lvplot.qrrvglm {VGAM} | R Documentation |
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, varlvI = FALSE, reference = NULL, add = FALSE, plot.it = TRUE, rug = TRUE, y = FALSE, type = c("fitted.values", "predictors"), xlab = paste("Latent Variable", if (Rank == 1) "" else " 1", sep = ""), 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, ...)
object |
A CQO or UQO object. |
varlvI |
Logical that is fed into Coef.qrrvglm .
|
reference |
Integer or character that is fed into Coef.qrrvglm .
|
add |
Logical. Add to an existing plot? If FALSE , a new
plot is made. |
plot.it |
Logical. Plot it? |
rug |
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.
|
y |
Logical. If TRUE , the responses will be plotted
(applies only to rank-1 models and if type="fitted.values" .)
|
type |
Either "fitted.values" or "predictors" ,
specifies whether the y-axis is on the response or eta-scales
respectively.
|
xlab |
Caption for the x-axis. See par . |
ylab |
Caption for the y-axis. See par . |
pcex |
Character expansion of the points.
Here, for rank-1 models, points are the response y data.
For rank-2 models, points are the optima.
See the cex argument in par . |
pcol |
Color of the points.
See the col argument in par . |
pch |
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 M, the number of species.
|
llty |
Line type.
Rank-1 models only.
See the lty argument of par . |
lcol |
Line color.
Rank-1 models only.
See the col argument of par . |
llwd |
Line width.
Rank-1 models only.
See the lwd argument of par . |
label.arg |
Logical. Label the optima and C? (applies only to rank-2 models only). |
adj.arg |
Justification of text strings for labelling the optima
(applies only to rank-2 models only).
See the adj argument of par . |
ellipse |
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
varlvI=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 optima.
|
Absolute |
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.
|
elty |
Line type of the ellipses.
See the lty argument of par . |
ecol |
Line color of the ellipses.
See the col argument of par . |
elwd |
Line width of the ellipses.
See the lwd argument of par . |
egrid |
Numerical. Line resolution of the ellipses. Choosing a larger value will result in smoother ellipses. Useful when ellipses are large. |
chull.arg |
Logical. Add a convex hull around the site scores? |
clty |
Line type of the convex hull.
See the lty argument of par . |
ccol |
Line color of the convex hull.
See the col argument of par . |
clwd |
Line width of the convex hull.
See the lwd argument of par . |
cpch |
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 . |
C |
Logical. Add C (represented by arrows emanating
from OriginC ) to the plot? |
OriginC |
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.
|
Clty |
Line type of the arrows representing C.
See the lty argument of par . |
Ccol |
Line color of the arrows representing C.
See the col argument of par . |
Clwd |
Line width of the arrows representing C.
See the lwd argument of par . |
Ccex |
Numeric. Character expansion of the labelling of C.
See the cex argument of par . |
Cadj.arg |
Justification of text strings when labelling C.
See the adj argument of par . |
stretchC |
Numerical. Stretching factor for C.
Instead of using C, stretchC * C is used. |
sites |
Logical. Add the site scores (aka latent variable values, nu's) to the plot? (applies only to rank-2 models only). |
spch |
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 .
|
scol |
Color of the site scores.
See the col argument of par .
|
scex |
Character expansion of the site scores.
See the cex argument of par .
|
sfont |
Font used for the site scores.
See the font argument of par .
|
check.ok |
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.
|
... |
Arguments passed into the plot function
when setting up the entire plot. Useful arguments here include
xlim and ylim .
|
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 optima.
Returns a matrix of latent variables (site scores) regardless of whether a plot was produced or not.
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.
A species which does not have an optimum will not have an ellipse drawn even if requested, i.e., if its tolerance matrix is not positive-definite.
Plotting C gives a visual display of the weights (loadings) of each of the variables used in the linear combination defining each latent variable.
The arguments elty
, ecol
and elwd
, may be replaced
in the future by llty
, lcol
and llwd
, respectively.
For rank-1 models, a similar function to this one is
persp.qrrvglm
. It plots the fitted values on a more
fine grid rather than at the actual site scores here. The result is a
collection of smooth bell-shaped curves. However, it has the weakness
that the plot is more divorced from the data; the user thinks it is
the truth without an appreciation of the statistical variability in
the estimates.
In the example below, the data comes from an equal-tolerances model. The species' tolerance matrices are all the identity matrix, and the optimums are at (0,0), (1,1) and (-2,0) for species 1, 2, 3 respectively.
Thomas W. Yee
Yee, T. W. (2004) A new technique for maximum-likelihood canonical Gaussian ordination. Ecological Monographs, 74, 685–701.
lvplot
,
persp.qrrvglm
,
Coef.qrrvglm
,
par
,
cqo
.
set.seed(123) x2 = rnorm(n <- 200) # Has mean 0 (needed when ITol=TRUE) x3 = rnorm(n) # Has mean 0 (needed when ITol=TRUE) x4 = rnorm(n) # Has mean 0 (needed when ITol=TRUE) lv1 = x2 + x3 - 2*x4 lv2 = -x2 + x3 + 0*x4 # lv2 is weakly correlated with lv1 lambda1 = exp(6 - 0.5 * (lv1-0)^2 - 0.5 * (lv2-0)^2) lambda2 = exp(5 - 0.5 * (lv1-1)^2 - 0.5 * (lv2-1)^2) lambda3 = exp(5 - 0.5 * (lv1+2)^2 - 0.5 * (lv2-0)^2) spp1 = rpois(n, lambda1) spp2 = rpois(n, lambda2) spp3 = rpois(n, lambda3) set.seed(111) p2 = cqo(cbind(spp1,spp2,spp3) ~ x2 + x3 + x4, poissonff, Rank=2, ITolerances=TRUE, Crow1positive=c(TRUE,FALSE)) # deviance = 505.81 if(deviance(p2) > 506) stop("suboptimal fit obtained") sort(p2@misc$deviance.Bestof) # A history of the fits Coef(p2) ## Not run: 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, C=TRUE, Cadj=c(-.3,-.3,1), Clwd=2, Ccex=1.4, Ccol="red", main=paste("Contours at Abundance=140 with", "convex hull of the site scores")) ## End(Not run) var(lv(p2)) # A diagonal matrix, i.e., uncorrelated latent variables var(lv(p2, varlvI=TRUE)) # Identity matrix Tol(p2)[,,1:2] # Identity matrix Tol(p2, varlvI=TRUE)[,,1:2] # A diagonal matrix