llgyuleall {degreenet}

Calculate the log-likelihood for Count Distributions

Description

Functions to Estimate the Log-likelihood for Discrete Probability Distributions Based on Categorical Response.

Usage

llgyuleall(v, x, cutoff = 2, cutabove = 1000,  np=1)

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.

np

wnumber of parameters in the model. For the Yule this is 1.

Value

the log-likelihood for the data x at parameter value v.

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, llgyule, dyule, llgwarall

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)