Type:	Package
Title:	Exponential Random Partition Models
Version:	0.2.0
Date:	2024-05-03
Description:	Simulates and estimates the Exponential Random Partition Model presented in the paper Hoffman, Block, and Snijders (2023) <doi:10.1177/00811750221145166>. It can also be used to estimate longitudinal partitions, following the model proposed in Hoffman and Chabot (2023) <doi:10.1016/j.socnet.2023.04.002>. The model is an exponential family distribution on the space of partitions (sets of non-overlapping groups) and is called in reference to the Exponential Random Graph Models (ERGM) for networks.
License:	GPL (≥ 3)
Depends:	R (≥ 4.2)
Imports:	numbers, utils, stats, igraph, RColorBrewer, snowfall
Suggests:	knitr, rmarkdown, testthat (≥ 3.0.0)
Config/testthat/edition:	3
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	7.3.1
Collate:	'erpm-package.R' 'functions_utility.R' 'functions_Metropolis.R' 'functions_burninthining.R' 'functions_change_statistics.R' 'functions_estimate.R' 'functions_exactcalculations.R' 'functions_exchange_algorithm.R' 'functions_loglikelihood.R' 'functions_output.R' 'functions_phase1.R' 'functions_phase2.R' 'functions_phase3.R' 'functions_statistics.R' 'functions_visualisation.R' 'outcomeObjects.R'
URL:	https://github.com/stocnet/ERPM
BugReports:	https://github.com/stocnet/ERPM/issues
NeedsCompilation:	no
Packaged:	2024-05-09 13:58:06 UTC; hoffman
Author:	Marion Hoffman [cre, aut, cph], Alexandra Amani [aut], Nico Keiser [aut]
Maintainer:	Marion Hoffman <marion.hoffman.31@gmail.com>
Repository:	CRAN
Date/Publication:	2024-05-10 17:53:16 UTC

ERPM: Exponential Random Partition Models

Description

Simulates and estimates the Exponential Random Partition Model presented in the paper Hoffman, Block, and Snijders (2023) doi:10.1177/00811750221145166. It can also be used to estimate longitudinal partitions, following the model proposed in Hoffman and Chabot (2023) doi:10.1016/j.socnet.2023.04.002. The model is an exponential family distribution on the space of partitions (sets of non-overlapping groups) and is called in reference to the Exponential Random Graph Models (ERGM) for networks.

Author(s)

Maintainer: Marion Hoffman marion.hoffman.31@gmail.com (ORCID) [copyright holder]

Authors:

• Alexandra Amani

• Nico Keiser

See Also

Useful links:

• https://github.com/stocnet/ERPM

• Report bugs at https://github.com/stocnet/ERPM/issues

Function to calculate the number of partitions with groups of sizes between smin and smax

Description

Function to calculate the number of partitions with groups of sizes between smin and smax

Usage

Bell_constraints(n, smin, smax)

Arguments

Value

a numeric

Examples

n <- 6
size_min <- 2
size_max <- 4
Bell_constraints(n,size_min,size_max)

CUP

Description

This function tests a partition statistic against a "conditional uniform partition null hypothesi: It compares a statistic computed on an observed partition and the same statistic computed on a set of permuted partition (partitions with the same group structure as the observed partition, with nodes being permuted).

Usage

CUP(observation, fun, permutations = NULL, num.permutations = 1000)

Arguments

Details

This test is similar to Conditional Uniform Graph tests in networks (we translate this into Condtional Uniform Partition tests).

Value

The value of the statistic calculated for the observed partition, the mean value of the statistic among permuted partitions, the standard deviation of the statistic among permuted partitions, the proportion of permutation below the observed statistic, the proportion of permutation above the observed statistic, the lower boundary of the 95% CI, the upper boundary of the 95% CI

Examples

p <- c(1,2,2,3,3,4,4,4,5)
at <- c(0,1,1,1,1,0,0,0,0)
CUP(p,fun=function(x){same_pairs(x,at,'avg_pergroup')})

Function to calculate the number of partitions with k groups of sizes between smin and smax

Description

Function to calculate the number of partitions with k groups of sizes between smin and smax

Usage

Stirling2_constraints(n, k, smin, smax)

Arguments

Value

a numeric

Examples

n <- 6
k <- 2
size_min <- 2
size_max <- 4
Stirling2_constraints(n,k,size_min,size_max)

Calculate Dirichlet denominator

Description

Recursive function to calculate the denominator for the model with a single statistic for the number of groups and a given parameter value. The set of possible partitions can be restricted to partitions with groups of a certain size.

