gyulemle {degreenet}R Documentation

Models for Count Distributions

Description

Functions to Estimate Parametric Discrete Probability Distributions via maximum likelihood Based on categorical response

Usage

gyulemle(x, cutoff = 1, cutabove = 1000, guess = 3.5, conc = FALSE, 
    method = "BFGS", hellinger = FALSE, hessian=TRUE)

Arguments

x A vector of categories for counts (one per observation). The values of x and the categories are: 0=0, 1=1, 2=2, 3=3, 4=4, 5=5-10, 6=11-20, 7=21-100, 8=>100
cutoff Calculate estimates conditional on exceeding this value.
cutabove Calculate estimates conditional on not exceeding this value.
guess Initial estimate at the MLE.
conc Calculate the concentration index of the distribution?
method Method of optimization. See "optim" for details.
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.

Value

result vector of parameter estimates - lower 95% confidence value, upper 95% confidence value, the PDF MLE, the asymptotic standard error, and the number of data values >=cutoff and <=cutabove.
theta The Yule MLE of the PDF exponent.
value The maximized value of the function.
conc The value of the concentration index (if calculated).

Note

See the working papers on http://www.csss.washington.edu/Papers 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.

Examples

#
# Simulate a Yule distribution over 100
# observations with rho=4.0
#

set.seed(1)
s4 <- simyule(n=100, rho=4)
table(s4)

#
# Recode it as categorical
#

s4[s4 >  4 & s4 < 11] <- 5
s4[s4 > 100] <- 8
s4[s4 >  20] <- 7
s4[s4 >  10] <- 6

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

s4est <- gyulemle(s4)
s4est

#
# Calculate the MLE and an asymptotic confidence
# interval for rho under the Waring model (i.e., rho=4, p=2/3)
#

s4warest <- gwarmle(s4)
s4warest

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

llgyuleall(v=s4est$theta,x=s4)
llgwarall(v=s4warest$theta,x=s4)


[Package degreenet version 1.0 Index]