| Title: | Models for Skewed Count Distributions Relevant to Networks |
|---|---|
| Description: | Likelihood-based inference for skewed count distributions, typically of degrees used in network modeling. "degreenet" is a part of the "statnet" suite of packages for network analysis. See Jones and Handcock <doi:10.1098/rspb.2003.2369>. |
| Authors: | Mark S. Handcock [aut, cre, cph]
|
| Maintainer: | Mark S. Handcock <[email protected]> |
| License: | GPL-3 + file LICENSE |
| Version: | 1.3-6 |
| Built: | 2024-10-26 03:39:37 UTC |
| Source: | https://github.com/cran/degreenet |
degreenet is a collection of functions to fit, diagnose, and simulate from distributions for skewed count data. The coverage of distributions is very selective, focusing on those that have been proposed to model the degree distribution on networks. For the rationale for this choice, see the papers in the references section below. For a list of functions type: help(package='degreenet')
For a complete list of the functions, use library(help="degreenet")
or read the rest of the manual. For a simple demonstration,
use demo(packages="degreenet").
The degreenet package is part of the statnet suite of packages. The suite was developed to facilitate the statistical analysis of network data.
When publishing results obtained using this package alone see the
citation in citation(package="degreenet"). The citation for the original
paper to use this package is Handcock and Jones (2003) and it should be cited
for the theoretical development.
If you use other packages in the statnet suite, please cite it as:
Mark S. Handcock, David R. Hunter, Carter T. Butts, Steven M. Goodreau,
and Martina Morris. 2003
statnet: Software tools for the Statistical Modeling of Network Data
https://statnet.org.
For complete citation information, usecitation(package="statnet").
All programs derived from this or other statnet packages must cite them appropriately.
See the Handcock and Jones (2003) reference (and the papers it cites and is cited by) for more information on the methodology.
Recent advances in the statistical modeling of random networks have had an impact on the empirical study of social networks. Statistical exponential family models (Strauss and Ikeda 1990) are a generalization of the Markov random network models introduced by Frank and Strauss (1986). These models recognize the complex dependencies within relational data structures. To date, the use of stochastic network models for networks has been limited by three interrelated factors: the complexity of realistic models, the lack of simulation tools for inference and validation, and a poor understanding of the inferential properties of nontrivial models.
This package relies on the network package which allows networks to be
represented in R. The statnet suite of packages allows maximum likelihood estimates of
exponential random network models to be calculated using Markov Chain Monte
Carlo, as well as a broad range of statistical analysis of networks, such as
tools for plotting networks, simulating
networks and assessing model goodness-of-fit.
For detailed information on how to download and install the software, go to the statnet website: https://statnet.org. A tutorial, support newsgroup, references and links to further resources are provided there.
Mark S. Handcock [email protected]
Maintainer: Mark S. Handcock [email protected]
Frank, O., and Strauss, D.(1986). Markov graphs. Journal of the American Statistical Association, 81, 832-842.
Jones, J. H. and Handcock, M. S. (2003). An assessment of preferential attachment as a mechanism for human sexual network formation, Proceedings of the Royal Society, B, 2003, 270, 1123-1128.
Handcock, M. S., Hunter, D. R., Butts, C. T., Goodreau,
S. M., and Morris, M. (2003),
statnet: Software tools for the Statistical Modeling of Network Data.,
URL https://statnet.org
Strauss, D., and Ikeda, M.(1990). Pseudolikelihood estimation for social networks. Journal of the American Statistical Association, 85, 204-212.
Functions to Estimate the Conway Maxwell Poisson Discrete Probability Distribution via maximum likelihood.
acmpmle(x, cutoff = 1, cutabove = 1000, guess=c(7,3), method="BFGS", conc=FALSE, hellinger=FALSE, hessian=TRUE)acmpmle(x, cutoff = 1, cutabove = 1000, guess=c(7,3), method="BFGS", conc=FALSE, hellinger=FALSE, hessian=TRUE)
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. |
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). |
See the papers on https://handcock.github.io/?q=Holland for details.
Based on the C code in the package compoisson written by Jeffrey Dunn (2008).
compoisson: Conway-Maxwell-Poisson Distribution, Jeffrey Dunn, 2008, R package version 0.3
ayulemle, awarmle, simcmp
# Simulate a Conway Maxwell Poisson distribution over 100 # observations with mean of 7 and variance of 3 # This leads to a mean of 1 set.seed(1) s4 <- simcmp(n=100, v=c(7,3)) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for the parameters # acmpmle(s4)# Simulate a Conway Maxwell Poisson distribution over 100 # observations with mean of 7 and variance of 3 # This leads to a mean of 1 set.seed(1) s4 <- simcmp(n=100, v=c(7,3)) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for the parameters # acmpmle(s4)
Functions to Estimate the Discrete version of q-Exponential Probability Distribution via maximum likelihood.
