VGAM (version 1.1-14)

perspqrrvglm: 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

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, ...)

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.

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.

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

if (FALSE) {
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
}