Variable 2",
                  zlab = "Expected value", labelSpecies = FALSE,
                  stretch = 1.05, main="", ticktype = "detailed",
                  col = if(Rank==1) par()$col else "white",
                  llty=par()$lty, llwd=par()$lwd,
                  add1 = FALSE, ...)

### Arguments

`x` | Object of class `"qrrvglm"`, i.e., a constrained quadratic ordination (CQO) object.
`varlvI` | Logical that is fed into `Coef.qrrvglm`.
`reference` | Integer or character that is fed into `Coef.qrrvglm`.
`plot.it` | Logical. Plot it?
`xlim, ylim` | Limits of the x- and y-axis. Both are numeric of length 2. See `par`.
`zlim` | Limits of the z-axis. Numeric of length 2. Ignored if rank is 1. See `par`.
`gridlength` | Numeric. The fitted values are evaluated on a grid, and this argument regulates the fineness of the grid. If `Rank=2` then the argument is recycled to length 2, and the two numbers are the number of grid points on the x- and y-axes respectively.
`whichSpecies` | Numeric or character vector. Indicates which species are to be plotted. The default is to plot all of them. If numeric, it should contain values in the set {1,2,...,S} where S is the number of species.
`xlab, ylab` | Character caption for the x-axis and y-axis. By default, a suitable caption is found. See the `xlab` argument in `plot` or `title`.
`zlab` | Character caption for the z-axis. Used only if `Rank=2`. By default, a suitable caption is found. See the `xlab` argument in `plot` or `title`.
`labelSpecies` | Logical. Whether the species should be labelled with their names. Used for `Rank=1` only. The position of the label is just above the species' maximum.
`stretch` | Numeric. A value slightly more than 1, this argument adjusts the height of the y-axis. Used for `Rank=1` only.
`main` | Character, giving the title of the plot. See the `main` argument in `plot` or `title`.
`ticktype` | Tick type. Used only if `Rank=2`. See `persp` for more information.
`col` | Color. See `persp` for more information.
`llty` | Line type. Rank-1 models only. See the `lty` argument of `par`.
`llwd` | Line width. Rank-1 models only. See the `lwd` argument of `par`.
`add1` | Logical. Add to an existing plot? Used only for rank-1 models.
`...` | Arguments passed into `persp`. Useful arguments here include `theta` and `phi`, which control the position of the eye.

### Details

For a rank-1 model, a perspective plot is similar to `lvplot.qrrvglm` but plots the curves along a fine grid and there is no rugplot to show the site scores.

For a rank-2 model, a perspective plot has the first latent variable as the x-axis, the second latent variable as the y-axis, and the expected value (fitted value) as the z-axis. The result of a CQO is that each species has a response surface with elliptical contours. This function will, at each grid point, work out the maximum fitted value over all the species. The resulting response surface is plotted. Thus rare species will be obscured and abundant species will dominate the plot. To view rare species, use the `whichSpecies` argument to select a subset of the species.

A perspective plot will be performed if `Norrr = ~ 1`, and `Rank = 1` or `2`. Also, all the tolerance matrices of those species to be plotted must be positive-definite.

### Value

For a rank-2 model, a list with the following components.

`fitted` | A (G1*G2) by M matrix of fitted values on the grid. Here, G1 and G2 are the two values of `gridlength`.
`lv1grid, lv2grid` | The grid points for the x-axis and y-axis.
`maxfitted` | A G1 by G2 matrix of maximum of the fitted values over all species. These are the values that are plotted on the z-axis.

For a rank-1 model, the components `lv2grid` and `maxfitted` are `NULL`.

### Note

Yee (2004) does not refer to perspective plots. Instead, contour plots via `lvplot.qrrvglm` are used.

For rank-1 models, a similar function to this one is `lvplot.qrrvglm`. It plots the fitted values at the actual site score values rather than on a fine grid here. The result has the advantage that the user sees the curves as a direct result from a model fitted to data whereas here, it is easy to think that the smooth bell-shaped curves are the truth because the data is more of a distance away.

### 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

`persp`, `cqo`, `Coef.qrrvglm`, `lvplot.qrrvglm`, `par`, `title`.

### Examples

    ## Not run:
    hspider[,1:6] = scale(hspider[,1:6]) # Good idea when ITolerances = TRUE
    set.seed(111)
    r1 = cqo(cbind(Alopacce, Alopcune, Alopfabr, Arctlute, Arctperi,
                   Auloalbi, Pardmont, Pardnigr, Pardpull, Trocterr) ~
             WaterCon + BareSand + FallTwig + CoveMoss + CoveHerb + ReflLux,
             poissonff, hspider, trace = FALSE, ITolerances = TRUE)
    set.seed(111)  # r2 below is an ill-conditioned model
    r2 = cqo(cbind(Alopacce, Alopcune, Alopfabr, Arctlute, Arctperi,
                   Auloalbi, Pardmont, Pardnigr, Pardpull, Trocterr) ~
             WaterCon + BareSand + FallTwig + CoveMoss + CoveHerb + ReflLux,
             isdlv = c(2.4,1.0), Muxfactor = 3.0, trace = FALSE,
             poissonff, hspider, Rank = 2, EqualTolerances = TRUE)

    sort(r1@misc$deviance.Bestof)  # A history of the fits
    sort(r2@misc$deviance.Bestof)  # A history of the fits
    if(deviance(r2) > 857) stop("suboptimal fit obtained")

    persp(r1, xlim=c(-6,5), col=1:4, label=TRUE)

    # Involves all species
    persp(r2, xlim=c(-6,5), ylim=c(-4,5), theta=10, phi=20, zlim=c(0,220))
    # Omit the two dominant species to see what's behind them
    persp(r2, xlim=c(-6,5), ylim=c(-4,5), theta=10, phi=20, zlim=c(0,220),
          which=(1:10)[-c(8,10)]) # Use zlim to retain the original z-scale
    ## End(Not run)

[Package VGAM version 0.7-9 Index]