R: Spatial autocorrelation parameter estimation

autoconst {prabclus} | R Documentation

## Spatial autocorrelation parameter estimation

### Description

Monte Carlo estimation of the disjunction/spatial autocorrelation parameter `pd` for the simulation model used in `randpop.nb`, used for tests for clustering of presence-absence data.

`autoconst` is the main function; `autoreg` performs the simulation and is executed within `autoconst`.

### Usage

    autoconst(x, prange = c(0, 1), twostep = TRUE, step1 = 0.1,
    step2 = 0.01, plot = TRUE, nperp = 4, ejprob = NULL,
    species.fixed = TRUE, pdfnb=FALSE, ignore.richness=FALSE)

    autoreg(x, probs, ejprob, plot = TRUE, nperp = 4, species.fixed = TRUE,
    pdfnb=FALSE, ignore.richness=FALSE)

### Arguments

`x` | object of class `prab` as generated by `prabinit`. Presence-absence data to be analyzed.
`prange` | numerical range vector, lower value not smaller than 0, larger value not larger than 1. Range where the parameter is to be found.
`twostep` | logical. If `TRUE`, a first estimation step is carried out in the whole `prange`, and then the final estimation is determined between the preliminary estimator `-5*step2` and `+5*step2`. Else, the first simulation determines the final estimator.
`step1` | numerical between 0 and 1. Interval length between subsequent choices of `pd` for the first simulation.
`step2` | numerical between 0 and 1. Interval length between subsequent choices of `pd` for the second simulation in case of `twostep=TRUE`.
`plot` | logical. If `TRUE`, a scatterplot of `pd`-values against resulting `ejprob` values (see below), with regression line and data value of `ejprob` is shown.
`nperp` | integer. Number of simulations per `pd`-value.
`ejprob` | numerical between 0 and 1. Observed disjunction probability for data `x`; if not specified in advance, it will be computed by `autoconst`.
`species.fixed` | logical. If `TRUE`, sizes of generated species match the species sizes in `x`, else they are generated from the empirical distribution of species sizes in `x`.
`probs` | vector of numericals between 0 and 1. `pd` values for the simulation.
`pdfnb` | logical. If `TRUE`, the probabilities of the regions are modified according to the number of neighboring regions in `randpop.nb`, see Hennig and Hausdorf (2002), p. 5.
`ignore.richness` | logical. If `TRUE`, there is no assumption of species richnesses to differ between regions in the null model. Regionwise probabilities don't differ in the generation of null data.

### Details

The spatial autocorrelation parameter `pd` of the model for the generation of presence-absence data sets used by `randpop.nb` can be estimated by use of the observed disjuction probability `ejprob` which is the sum of all species' connectivity components minus the number of species divided by the number of "presence" entries minus the number of species. This is done by a simulation of artificial data sets with characteristics of `x` and different `pd`-values, governed by `prange, step1, step2` and `nperp`. `ejprob` is then calculated for all simulated populations. A linear regression of `ejprob` on `pd` is performed and the estimator of `pd` is determined by computing the inverse of the regression function for the `ejprob`-value of `x`.

### Value

`autoconst` produces the same list as `autoreg` with additional component `ejprob`. The components are

`pd` | (eventually) estimated parameter `pd`.
`coef` | (eventually) estimated regression coefficients.
`ejprob` | see above.

### Author(s)

Christian Hennig chrish@stats.ucl.ac.uk http://www.homepages.ucl.ac.uk/~ucakche

### References

Hausdorf, B. and Hennig, C. (2003) Biotic Element Analysis in Biogeography. To appear in Systematic Biology.

Hausdorf, B. and Hennig, C. (2003) Nestedness of north-west European land snail ranges as a consequence of differential immigration from Pleistocene glacial refuges. Oecologia 135, 102-109.

Hennig, C. and Hausdorf, B. (2004) Distance-based parametric bootstrap tests for clustering of species ranges. Computational Statistics and Data Analysis 45, 875-896.

### See Also

`randpop.nb`, `prabinit`, `con.comp`

### Examples

    options(digits=4)
    data(kykladspecreg)
    data(nb)
    set.seed(1234)
    x <- prabinit(prabmatrix=kykladspecreg, neighborhood=nb)
    ax <- autoconst(x,nperp=2,step1=0.3,twostep=FALSE)

[Package prabclus version 2.2-6 Index]