Principal Response Curves (PRC) are a special case of
Redundancy Analysis (rda) for multivariate responses in
repeated observation design. They were originally suggested for
ecological communities. They should be easier to interpret than
traditional constrained ordination. They can also be used to study how
the effects of a factor A depend on the levels of a factor
B, that is A + A:B, in a multivariate response
experiment.
prc(response, treatment, time, ...)
# S3 method for prc
summary(object, axis = 1, scaling = "sites", const,
digits = 4, correlation = FALSE, ...)
# S3 method for prc
plot(x, species = TRUE, select, scaling = "symmetric",
axis = 1, correlation = FALSE, const, type = "l", xlab, ylab, ylim,
lty = 1:5, col = 1:6, pch, legpos, cex = 0.8, ...)The function is a special case of rda and returns its
result object (see cca.object). However, a special
summary and plot methods display returns differently
than in rda.
Multivariate response data. Typically these are community (species) data. If the data are counts, they probably should be log transformed prior to the analysis.
A factor for treatments.
An unordered factor defining the observations times in the repeated design.
An prc result object.
Axis shown (only one axis can be selected).
Scaling of species scores, identical to the
scaling in scores.rda.
The type of scores can also be specified as one of "none",
"sites", "species", or "symmetric", which
correspond to the values 0, 1, 2, and 3
respectively. Argument correlation can be used in combination
with these character descriptions to get the corresponding negative
value.
General scaling constant for species scores (see
scores.rda for details). Lower values will reduce the
range of species scores, but will not influence the regression
coefficients.
Number of significant digits displayed.
logical; if scaling is a character
description of the scaling type, correlation can be used to
select correlation-like scores for PCA. See argument scaling
for details.
Display species scores.
Vector to select displayed species. This can be a vector
of indices or a logical vector which is TRUE for the selected
species
Type of plot: "l" for lines, "p" for points
or "b" for both.
Text to replace default axis labels.
Limits for the vertical axis.
Line type, colour and plotting characters (defaults supplied).
The position of the legend. A guess is
made if this is not supplied, and NA will suppress legend.
Character expansion for symbols and species labels.
Other parameters passed to functions.
Jari Oksanen and Cajo ter Braak
The first level of treatment must be the
control: use function relevel to guarantee the correct
reference level. The current version will ignore user setting of
contrasts and always use treatment contrasts
(contr.treatment). The time must be an unordered
factor.
PRC is a special case of rda with a single
factor for treatment and a single factor for time points
in repeated observations. In vegan, the corresponding
rda model is defined as rda(response ~ treatment *
time + Condition(time)). Since the time appears twice in the
model formula, its main effects will be aliased, and only the main
effect of treatment and interaction terms are available, and will be
used in PRC. Instead of usual multivariate ordination diagrams, PRC
uses canonical (regression) coefficients and species scores for a
single axis. All that the current functions do is to provide a special
summary and plot methods that display the
rda results in the PRC fashion. The current version only
works with default contrasts (contr.treatment) in which
the coefficients are contrasts against the first level, and the levels
must be arranged so that the first level is the control (or a
baseline). If necessary, you must change the baseline level with
function relevel.
Function summary prints the species scores and the
coefficients. Function plot plots coefficients against
time using matplot, and has similar defaults.
The graph (and PRC) is meaningful only if the first treatment
level is the control, as the results are contrasts to the first level
when unordered factors are used. The plot also displays species scores
on the right vertical axis using function
linestack. Typically the number of species is so high
that not all can be displayed with the default settings, but users can
reduce character size or padding (air) in
linestack, or select only a subset of the
species. A legend will be displayed unless suppressed with
legpos = NA, and the functions tries to guess where to put the
legend if legpos is not supplied.
van den Brink, P.J. & ter Braak, C.J.F. (1999). Principal response curves: Analysis of time-dependent multivariate responses of biological community to stress. Environmental Toxicology and Chemistry, 18, 138--148.
rda, anova.cca.
## Chlorpyrifos experiment and experimental design: Pesticide
## treatment in ditches (replicated) and followed over from 4 weeks
## before to 24 weeks after exposure
data(pyrifos)
week <- gl(11, 12, labels=c(-4, -1, 0.1, 1, 2, 4, 8, 12, 15, 19, 24))
dose <- factor(rep(c(0.1, 0, 0, 0.9, 0, 44, 6, 0.1, 44, 0.9, 0, 6), 11))
ditch <- gl(12, 1, length=132)
## IGNORE_RDIFF_BEGIN
## PRC
mod <- prc(pyrifos, dose, week)
mod # RDA
summary(mod) # PRC
logabu <- colSums(pyrifos)
plot(mod, select = logabu > 100)
## IGNORE_RDIFF_END
## Ditches are randomized, we have a time series, and are only
## interested in the first axis
ctrl <- how(plots = Plots(strata = ditch,type = "free"),
within = Within(type = "series"), nperm = 99)
anova(mod, permutations = ctrl, first=TRUE)
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