Principal Response Curves for Treatments with Repeated Observations

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Description

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.

Usage

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prc(response, treatment, time, ...)
## S3 method for class 'prc'
summary(object, axis = 1, scaling = "symmetric",
        digits = 4, correlation = FALSE, ...)
## S3 method for class 'prc'
plot(x, species = TRUE, select, scaling = "symmetric",
     axis = 1, correlation = FALSE, type = "l", xlab, ylab, ylim,
     lty = 1:5, col = 1:6, pch, legpos, cex = 0.8, ...)  

Arguments

response

Multivariate response data. Typically these are community (species) data. If the data are counts, they probably should be log transformed prior to the analysis.

treatment

A factor for treatments.

time

An unordered factor defining the observations times in the repeated design.

object, x

An prc result object.

axis

Axis shown (only one axis can be selected).

scaling

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.

digits

Number of significant digits displayed.

correlation

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.

species

Display species scores.

select

Vector to select displayed species. This can be a vector of indices or a logical vector which is TRUE for the selected species

type

Type of plot: "l" for lines, "p" for points or "b" for both.

xlab, ylab

Text to replace default axis labels.

ylim

Limits for the vertical axis.

lty, col, pch

Line type, colour and plotting characters (defaults supplied).

legpos

The position of the legend. A guess is made if this is not supplied, and NA will suppress legend.

cex

Character expansion for symbols and species labels.

...

Other parameters passed to functions.

Details

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.

Value

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.

Warning

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.

Author(s)

Jari Oksanen and Cajo ter Braak

References

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.

See Also

rda, anova.cca.

Examples

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## 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)
# PRC
mod <- prc(pyrifos, dose, week)
mod            # RDA
summary(mod)   # PRC
logabu <- colSums(pyrifos)
plot(mod, select = logabu > 100)
## 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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