adqemle(x, cutoff = 1, cutabove = 1000, guess = c(3.5,1), method = "BFGS", conc = FALSE, hellinger = FALSE, hessian=TRUE)adqemle(x, cutoff = 1, cutabove = 1000, guess = c(3.5,1), method = "BFGS", conc = FALSE, hellinger = FALSE, hessian=TRUE)
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. |
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. |
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). |
See the papers on https://handcock.github.io/?q=Holland for details
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.
ayulemle, adqemle, simdqe
# Simulate a Discrete version of q-Exponential distribution over 100 # observations with a PDF exponent of 3.5 and a # sigma scale of 1 set.seed(1) s4 <- simdqe(n=100, v=c(3.5,1)) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for the parameters # s4est <- adqemle(s4) s4est # Calculate the MLE and an asymptotic confidence # interval for rho under the Yule model # s4yuleest <- ayulemle(s4) s4yuleest # # Compare the AICC and BIC for the two models # lldqeall(v=s4est$theta,x=s4) llyuleall(v=s4yuleest$theta,x=s4)# Simulate a Discrete version of q-Exponential distribution over 100 # observations with a PDF exponent of 3.5 and a # sigma scale of 1 set.seed(1) s4 <- simdqe(n=100, v=c(3.5,1)) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for the parameters # s4est <- adqemle(s4) s4est # Calculate the MLE and an asymptotic confidence # interval for rho under the Yule model # s4yuleest <- ayulemle(s4) s4yuleest # # Compare the AICC and BIC for the two models # lldqeall(v=s4est$theta,x=s4) llyuleall(v=s4yuleest$theta,x=s4)
Functions to Estimate the Poisson Lognormal Discrete Probability Distribution via maximum likelihood.
aplnmle(x, cutoff = 1, cutabove = 1000, guess = c(0.6,1.2), method = "BFGS", conc = FALSE, hellinger = FALSE, hessian=TRUE,logn=TRUE)aplnmle(x, cutoff = 1, cutabove = 1000, guess = c(0.6,1.2), method = "BFGS", conc = FALSE, hellinger = FALSE, hessian=TRUE,logn=TRUE)
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. |
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). |
See the papers on https://handcock.github.io/?q=Holland for details
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.
ayulemle, awarmle, simpln
# 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$theta,x=s4)# Simulate a Poisson Lognormal distribution over 100 # observations with lognormal mean of -1 and lognormal variance of 1 # This leads to a mean of 1 set.seed(1) s4 <- simpln(n=100, v=c(-1,1)) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for the parameters # s4est <- aplnmle(s4) s4est # Calculate the MLE and an asymptotic confidence # interval for rho under the Yule model # s4yuleest <- ayulemle(s4) s4yuleest # Calculate the MLE and an asymptotic confidence # interval for rho under the Waring model # s4warest <- awarmle(s4) s4warest # # Compare the AICC and BIC for the three models # llplnall(v=s4est$theta,x=s4) llyuleall(v=s4yuleest$theta,x=s4) llwarall(v=s4warest$theta,x=s4)
Functions to Estimate the Waring Discrete Probability Distribution via maximum likelihood.
awarmle(x, cutoff = 1, cutabove = 1000, guess = c(3.5,0.1), method = "BFGS", conc = FALSE, hellinger = FALSE, hessian=TRUE)awarmle(x, cutoff = 1, cutabove = 1000, guess = c(3.5,0.1), method = "BFGS", conc = FALSE, hellinger = FALSE, hessian=TRUE)
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. |
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. |
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). |
See the papers on https://handcock.github.io/?q=Holland for details
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.
ayulemle, awarmle, simwar
# Simulate a Waring distribution over 100 # observations with a PDf exponent of 3.5 and a # probability of including a new actor of 0.1 set.seed(1) s4 <- simwar(n=100, v=c(3.5,0.1)) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for the parameters # s4est <- awarmle(s4) s4est # Calculate the MLE and an asymptotic confidence # interval for rho under the Yule model # s4yuleest <- ayulemle(s4) s4yuleest # # Compare the AICC and BIC for the two models # llwarall(v=s4est$theta,x=s4) llyuleall(v=s4yuleest$theta,x=s4)# Simulate a Waring distribution over 100 # observations with a PDf exponent of 3.5 and a # probability of including a new actor of 0.1 set.seed(1) s4 <- simwar(n=100, v=c(3.5,0.1)) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for the parameters # s4est <- awarmle(s4) s4est # Calculate the MLE and an asymptotic confidence # interval for rho under the Yule model # s4yuleest <- ayulemle(s4) s4yuleest # # Compare the AICC and BIC for the two models # llwarall(v=s4est$theta,x=s4) llyuleall(v=s4yuleest$theta,x=s4)
Functions to Estimate the Yule Discrete Probability Distribution via maximum likelihood.
ayulemle(x, cutoff = 1, cutabove = 1000, guess = 3.5, conc = FALSE, method = "BFGS", hellinger = FALSE, hessian = TRUE, weights = rep(1, length(x)))ayulemle(x, cutoff = 1, cutabove = 1000, guess = 3.5, conc = FALSE, method = "BFGS", hellinger = FALSE, hessian = TRUE, weights = rep(1, length(x)))
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. |
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. |
weights |
sample weights on the observed counts. |
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). |
See the papers on https://handcock.github.io/?q=Holland for details
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.
