aplnmle: Poisson Lognormal Modeling of Discrete Data

Description

Functions to Estimate the Poisson Lognormal Discrete Probability Distribution via maximum likelihood.

Usage

aplnmle(x, cutoff = 1, cutabove = 1000, guess = c(0.6,1.2),
    method = "BFGS", conc = FALSE, hellinger = FALSE, hessian=TRUE,logn=TRUE)

Value

theta: vector of MLE of the parameters.
asycov: asymptotic covariance matrix.
asycor: asymptotic correlation matrix.
se: vector of standard errors for the MLE.

conc: The value of the concentration index (if calculated).

Arguments

x: A vector of counts (one per observation).
cutoff: Calculate estimates conditional on exceeding this value.
cutabove: Calculate estimates conditional on not exceeding this value.
guess: Initial estimate at the MLE.
method: Method of optimization. See "optim" for details.
conc: Calculate the concentration index of the distribution?
hellinger: Minimize Hellinger distance of the parametric model from the data instead of maximizing the likelihood.
hessian: Calculate the hessian of the information matrix (for use with calculating the standard errors.
logn: Use logn parametrization, that is, mean and variance on the observation scale.

References

Jones, J. H. and Handcock, M. S. "An assessment of preferential attachment as a mechanism for human sexual network formation," Proceedings of the Royal Society, B, 2003, 270, 1123-1128.

Examples

Run this code


# Simulate a Poisson Lognormal distribution over 100
# observations with lognormal mean of -1 and lognormal variance of 1
# This leads to a mean of 1

set.seed(1)
s4 <- simpln(n=100, v=c(-1,1))
table(s4)

#
# Calculate the MLE and an asymptotic confidence
# interval for the parameters
#

s4est <- aplnmle(s4)
s4est

# Calculate the MLE and an asymptotic confidence
# interval for rho under the Yule model
#

s4yuleest <- ayulemle(s4)
s4yuleest

# Calculate the MLE and an asymptotic confidence
# interval for rho under the Waring model
#

s4warest <- awarmle(s4)
s4warest

#
# Compare the AICC and BIC for the three models
#

llplnall(v=s4est$theta,x=s4)
llyuleall(v=s4yuleest$theta,x=s4)
llwarall(v=s4warest$theta,x=s4)