Perspective plot for QRR-VGLMs

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

perspqrrvglm(x, varI.latvar = FALSE, refResponse = NULL, show.plot = TRUE,
             xlim = NULL, ylim = NULL, zlim = NULL,
             gridlength = if (Rank == 1) 301 else c(51,51),
             which.species = 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.

varI.latvar

Logical that is fed into Coef.qrrvglm.

refResponse

Integer or character that is fed into Coef.qrrvglm.

show.plot

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.

which.species

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 which.species 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 \((G_1 \times G_2)\) by \(M\) matrix of fitted values on the grid. Here, \(G_1\) and \(G_2\) are the two values of gridlength.

latvar1grid, latvar2grid

The grid points for the x-axis and y-axis.

max.fitted

A \(G_1\) by \(G_2\) 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 latvar2grid and max.fitted are NULL.

References

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

Author

Thomas W. Yee

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.

Examples

if (FALSE) { # \dontrun{
hspider[, 1:6] <- scale(hspider[, 1:6])  # Good idea when I.tolerances = TRUE
set.seed(111)
r1 <- cqo(cbind(Alopacce, Alopcune, Alopfabr, Arctlute, Arctperi,
                Auloalbi, Pardmont, Pardnigr, Pardpull, Trocterr) ~
          WaterCon + BareSand + FallTwig + CoveMoss + CoveHerb + ReflLux,
          poissonff, data = hspider, trace = FALSE, I.tolerances = 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,
          isd.lv = c(2.4, 1.0), Muxfactor = 3.0, trace = FALSE,
          poissonff, data = hspider, Rank = 2, eq.tolerances = TRUE)

sort(deviance(r1, history = TRUE))  # A history of all the fits
sort(deviance(r2, history = TRUE))  # A history of all 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 is 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
} # }