ayulemle, awarmle, simyule
# Simulate a Yule distribution over 100 # observations with PDf exponent of 3.5 set.seed(1) s4 <- simyule(n=100, rho=3.5) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for the parameters # s4est <- ayulemle(s4) s4est # # Compute the AICC and BIC for the model # llyuleall(v=s4est$theta,x=s4)# Simulate a Yule distribution over 100 # observations with PDf exponent of 3.5 set.seed(1) s4 <- simyule(n=100, rho=3.5) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for the parameters # s4est <- ayulemle(s4) s4est # # Compute the AICC and BIC for the model # llyuleall(v=s4est$theta,x=s4)
Uses the parametric bootstrap to estimate the bias and confidence interval of the MLE of the Discrete Pareto Distribution.
bsdp(x, cutoff=1, m=200, np=1, alpha=0.95) bootstrapdp(x,cutoff=1,cutabove=1000, m=200,alpha=0.95,guess=3.31,hellinger=FALSE, mle.meth="adpmle")bsdp(x, cutoff=1, m=200, np=1, alpha=0.95) bootstrapdp(x,cutoff=1,cutabove=1000, m=200,alpha=0.95,guess=3.31,hellinger=FALSE, mle.meth="adpmle")
x |
A vector of counts (one per observation). |
cutoff |
Calculate estimates conditional on exceeding this value. |
m |
Number of bootstrap samples to draw. |
np |
Number of parameters in the model (1 by default). |
alpha |
Type I error for the confidence interval. |
hellinger |
Minimize Hellinger distance of the parametric model from the data instead of maximizing the likelihood. |
cutabove |
Calculate estimates conditional on not exceeding this value. |
guess |
Initial estimate at the MLE. |
mle.meth |
Method to use to compute the MLE. |
dist |
matrix of sample CDFs, one per row. |
obsmle |
The Discrete Pareto MLE of the PDF exponent. |
bsmles |
Vector of bootstrap MLE. |
quantiles |
Quantiles of the bootstrap MLEs. |
pvalue |
p-value of the Anderson-Darling statistics relative to the bootstrap MLEs. |
obsmands |
Observed Anderson-Darling Statistic. |
meanmles |
Mean of the bootstrap MLEs. |
guess |
Initial estimate at the MLE. |
mle.meth |
Method to use to compute the MLE. |
See the papers on https://handcock.github.io/?q=Holland for details
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.
anbmle, simdp, lldp
## Not run: # Now, simulate a Discrete Pareto distribution over 100 # observations with expected count 1 and probability of another # of 0.2 set.seed(1) s4 <- simdp(n=100, v=3.31) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for the parameter. # s4est <- adpmle(s4) s4est # # Use the bootstrap to compute a confidence interval rather than using the # asymptotic confidence interval for the parameter. # bsdp(s4, m=20) ## End(Not run)## Not run: # Now, simulate a Discrete Pareto distribution over 100 # observations with expected count 1 and probability of another # of 0.2 set.seed(1) s4 <- simdp(n=100, v=3.31) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for the parameter. # s4est <- adpmle(s4) s4est # # Use the bootstrap to compute a confidence interval rather than using the # asymptotic confidence interval for the parameter. # bsdp(s4, m=20) ## End(Not run)
Uses the parametric bootstrap to estimate the bias and confidence interval of the MLE of the Negative Binomial Distribution.
bsnb(x, cutoff=1, m=200, np=2, alpha=0.95, hellinger=FALSE) bootstrapnb(x,cutoff=1,cutabove=1000, m=200,alpha=0.95,guess=c(5, 0.2), file="none")bsnb(x, cutoff=1, m=200, np=2, alpha=0.95, hellinger=FALSE) bootstrapnb(x,cutoff=1,cutabove=1000, m=200,alpha=0.95,guess=c(5, 0.2), file="none")
x |
A vector of counts (one per observation). |
cutoff |
Calculate estimates conditional on exceeding this value. |
m |
Number of bootstrap samples to draw. |
np |
Number of parameters in the model (1 by default). |
alpha |
Type I error for the confidence interval. |
hellinger |
Minimize Hellinger distance of the parametric model from the data instead of maximizing the likelihood. |
cutabove |
Calculate estimates conditional on not exceeding this value. |
guess |
Guess at the parameter value. |
file |
Name of the file to store the results. By default do not save the results. |
dist |
matrix of sample CDFs, one per row. |
obsmle |
The Negative Binomial MLE of the PDF exponent. |
bsmles |
Vector of bootstrap MLE. |
quantiles |
Quantiles of the bootstrap MLEs. |
pvalue |
p-value of the Anderson-Darling statistics relative to the bootstrap MLEs. |
obsmands |
Observed Anderson-Darling Statistic. |
meanmles |
Mean of the bootstrap MLEs. |
guess |
Initial estimate at the MLE. |
mle.meth |
Method to use to compute the MLE. |
See the papers on https://handcock.github.io/?q=Holland for details
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.
