R: Estimate the Simpson index from several samples

estSimpsonf {MCPAN} | R Documentation

## 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`

### 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.

### 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

### References

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

### See Also

estShannonf

### Examples

    # 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.

[Package MCPAN version 1.1-21 Index]