4bipoilogMLE: Maximum Likelihood Estimation for Bivariate Poisson Lognormal... In poilog: Poisson lognormal and bivariate Poisson lognormal distribution

Description

bipoilogMLE fits the bivariate Poisson lognormal distribution to data

Usage

 1 2 3 4 bipoilogMLE(n1, n2 = NULL, startVals = c(mu1=1, mu2=1, sig1=2, sig2=2, rho=0.5), nboot = 0, zTrunc = TRUE, file = NULL, method = "BFGS", control = list(maxit=1000)) 

Arguments

 n1 a vector or a matrix with two columns of pairwise counts of observed individuals for each species n2 if n1 is not given as a matrix, a vector of counts with same ordering of species as in argument n1 startVals starting values of parameters nboot number of parametric bootstraps, defaults to zero zTrunc logical; if TRUE (default) the zero-truncated distribution is fitted file text file to hold copies of bootstrap estimates method method to use during optimization, see details control a list of control parameters for the optimization routine, see details

Details

The function estimates the parameters mu1, sig1, mu2, sig2 and rho. In cases of incomplete sampling the estimates of mu1 and mu2 will be confounded with the sampling intensities (see rbipoilog). Assuming sampling intensities ν1 and ν2, the estimates of the means are \code{mu1}+ \ln nu1 and \code{mu2}+ \ln nu2. Parameters sig1, sig2 and rho can be estimated without any knowledge of sampling intensities. 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).

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

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.

The approximate fraction of species revealed by each sample is estimated as 1 minus the zero term of the univariate Poisson lognormal distribution: 1-q(0;\code{mu1},\code{sig1}) and 1-q(0;\code{mu2},\code{sig2}).

Parametric bootstrapping could be time consuming for large data sets. If argument file is specified, e.g. file =C:\\myboots.txt’, the matrix with bootstrap estimates are copied into a tab-seperated text-file providing extra backup. Bootstrapping is done by simulating new sets of observations conditioned on the observed number of species (see rbipoilog).

Value

 par  Maximum likelihood estimates of the parameters p  Approximate fraction of species revealed by the samples for sample 1 and 2 respectively 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

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.

optim, dbipoilog, rbipoilog
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 ## simulate observations xy <- rbipoilog(S=30,mu1=1,mu2=1,sig1=2,sig2=2,rho=0.5) ## obtain estimates of parameters est <- bipoilogMLE(xy) ## similar, but now with bootstrapping ## Not run: est <- bipoilogMLE(xy,nboot=10) ## change start values and request tracing information ## from optimization procedure est <- bipoilogMLE(xy,startVals=c(2,2,4,4,0.3), control=list(maxit=1000,trace=1, REPORT=1)) ## effect of sampling intensity xy <- rbipoilog(S=100,mu1=1,mu2=1,sig1=2,sig2=2,rho=0.5,nu1=0.5,nu2=0.5) est <- bipoilogMLE(xy) ## the expected estimates of mu1 and mu2 are now 1-log(0.5) = 0.3 (approximately)