anbmle, simnb, llnb
# Now, simulate a Negative Binomial distribution over 100 # observations with expected count 1 and probability of another # of 0.2 set.seed(1) s4 <- simnb(n=100, v=c(5,0.2)) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for the parameter. # s4est <- anbmle(s4) s4est # # Use the bootstrap to compute a confidence interval rather than using the # asymptotic confidence interval for the parameter. # bsnb(s4, m=20)# Now, simulate a Negative Binomial distribution over 100 # observations with expected count 1 and probability of another # of 0.2 set.seed(1) s4 <- simnb(n=100, v=c(5,0.2)) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for the parameter. # s4est <- anbmle(s4) s4est # # Use the bootstrap to compute a confidence interval rather than using the # asymptotic confidence interval for the parameter. # bsnb(s4, m=20)
Uses the parametric bootstrap to estimate the bias and confidence interval of the MLE of the Poisson Lognormal Distribution.
bspln(x, cutoff=1, m=200, np=2, alpha=0.95, v=NULL, hellinger=FALSE) bootstrappln(x,cutoff=1,cutabove=1000, m=200,alpha=0.95,guess=c(0.6,1.2), file = "none")bspln(x, cutoff=1, m=200, np=2, alpha=0.95, v=NULL, hellinger=FALSE) bootstrappln(x,cutoff=1,cutabove=1000, m=200,alpha=0.95,guess=c(0.6,1.2), file = "none")
x |
A vector of counts (one per observation). |
cutoff |
Calculate estimates conditional on exceeding this value. |
m |
Number of bootstrap samples to draw. |
np |
Number of parameters in the model (1 by default). |
alpha |
Type I error for the confidence interval. |
v |
Parameter value to use for the bootstrap distribution. By default it is the MLE of the data. |
hellinger |
Minimize Hellinger distance of the parametric model from the data instead of maximizing the likelihood. |
cutabove |
Calculate estimates conditional on not exceeding this value. |
guess |
Initial estimate at the MLE. |
file |
Name of the file to store the results. By default do not save the results. |
dist |
matrix of sample CDFs, one per row. |
obsmle |
The Poisson Lognormal MLE of the PDF exponent. |
bsmles |
Vector of bootstrap MLE. |
quantiles |
Quantiles of the bootstrap MLEs. |
pvalue |
p-value of the Anderson-Darling statistics relative to the bootstrap MLEs. |
obsmands |
Observed Anderson-Darling Statistic. |
meanmles |
Mean of the bootstrap MLEs. |
See the papers on https://handcock.github.io/?q=Holland for details
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.
anbmle, simpln, llpln
# Now, simulate a Poisson Lognormal distribution over 100 # observations with expected count 1 and probability of another # of 0.2 set.seed(1) s4 <- simpln(n=100, v=c(5,0.2)) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for the parameter. # s4est <- aplnmle(s4) s4est # # Use the bootstrap to compute a confidence interval rather than using the # asymptotic confidence interval for the parameter. # bspln(s4, m=5)# Now, simulate a Poisson Lognormal distribution over 100 # observations with expected count 1 and probability of another # of 0.2 set.seed(1) s4 <- simpln(n=100, v=c(5,0.2)) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for the parameter. # s4est <- aplnmle(s4) s4est # # Use the bootstrap to compute a confidence interval rather than using the # asymptotic confidence interval for the parameter. # bspln(s4, m=5)
Uses the parametric bootstrap to estimate the bias and confidence interval of the MLE of the Waring Distribution.
bswar(x, cutoff=1, m=200, np=2, alpha=0.95, v=NULL, hellinger=FALSE) bootstrapwar(x,cutoff=1,cutabove=1000, m=200,alpha=0.95,guess=c(3.31, 0.1),file="none", conc = FALSE)bswar(x, cutoff=1, m=200, np=2, alpha=0.95, v=NULL, hellinger=FALSE) bootstrapwar(x,cutoff=1,cutabove=1000, m=200,alpha=0.95,guess=c(3.31, 0.1),file="none", conc = FALSE)
x |
A vector of counts (one per observation). |
cutoff |
Calculate estimates conditional on exceeding this value. |
m |
Number of bootstrap samples to draw. |
np |
Number of parameters in the model (1 by default). |
alpha |
Type I error for the confidence interval. |
v |
Parameter value to use for the bootstrap distribution. By default it is the MLE of the data. |
hellinger |
Minimize Hellinger distance of the parametric model from the data instead of maximizing the likelihood. |
cutabove |
Calculate estimates conditional on not exceeding this value. |
guess |
Guess at the parameter value. |
file |
Name of the file to store the results. By default do not save the results. |
conc |
Calculate the concentration index of the distribution? |
dist |
matrix of sample CDFs, one per row. |
obsmle |
The Waring MLE of the PDF exponent. |
bsmles |
Vector of bootstrap MLE. |
quantiles |
Quantiles of the bootstrap MLEs. |
pvalue |
p-value of the Anderson-Darling statistics relative to the bootstrap MLEs. |
obsmands |
Observed Anderson-Darling Statistic. |
meanmles |
Mean of the bootstrap MLEs. |
guess |
Initial estimate at the MLE. |
mle.meth |
Method to use to compute the MLE. |
See the papers on https://handcock.github.io/?q=Holland for details
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.
