aplnmle: Poisson Lognormal Modeling of Discrete Data

In degreenet: Models for Skewed Count Distributions Relevant to Networks

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)

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.

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).

Note

See the papers on https://handcock.github.io/?q=Holland for details

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.

See Also

ayulemle, awarmle, simpln

Examples

# 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)

degreenet documentation built on Sept. 26, 2024, 1:08 a.m.