R: Confidence intervals for differences of Simpson indices

Simpsonci {MCPAN} | R Documentation

## Confidence intervals for differences of Simpson indices

### Description

Calculates simultaneous and local confidence intervals for differences of Simpson indices under the assumption of multinomial count data.

### Usage

    Simpsonci(X, f, cmat = NULL, type = "Dunnett",
     alternative = "two.sided", conf.level = 0.95, dist = "MVN", ...)

### Arguments

`X` | a data.frame of dimensions n times p with integer entries, where n is the number of samples and p is the number of species
`f` | a factor variable of length n, grouping the observations in `X`
`cmat` | an contrast matrix; the number of columns should match the number of levels in `f`
`type` | a single character string, currently one of "Dunnett","Tukey","Sequen"
`alternative` | a single character string, one of "two.sided","less" (upper bounds),"greater" (lower bounds)
`conf.level` | the confidence level of the simultaneous (or local) confidence intervals
`dist` | a single character string, defining the type of quantiles to be used for interval calculation; "MVN" invokes simultaneous intervals, "N" invokes unadjusted confidence intervals with coverage probability conf.level for each of them
`...` | further arguments to be passed; currently only `base` is used,a single integer value, specifying which group to be taken as the control in case that `type="Dunnett"`, ignored otherwise

### Details

This function implements confidence intervals described by Rogers and Hsu (1999) for the difference of Shannon indices between several groups. Deviating from Fritsch and Hsu, quantiles of the multivariate normal distribution based on a plug-in-estamator for the correlation matrix.

Note, that this approach, by assuming multinomial distribution for the vectors of counts, ignores the variability of the individual samples. If such extra-multinomial variatio is present in the data, the intervals will be too narrow, coverage probability will be substantially lower than specified in 'conf.level'. Consider approaches based on bootstrap instead (e.g., package simboot).

### Value

A list containing the elements:

`conf.int` | a matrix, containing the lower and upper confidence limits in the columns
`quantile` | a single numeric value, the quantile used for interval calculation
`estimate` | a matrix,containing the point estimates of the contrasts in its column
`cmat` | the contrast matrix used
`methodname` | a character string, for printing
`sample.estimate` | A list of sample estimates as returned by estShannonf

and some of the input arguments.

### Author(s)

Frank Schaarschmidt

### References

Rogers, JA and Hsu, JC (2001): Multiple Comparisons of Biodiversity. Biometrical Journal 43, 617-625.

### See Also

Shannonci

### Examples

    data(HCD)

    HCDcounts<-HCD[,-1]
    HCDf<-HCD[,1]

    # Rogers and Hsu (2001), Table 2:
    # All pair wise comparisons:

    Simpsonci(X=HCDcounts, f=HCDf, type = "Tukey",
     conf.level = 0.95, dist = "MVN")

    # Rogers and Hsu (2001), Table 3:
    # Comparison to the lower cretaceous:

    Simpsonci(X=HCDcounts, f=HCDf, type = "Dunnett",
     alternative = "less", conf.level = 0.95, dist = "MVN")

    # Note, that the confidence bounds here differ
    # from the bounds in Rogers and Hsu (2001)
    # in the second digit, whenever the group Upper
    # is involved in the comparison.

    # Stepwise comparison between the strata:

    SimpsonS<-Simpsonci(X=HCDcounts, f=HCDf, type = "Sequen",
     alternative = "greater", conf.level = 0.95, dist = "MVN")

    SimpsonS
    summary(SimpsonS)

    plot(SimpsonS)

    # # # Hell Creek Dinosaur data:
    # Is there a downward trend in biodiversity during the
    # Creataceous period?

    # A trend test based on multiple contrasts:

    cmatTREND<-rbind(
    "U-LM"=c(-0.5,-0.5,1),
    "MU-L"=c(-1,0.5,0.5),
    "U-L"=c(-1,0,1)
    )

    TrendCI<-Simpsonci(X=HCDcounts, f=HCDf, cmat=cmatTREND,
     alternative = "greater", conf.level = 0.95, dist = "MVN")
    TrendCI

    plot(TrendCI)

[Package MCPAN version 1.1-21 Index]