anbmle, simwar, llwar
# Now, simulate a Waring distribution over 100 # observations with expected count 1 and probability of another # of 0.2 set.seed(1) s4 <- simwar(n=100, v=c(5,0.2)) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for the parameter. # s4est <- awarmle(s4) s4est # # Use the bootstrap to compute a confidence interval rather than using the # asymptotic confidence interval for the parameter. # bswar(s4, m=20)# Now, simulate a Waring distribution over 100 # observations with expected count 1 and probability of another # of 0.2 set.seed(1) s4 <- simwar(n=100, v=c(5,0.2)) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for the parameter. # s4est <- awarmle(s4) s4est # # Use the bootstrap to compute a confidence interval rather than using the # asymptotic confidence interval for the parameter. # bswar(s4, m=20)
Uses the parametric bootstrap to estimate the bias and confidence interval of the MLE of the Yule Distribution.
bsyule(x, cutoff=1, m=200, np=1, alpha=0.95, v=NULL, hellinger=FALSE, cutabove=1000) bootstrapyule(x,cutoff=1,cutabove=1000, m=200,alpha=0.95,guess=3.31,hellinger=FALSE, mle.meth="ayulemle")bsyule(x, cutoff=1, m=200, np=1, alpha=0.95, v=NULL, hellinger=FALSE, cutabove=1000) bootstrapyule(x,cutoff=1,cutabove=1000, m=200,alpha=0.95,guess=3.31,hellinger=FALSE, mle.meth="ayulemle")
x |
A vector of counts (one per observation). |
cutoff |
Calculate estimates conditional on exceeding this value. |
m |
Number of bootstrap samples to draw. |
np |
Number of parameters in the model (1 by default). |
alpha |
Type I error for the confidence interval. |
v |
Parameter value to use for the bootstrap distribution. By default it is the MLE of the data. |
hellinger |
Minimize Hellinger distance of the parametric model from the data instead of maximizing the likelihood. |
cutabove |
Calculate estimates conditional on not exceeding this value. |
guess |
Initial estimate at the MLE. |
mle.meth |
Method to use to compute the MLE. |
dist |
matrix of sample CDFs, one per row. |
obsmle |
The Yule MLE of the PDF exponent. |
bsmles |
Vector of bootstrap MLE. |
quantiles |
Quantiles of the bootstrap MLEs. |
pvalue |
p-value of the Anderson-Darling statistics relative to the bootstrap MLEs. |
obsmands |
Observed Anderson-Darling Statistic. |
meanmles |
Mean of the bootstrap MLEs. |
See the papers on https://handcock.github.io/?q=Holland for details
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.
ayulemle, simyule, llyule
# Now, simulate a Yule distribution over 100 # observations with rho=4.0 set.seed(1) s4 <- simyule(n=100, rho=4) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for rho # s4est <- ayulemle(s4) s4est # # Use the bootstrap to compute a confidence interval rather than using the # asymptotic confidence interval for rho. # bsyule(s4, m=20)# Now, simulate a Yule distribution over 100 # observations with rho=4.0 set.seed(1) s4 <- simyule(n=100, rho=4) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for rho # s4est <- ayulemle(s4) s4est # # Use the bootstrap to compute a confidence interval rather than using the # asymptotic confidence interval for rho. # bsyule(s4, m=20)
Functions to Estimate Parametric Discrete Probability Distributions via maximum likelihood Based on categorical response
gyulemle(x, cutoff = 1, cutabove = 1000, guess = 3.5, conc = FALSE, method = "BFGS", hellinger = FALSE, hessian=TRUE)gyulemle(x, cutoff = 1, cutabove = 1000, guess = 3.5, conc = FALSE, method = "BFGS", hellinger = FALSE, hessian=TRUE)
x |
A vector of categories for counts (one per observation). The values of |
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. |
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). |
See the papers on https://handcock.github.io/?q=Holland for details
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.
# # 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)# # 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)
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.
llgyule(v, x, cutoff=1,cutabove=1000,xr=1:10000,hellinger=FALSE)llgyule(v, x, cutoff=1,cutabove=1000,xr=1:10000,hellinger=FALSE)
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 |
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? |
the log-likelihood for the data x at parameter value v
(or the Hellinder distance if hellinger=TRUE).
See the papers on https://handcock.github.io/?q=Holland for details
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.
gyulemle, llgyuleall, dyule
# # 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)# # 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)
Functions to Estimate the Log-likelihood for Discrete Probability Distributions Based on Categorical Response.
llgyuleall(v, x, cutoff = 2, cutabove = 1000, np=1)llgyuleall(v, x, cutoff = 2, cutabove = 1000, np=1)
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 |
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. |
the log-likelihood for the data x at parameter value v.
