R: Maximum Likelihood Estimation for Poisson Lognormal...

MLE for Poisson lognormal distribution {poilog} | R Documentation

## Maximum Likelihood Estimation for Poisson Lognormal Distribution

### Description

`poilogMLE` fits the Poisson lognormal distribution to data and estimates parameters mean `mu` and standard deviation `sig` in the lognormal distribution

### Usage

    poilogMLE(n, startVals = c(mu=1, sig=2),
              nboot = 0, zTrunc = TRUE,
              method = "BFGS", control = list(maxit=1000))

### Arguments

`n` | A vector of counts
`startVals` | Starting values of parameters, see details
`nboot` | Number of parametric bootstraps, defaults to zero
`zTrunc` | Zero-truncated distribution, defaults to TRUE
`method` | Method to use during optimization, see details
`control` | A list of control parameters for the optimization routine, see details

### Details

The function estimates parameters mean `mu` and standard deviation `sig`. In cases of incomplete sampling the estimate of `mu` will be confounded with the sampling intensity (see `rpoilog`). Assuming sampling intensity ν, the estimates of the mean is \code{mu}+\ln(ν). Parameter `sig` can be estimated without any knowledge of sampling intensity.
The parameters must be given starting values for the optimization procedure (default starting values are used if starting values are not specified in the function call).

The function uses the optimization procedures in `optim` to obtain the maximum likelihood estimate. The `method` and `control` arguments are passed to `optim`, see the help page for this function for additional methods and control parameters.

A zero-truncated distribution (see `dpoilog`) is assumed by default (`zTrunc = TRUE`). In cases where the number of zeros is known the `zTrunc` argument should be set to `FALSE`.

The approximate fraction of species revealed by the sample is 1-q(0;\code{mu},\code{sig}).

Parametric bootstrapping is done by simulating new sets of observations using the estimated parameters (see `rbipoilog`).

### Value

`par` | Maximum likelihood estimates of the parameters
`p` | Approximate fraction of species revealed by the sample
`logLval` | Log likelihood of the data given the estimated parameters
`gof` | Godness of fit measure obtained by checking the rank of logLval against logLval's obtained during the bootstrap procedure, (gof<0.05) or (gof>0.95) indicates lack of fit
`boot` | A data frame containing the bootstrap replicates of parameters and logLval

### Author(s)

Vidar Grøtan vidar.grotan@bio.ntnu.no, Steinar Engen

### References

Bulmer, M. G. 1974. On fitting the Poisson lognormal distribution to species abundance data. Biometrics 30, 651-660.
Engen, S., R. Lande, T. Walla and P. J. DeVries. 2002. Analyzing spatial structure of communities using the two-dimensional Poisson lognormal species abundance model. American Naturalist 160, 60-73.

### See Also

`optim`, `dpoilog`, `rpoilog`

### Examples

    ### simulate observations

    n <- rpoilog(S=80,mu=1,sig=2)

    ### obtain estimates of parameters
    est <- poilogMLE(n)

    ### similar, but now with bootstrapping ###
    ## Not run: est <- poilogMLE(n,nboot=10)

    ### change start values and request tracing information
    ### from optimization procedure
    est <- poilogMLE(n,startVals=c(2,3),
                     control=list(maxit=1000,trace=1, REPORT=1))

[Package poilog version 0.4 Index]