R: Principal Response Curves for Treatments with Repeated...

prc {vegan} | R Documentation

## Principal Response Curves for Treatments with Repeated Observations

### 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

    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

    ## 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)

[Package vegan version 2.4-3 Index]