Simpsonci {MCPAN}R Documentation

Confidence intervals for differences of Simpson indices

Description

Calculates simultaneous and local confidence intervals for differences of Simpson indices.

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 are used which take the sample variance into account.

Note, that this approach ignores the variability of the individual samples.

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 1.1-7 Index]