llgyule: Calculate the Conditional log-likelihood for Count...

In degreenet: Models for Skewed Count Distributions Relevant to Networks

Calculate the Conditional log-likelihood for Count Distributions

Description

Functions to Estimate the Conditional Log-likelihood for Discrete Probability Distributions. The likelihood is calcualted condition on the count being at least the cutoff value and less than or equal to the cutabove value.

Usage

llgyule(v, x, cutoff=1,cutabove=1000,xr=1:10000,hellinger=FALSE)

Arguments

v	A vector of parameters for the Yule (a 1-vector - the scaling exponent).
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.
xr	range of count values to use to approximate the set of all realistic counts.
hellinger	Calculate the Hellinger distance of the parametric model from the data instead of the log-likelihood?

Value

the log-likelihood for the data x at parameter value v (or the Hellinder distance if hellinger=TRUE).

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

gyulemle, llgyuleall, dyule

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 log-likelihoods for the two models
#

llgyule(v=s4est$theta,x=s4)
llgwar(v=s4warest$theta,x=s4)

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