See the papers on https://handcock.github.io/?q=Holland for details
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.
gyulemle, llgyule, dyule, llgwarall
# # 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)# # 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)
Compute the Conditional Log-likelihood for the Poisson Lognormal Discrete Probability Distribution. The likelihood is calculated conditionl on the count being at least the cutoff value and less than or equal to the cutabove value.
llpln(v, x, cutoff=1,cutabove=1000,xr=1:10000,hellinger=FALSE,logn = TRUE)llpln(v, x, cutoff=1,cutabove=1000,xr=1:10000,hellinger=FALSE,logn = TRUE)
v |
A vector of parameters for the Yule (a 1-vector - the scaling exponent). |
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. |
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? |
logn |
Use logn parametrization, that is, mean and variance on the observation scale. |
the log-likelihood for the data x at parameter value v
(or the Hellinder distance if hellinger=TRUE).
See the papers on https://handcock.github.io/?q=Holland for details
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.
aplnmle, llplnall, dpln
# Simulate a Poisson Lognormal distribution over 100 # observations with lognormal mean -1 and logormal standard deviation 1. set.seed(1) s4 <- simpln(n=100, v=c(-1,1)) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for rho # s4est <- aplnmle(s4) s4est # # Calculate the MLE and an asymptotic confidence # interval for rho under the Waring model # s4warest <- awarmle(s4) s4warest # # Compare the log-likelihoods for the two models # llpln(v=s4est$theta,x=s4) llwar(v=s4warest$theta,x=s4)# Simulate a Poisson Lognormal distribution over 100 # observations with lognormal mean -1 and logormal standard deviation 1. set.seed(1) s4 <- simpln(n=100, v=c(-1,1)) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for rho # s4est <- aplnmle(s4) s4est # # Calculate the MLE and an asymptotic confidence # interval for rho under the Waring model # s4warest <- awarmle(s4) s4warest # # Compare the log-likelihoods for the two models # llpln(v=s4est$theta,x=s4) llwar(v=s4warest$theta,x=s4)
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.
llyule(v, x, cutoff=1,cutabove=1000, xr=1:10000 ,hellinger=FALSE, weights = rep(1, length(x)))llyule(v, x, cutoff=1,cutabove=1000, xr=1:10000 ,hellinger=FALSE, weights = rep(1, length(x)))
v |
A vector of parameters for the Yule (a 1-vector - the scaling exponent). |
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. |
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? |
weights |
sample weights on the observed counts. |
the log-likelihood for the data x at parameter value v
(or the Hellinder distance if hellinger=TRUE).
See the papers on https://handcock.github.io/?q=Holland for details
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.
ayulemle, llyuleall, dyule
# Simulate a Yule distribution over 100 # observations with rho=4.0 set.seed(1) s4 <- simyule(n=100, rho=4) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for rho # s4est <- ayulemle(s4) s4est # # Calculate the MLE and an asymptotic confidence # interval for rho under the Waring model (i.e., rho=4, p=2/3) # s4warest <- awarmle(s4) s4warest # # Compare the log-likelihoods for the two models # llyule(v=s4est$theta,x=s4) llwar(v=s4warest$theta,x=s4)# Simulate a Yule distribution over 100 # observations with rho=4.0 set.seed(1) s4 <- simyule(n=100, rho=4) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for rho # s4est <- ayulemle(s4) s4est # # Calculate the MLE and an asymptotic confidence # interval for rho under the Waring model (i.e., rho=4, p=2/3) # s4warest <- awarmle(s4) s4warest # # Compare the log-likelihoods for the two models # llyule(v=s4est$theta,x=s4) llwar(v=s4warest$theta,x=s4)
Functions to Estimate the Log-likelihood for Discrete Probability Distributions.
llyuleall(v, x, cutoff = 2, cutabove = 1000, np=1)llyuleall(v, x, cutoff = 2, cutabove = 1000, np=1)
v |
A vector of parameters for the Yule (a 1-vector - the scaling exponent). |
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. |
np |
wnumber of parameters in the model. For the Yule this is 1. |
the log-likelihood for the data x at parameter value v.
See the papers on https://handcock.github.io/?q=Holland for details
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.
ayulemle, llyule, dyule, llwarall
# Simulate a Yule distribution over 100 # observations with rho=4.0 set.seed(1) s4 <- simyule(n=100, rho=4) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for rho # s4est <- ayulemle(s4) s4est # Calculate the MLE and an asymptotic confidence # interval for rho under the Waring model (i.e., rho=4, p=2/3) # s4warest <- awarmle(s4) s4warest # # Compare the AICC and BIC for the two models # llyuleall(v=s4est$theta,x=s4) llwarall(v=s4warest$theta,x=s4)# Simulate a Yule distribution over 100 # observations with rho=4.0 set.seed(1) s4 <- simyule(n=100, rho=4) table(s4) # # Calculate the MLE and an asymptotic confidence # interval for rho # s4est <- ayulemle(s4) s4est # Calculate the MLE and an asymptotic confidence # interval for rho under the Waring model (i.e., rho=4, p=2/3) # s4warest <- awarmle(s4) s4warest # # Compare the AICC and BIC for the two models # llyuleall(v=s4est$theta,x=s4) llwarall(v=s4warest$theta,x=s4)
Generate a undirected network where the degree of each actor is specified. The degree is the number of actors the actor is tied to.
