VGAM (version 1.1-14)

lvplot.qrrvglm: Latent Variable Plot for QO models

Description

Produces an ordination diagram (latent variable plot) for quadratic ordination (QO) models. For rank-1 models, the x-axis is the first ordination/constrained/canonical axis. For rank-2 models, the x- and y-axis are the first and second ordination axes respectively.

Usage

lvplot.qrrvglm(object, varI.latvar = FALSE, refResponse = NULL,
    add = FALSE, show.plot = TRUE,
    rug = TRUE, y = FALSE, type = c("fitted.values", "predictors"),
    xlab = paste0("Latent Variable", if (Rank == 1) "" else " 1"),
    ylab = if (Rank == 1) switch(type, predictors = "Predictors",
    fitted.values = "Fitted values") else "Latent Variable 2",
    pcex = par()$cex, pcol = par()$col, pch = par()$pch,
    llty = par()$lty, lcol = par()$col, llwd = par()$lwd,
    label.arg = FALSE, adj.arg = -0.1,
    ellipse = 0.95, Absolute = FALSE, elty = par()$lty,
    ecol = par()$col, elwd = par()$lwd, egrid = 200,
    chull.arg = FALSE, clty = 2, ccol = par()$col, clwd = par()$lwd,
    cpch = "   ",
    C = FALSE, OriginC = c("origin", "mean"),
    Clty = par()$lty, Ccol = par()$col, Clwd = par()$lwd,
    Ccex = par()$cex, Cadj.arg = -0.1, stretchC = 1,
    sites = FALSE, spch = NULL, scol = par()$col, scex = par()$cex,
    sfont = par()$font, check.ok = TRUE, jitter.y = FALSE, ...)

Value

Returns a matrix of latent variables (site scores) regardless of whether a plot was produced or not.

Details

This function only works for rank-1 and rank-2 QRR-VGLMs with argument noRRR = ~ 1.

For unequal-tolerances models, the latent variable axes can be rotated so that at least one of the tolerance matrices is diagonal; see Coef.qrrvglm for details.

Arguments beginning with ``p'' correspond to the points e.g., pcex and pcol correspond to the size and color of the points. Such ``p'' arguments should be vectors of length 1, or \(n\), the number of sites. For the rank-2 model, arguments beginning with ``p'' correspond to the optimums.

References

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

See Also

lvplot, perspqrrvglm, Coef.qrrvglm, par, cqo.

Examples

set.seed(123); nn <- 200
cdata <- data.frame(x2 = rnorm(nn),  # Mean 0 (needed when I.tol=TRUE)
                    x3 = rnorm(nn),  # Mean 0 (needed when I.tol=TRUE)
                    x4 = rnorm(nn))  # Mean 0 (needed when I.tol=TRUE)
cdata <- transform(cdata, latvar1 =  x2 + x3 - 2*x4,
                          latvar2 = -x2 + x3 + 0*x4)
# Nb. latvar2 is weakly correlated with latvar1
cdata <- transform(cdata,
           lambda1 = exp(6 - 0.5 * (latvar1-0)^2 - 0.5 * (latvar2-0)^2),
           lambda2 = exp(5 - 0.5 * (latvar1-1)^2 - 0.5 * (latvar2-1)^2),
           lambda3 = exp(5 - 0.5 * (latvar1+2)^2 - 0.5 * (latvar2-0)^2))
cdata <- transform(cdata,
            spp1 = rpois(nn, lambda1),
            spp2 = rpois(nn, lambda2),
            spp3 = rpois(nn, lambda3))
set.seed(111)
if (FALSE) {
p2 <- cqo(cbind(spp1, spp2, spp3) ~ x2 + x3 + x4, poissonff,
          data = cdata, Rank = 2, I.tolerances = TRUE,
          Crow1positive = c(TRUE, FALSE))  # deviance = 505.81
if (deviance(p2) > 506) stop("suboptimal fit obtained")
sort(deviance(p2, history = TRUE))  # A history of the iterations
Coef(p2)
}

if (FALSE) {
lvplot(p2, sites = TRUE, spch = "*", scol = "darkgreen", scex = 1.5,
  chull = TRUE, label = TRUE, Absolute = TRUE, ellipse = 140,
  adj = -0.5, pcol = "blue", pcex = 1.3, las = 1, Ccol = "orange",
  C = TRUE, Cadj = c(-0.3, -0.3, 1), Clwd = 2, Ccex = 1.4,
  main = paste("Contours at Abundance = 140 with",
               "convex hull of the site scores")) }
if (FALSE) {
var(latvar(p2))  # A diagonal matrix, i.e., uncorrelated latent vars
var(latvar(p2, varI.latvar = TRUE))  # Identity matrix
Tol(p2)[, , 1:2]  # Identity matrix
Tol(p2, varI.latvar = TRUE)[, , 1:2]  # A diagonal matrix
}