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.
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, ...)Returns a matrix of latent variables (site scores) regardless of whether a plot was produced or not.
A CQO object.
Logical that is fed into Coef.qrrvglm.
Integer or character that is fed into Coef.qrrvglm.
Logical.
Add to an existing plot? If FALSE, a new
plot is made.
Logical. Plot it?
Logical.
If TRUE, a rug plot is plotted at the
foot of the plot (applies to rank-1 models only).
These values are jittered to expose ties.
Logical. If TRUE, the responses will be
plotted (applies only to rank-1 models and if
type = "fitted.values".)
Either "fitted.values" or "predictors",
specifies whether the y-axis is on the response or eta-scales
respectively.
Caption for the x-axis. See
par.
Caption for the y-axis. See
par.
Character expansion of the points.
Here, for rank-1 models, points are the response y data.
For rank-2 models, points are the optimums.
See the cex argument in par.
Color of the points.
See the col argument in par.
Either an integer specifying a symbol or a single
character to be used as the default in plotting points.
See par.
The pch argument can be of length
Line type.
Rank-1 models only.
See the lty argument of par.
Line color.
Rank-1 models only.
See the col argument of par.
Line width.
Rank-1 models only.
See the lwd argument of par.
Logical. Label the optimums and C? (applies only to rank-2 models only).
Justification of text strings for labelling
the optimums
(applies only to rank-2 models only).
See the adj argument of par.
Numerical, of length 0 or 1 (applies only to rank-2 models only).
If Absolute is TRUE then ellipse should be
assigned a value that is used for the elliptical contouring.
If Absolute is FALSE then ellipse
should be assigned a value between 0 and 1, for example,
setting ellipse = 0.9 means an ellipse with contour
= 90% of the maximum will be plotted about each optimum.
If ellipse is a negative value, then the function checks
that the model is an equal-tolerances model and
varI.latvar = FALSE, and if so, plots circles with
radius -ellipse. For example, setting ellipse = -1
will result in circular contours that have unit radius (in latent
variable units). If ellipse is NULL or FALSE
then no ellipse is drawn around the optimums.
Logical.
If TRUE, the contours corresponding to ellipse
are on an absolute scale.
If FALSE, the contours corresponding to ellipse
are on a relative scale.
Line type of the ellipses.
See the lty argument of par.
Line color of the ellipses.
See the col argument of par.
Line width of the ellipses.
See the lwd argument of par.
Numerical. Line resolution of the ellipses. Choosing a larger value will result in smoother ellipses. Useful when ellipses are large.
Logical. Add a convex hull around the site scores?
Line type of the convex hull.
See the lty argument of par.
Line color of the convex hull.
See the col argument of par.
Line width of the convex hull.
See the lwd argument of par.
Character to be plotted at the intersection points of
the convex hull. Having white spaces means that site
labels are not obscured there.
See the pch argument of par.
Logical. Add C (represented by arrows emanating
from OriginC) to the plot?
Character or numeric.
Where the arrows representing C emanate from.
If character, it must be one of the choices given. By default the
first is chosen.
The value "origin" means c(0,0).
The value "mean" means
the sample mean of the latent variables (centroid).
Alternatively, the user may specify a numerical vector of length 2.
Line type of the arrows representing C.
See the lty argument of par.
Line color of the arrows representing C.
See the col argument of par.
Line width of the arrows representing C.
See the lwd argument of par.
Numeric.
Character expansion of the labelling of C.
See the cex argument of par.
Justification of text strings when labelling C.
See the adj argument of par.
Numerical. Stretching factor for C.
Instead of using C, stretchC * C is used.
Logical. Add the site scores (aka latent variable values, nu's) to the plot? (applies only to rank-2 models only).
Plotting character of the site scores.
The default value of NULL means the row labels of the
data frame are used. They often are the site numbers.
See the pch argument of par.
Color of the site scores.
See the col argument of par.
Character expansion of the site scores.
See the cex argument of par.
Font used for the site scores.
See the font argument of par.
Logical. Whether a check is performed to see
that noRRR = ~ 1 was used.
It doesn't make sense to have a latent variable plot unless
this is so.
Logical. If y is plotted, jitter it first?
This may be useful for counts and proportions.
Arguments passed into the plot function
when setting up the entire plot. Useful arguments here include
xlim and ylim.
Thomas W. Yee
Interpretation of a latent variable plot (CQO diagram) is potentially very misleading in terms of distances if (i) the tolerance matrices of the species are unequal and (ii) the contours of these tolerance matrices are not included in the ordination diagram.
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 p'' correspond
to the optimums.
Yee, T. W. (2004). A new technique for maximum-likelihood canonical Gaussian ordination. Ecological Monographs, 74, 685--701.
lvplot,
perspqrrvglm,
Coef.qrrvglm,
par,
cqo.
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
}
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