This returns a network object and requires the igraph package.
reedmolloy(deg, maxit=10, verbose=TRUE)reedmolloy(deg, maxit=10, verbose=TRUE)
deg |
vector of counts where element |
maxit |
integer; maximum number of jitterings of the degree sequence to find a valid network. |
verbose |
Print out details of the progress of the algorithm. |
The network is returned as a network object.
See the papers on https://handcock.github.io/?q=Holland for details
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.
ayulemle, dyule
# Now, simulate a Poisson Lognormal distribution over 100 # observations with mean = -1 and s.d. = 1. set.seed(2) s4 <- simpln(n=100, v=c(-1,1)) table(s4) # simr <- reedmolloy(s4) simr# Now, simulate a Poisson Lognormal distribution over 100 # observations with mean = -1 and s.d. = 1. set.seed(2) s4 <- simpln(n=100, v=c(-1,1)) table(s4) # simr <- reedmolloy(s4) simr
Functions to Estimate the Rounded Poisson Lognormal Discrete Probability Distribution via maximum likelihood.
rplnmle(x, cutoff = 1, cutabove = 1000, guess = c(0.6,1.2), method = "BFGS", conc = FALSE, hellinger = FALSE, hessian=TRUE)rplnmle(x, cutoff = 1, cutabove = 1000, guess = c(0.6,1.2), method = "BFGS", conc = FALSE, hellinger = FALSE, hessian=TRUE)
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. |
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. |
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). |
See the papers on https://handcock.github.io/?q=Holland for details
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.
aplnmle
# 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 <- rplnmle(s4) s4est# 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 <- rplnmle(s4) s4est
Generate a network with a given number of actors having a degree distribution draw from a Yule distribution. The resultant network is not random - that is, is not a random draw from all such networks.
ryule(n=20,rho=2.5, maxdeg=n-1, maxit=10, verbose=FALSE)ryule(n=20,rho=2.5, maxdeg=n-1, maxit=10, verbose=FALSE)
n |
Number of actors in the network. |
rho |
PDF exponent of the Yule distribution. |
maxdeg |
Maximum degree to sample (using truncation of the distribution). If this is greater then |
maxit |
integer; maximum number of resamplings of the degree sequence to find a valid network. |
verbose |
Print out details of the progress of the algorithm. |
If the network package is available, the network is returned as
a network object. If not a sociomatrix is returned.
See the papers on https://handcock.github.io/?q=Holland for details
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.
ayulemle, dyule, reedmolloy
# Now, simulate a Yule network of 30 # actors with rho=4.0 ryule(n=30, rho=4)# Now, simulate a Yule network of 30 # actors with rho=4.0 ryule(n=30, rho=4)
Functions to generate random samples from a Conway Maxwell Poisson Probability Distribution
simcmp(n=100, v=c(7,2.6), maxdeg=10000)simcmp(n=100, v=c(7,2.6), maxdeg=10000)
n |
number of samples to draw. |
v |
Conway Maxwell Poisson parameters: lognormal mean and lognormal s.d. |
maxdeg |
Maximum degree to sample (using truncation of the distribution). |
vector of random draws or samples.
See the papers on https://handcock.github.io/?q=Holland for details
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.
acmpmle, dcmp
# Now, simulate a Conway Maxwell Poisson distribution over 100 # observations with lognormal mean -1 and lognormal standard deviation 1. set.seed(1) s4 <- simcmp(n=100, v=c(7,3)) table(s4)# Now, simulate a Conway Maxwell Poisson distribution over 100 # observations with lognormal mean -1 and lognormal standard deviation 1. set.seed(1) s4 <- simcmp(n=100, v=c(7,3)) table(s4)
Functions to generate random samples from a Discrete Pareto Probability Distribution
simdp(n=100, v=3.5, maxdeg=10000)simdp(n=100, v=3.5, maxdeg=10000)
n |
number of samples to draw. |
v |
Discrete Pareto parameters: PDF exponent. |
maxdeg |
Maximum degree to sample (using truncation of the distribution). |
vector of random draws or samples.
