MCPAN (version 1.1-21)

estSimpsonf: Estimate the Simpson index from several samples

Description

Calculate estimates of the Simpson index after pooling over several samples, grouped by a factor variable.

Usage

estSimpsonf(X, f)

Arguments

X

a data.frame of dimension 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

Value

A list containing the items:

estimate

the groupwise point estimates of the Simpson index

varest

the groupwise variance estimates of the Simpson index

table

a matrix of counts,containing the summed observations for each level of f in its rows

Details

The function splits X according to the levels of the grouping variable f, builds the sum over each column and calculates the Shannon index ove the resulting counts.

References

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

See Also

estShannonf

Examples

# NOT RUN {
# Here, the estimates for the Hell Creek Dinosaur 
# example are compared to the estimates in 
# Tables 2 and 3 of Rogers and Hsu (2001).

data(HCD)
HCD

# Groupwise point estimates:

est<-estSimpsonf(X=HCD[,-1], f=HCD[,1])

est

# Table 2:


cmat<-rbind(
"lower-middle"=c(1,-1,0),
"lower-upper"=c(1, 0,-1),
"middle-upper"=c(0,1,-1))


# the point estimates:

# cmat %*% est$estimate
crossprod(t(cmat), est$estimate)


# the standard errors:
# sqrt(diag(cmat %*% diag(est$varest) %*% t(cmat)))

sqrt(diag(crossprod(t(cmat), crossprod(diag(est$varest), t(cmat)) ) ))


# Table 3:

cmat<-rbind(
"middle-lower"=c(-1,1,0),
"upper-lower"=c(-1,0,1))

# cmat %*% est$estimate
crossprod(t(cmat), est$estimate)


# sqrt(diag(cmat %*% diag(est$varest) %*% t(cmat)))

sqrt(diag(crossprod(t(cmat), crossprod(diag(est$varest), t(cmat)) ) ))

# Note, that the point estimates are exactly
# the same as in Rogers and Hsu (2001),
# but the variance estimates are not, whenever
# the Upper group is involved.


# }