See the papers on https://handcock.github.io/?q=Holland for details
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.
adpmle, ddp
## Not run: # Now, simulate a Discrete Pareto distribution over 100 # observations with lognormal mean -1 and lognormal standard deviation 1. set.seed(1) s4 <- simdp(n=100, v=3.5) table(s4) ## End(Not run)## Not run: # Now, simulate a Discrete Pareto distribution over 100 # observations with lognormal mean -1 and lognormal standard deviation 1. set.seed(1) s4 <- simdp(n=100, v=3.5) table(s4) ## End(Not run)
Functions to generate random samples from a Negative Binomial Probability Distribution
simnb(n=100, v=c(5,0.2), maxdeg=10000)simnb(n=100, v=c(5,0.2), maxdeg=10000)
n |
number of samples to draw. |
v |
Negative Binomial parameters: expected count and probability of another. |
maxdeg |
Maximum degree to sample (using truncation of the distribution). |
vector of random draws or samples.
See the papers on https://handcock.github.io/?q=Holland for details
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.
anbmle, dnb
# Now, simulate a Negative Binomial distribution over 100 # observations with lognormal mean -1 and lognormal standard deviation 1. set.seed(1) s4 <- simnb(n=100, v=c(5,0.2)) table(s4)# Now, simulate a Negative Binomial distribution over 100 # observations with lognormal mean -1 and lognormal standard deviation 1. set.seed(1) s4 <- simnb(n=100, v=c(5,0.2)) table(s4)
Functions to generate random samples from a Poisson Lognormal Probability Distribution
simpln(n=100, v=c(0.6,1.2), maxdeg=10000, cutoff=1)simpln(n=100, v=c(0.6,1.2), maxdeg=10000, cutoff=1)
n |
number of samples to draw. |
v |
Poisson Lognormal parameters: lognormal mean and lognormal s.d. |
maxdeg |
Maximum degree to sample (using truncation of the distribution). |
cutoff |
Calculate estimates conditional on exceeding this value. |
vector of random draws or samples.
See the papers on https://handcock.github.io/?q=Holland for details
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.
aplnmle, dpln
# Now, simulate a Poisson Lognormal distribution over 100 # observations with lognormal mean -1 and lognormal standard deviation 1. set.seed(1) s4 <- simpln(n=100, v=c(-1,1)) table(s4)# Now, simulate a Poisson Lognormal distribution over 100 # observations with lognormal mean -1 and lognormal standard deviation 1. set.seed(1) s4 <- simpln(n=100, v=c(-1,1)) table(s4)
Functions to generate random samples from a Waring Probability Distribution
simwar(n=100, v=c(3.5, 0.1), maxdeg=10000)simwar(n=100, v=c(3.5, 0.1), maxdeg=10000)
n |
number of samples to draw. |
v |
Waring parameters: scaling exponent and probability of a new actor. |
maxdeg |
Maximum degree to sample (using truncation of the distribution). |
vector of random draws or samples.
See the papers on https://handcock.github.io/?q=Holland for details
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.
awarmle, dwar
# Now, simulate a Waring distribution over 100 # observations with Waring with exponent 3.5 and probability of a new # actor 0.1. set.seed(1) s4 <- simwar(n=100, v=c(3.5, 0.1)) table(s4)# Now, simulate a Waring distribution over 100 # observations with Waring with exponent 3.5 and probability of a new # actor 0.1. set.seed(1) s4 <- simwar(n=100, v=c(3.5, 0.1)) table(s4)
Functions to generate random samples from a Yule Probability Distribution
simyule(n=100, rho=4, maxdeg=10000)simyule(n=100, rho=4, maxdeg=10000)
n |
number of samples to draw. |
rho |
Yule PDF exponent. |
maxdeg |
Maximum degree to sample (using truncation of the distribution). |
vector of random draws or samples.
See the papers on https://handcock.github.io/?q=Holland for details
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.
ayulemle, dyule
# Now, simulate a Yule distribution over 100 # observations with rho=4.0 set.seed(1) s4 <- simyule(n=100, rho=4) table(s4)# Now, simulate a Yule distribution over 100 # observations with rho=4.0 set.seed(1) s4 <- simyule(n=100, rho=4) table(s4)
This is a data set used in Jones and Handcock (2002) and
The data are counts of the numbers of sex partners for men and women in the last twelve months. The data from the 1996 “Sex in Sweden" survey based on a nationwide probability sample and financed by the Swedish National Board of Health.
data(sweden)data(sweden)
We thanks Dr. Bo Lewin, Professor of Sociology, Uppsala University and head of the research team responsible for the “Sex in Sweden" study for providing the Swedish data used in this study. This research supported by Grant 7R01DA012831-02 from NIDA and Grant 1R01HD041877 from NICHD.
Lewin, B. (1996). Sex in Sweden, Stockholm: National Institute of Public Health.
Handcock, Mark S. and Jones, James Holland (2004), “Likelihood-Based Inference for Stochastic Models of Sexual Network Formation" Theoretical Population Biology, doi:10.1016/j.tpb.2003.09.006.
Jones, James Holland and Handcock, Mark S. (2003), Nature, 423, 6940, 605-606.
Handcock, Mark S. and Jones, James Holland (2003), “An assessment of preferential attachment as a mechanism for human sexual network formation" Proceedings of the Royal Society, B., 270, 1123-1128.
ayulemle