Usage

calculate_denominator_Dirichlet_restricted(n, smin, smax, alpha, results)

Arguments

Value

a numeric

Calculate Dirichlet probability

Description

Calculate the probability of observing a partition with a given number of groups for a model with a single statistic for the number of groups and a given parameter value. The set of possible partitions can be restricted to partitions with groups of a certain size.

Usage

calculate_proba_Dirichlet_restricted(alpha, stat, n, smin, smax)

Arguments

Value

a numeric

Function to determine whether a partition contains the allowed group sizes

Description

Function to determine whether a partition contains the allowed group sizes

Usage

check_sizes(partition, sizes.allowed, numgroups.allowed)

Arguments

Value

boolean

Compute Statistics

Description

Function that computes the statistic vector for a given partition and a given model

Usage

computeStatistics(partition, nodes, effects, objects)

Arguments

Value

the statistics

Compute Statistics multiple

Description

Function that computes the statistic vector for given (multiple) partitions and a given model

Usage

computeStatistics_multiple(
  partitions,
  presence.tables,
  nodes,
  effects,
  objects,
  single.obs = NULL
)

Arguments

Value

A list

Compute the average size of a random partition

Description

Recursive function to compute the average size of a random partition for a given number of nodes

Usage

compute_averagesize(num.nodes)

Arguments

Value

a numeric

Examples

n <- 6
compute_averagesize(n)

Compute denominator for model with number of groups

Description

Recursive function to compute the value of the denominator for the model with a single statistic which is the number of groups

Usage

compute_numgroups_denominator(num.nodes, alpha)

Arguments

Value

a numeric

Between groups correlation

Description

This function computes the correlation between the group averages of the two attributes.

Usage

correlation_between(partition, attribute1, attribute2)

Arguments

Value

A number corresponding to the correlation coefficient

Examples

p <- c(1,2,2,3,3,4,4,4,5)
at <- c(3,5,23,2,1,0,3,9,2)
at2 <- c(3,5,20,2,1,0,0,9,0)
correlation_between(p,at,at2)

Correlation with size

Description

This function computes the correlation between an attribute and the size of the groups.

Usage

correlation_with_size(partition, attribute, categorical)

Arguments

Value

A number corresponding to the correlation coefficient if the attribute is numerical or the correlation ratio if the attribute is categorical.

Examples

p <- c(1,2,2,3,3,4,4,4,5)
at <- c(3,5,23,2,1,0,3,9,2)
correlation_with_size(p,at,categorical=FALSE)

Within groups correlation

Description

This function computes the correlation between the two attributes for individuals in the same group.

Usage

correlation_within(partition, attribute1, attribute2, group)

Arguments

Value

A number corresponding to the correlation coefficient

Examples

p <- c(1,2,2,3,3,4,4,4,5)
at <- c(3,5,23,2,1,0,3,9,2)
at2 <- c(3,5,20,2,1,0,0,9,0)
correlation_within(p,at,at2,4)

Function to count the number of partitions with a certain group size structure, for all possible group size structure. Function to use after calling the "find_all_partitions" function.

Description

Function to count the number of partitions with a certain group size structure, for all possible group size structure. Function to use after calling the "find_all_partitions" function.

Usage

count_classes(allpartitions)

Arguments

Value

integer(number of partitions with different group structures)

Examples

#find partitions first
n <- 6
all_partitions <- find_all_partitions(n)
# count classes
counts_partition_classes <- count_classes(all_partitions)

Draw Metropolis multiple

Description

Function to sample the model with a Markov chain (single partition procedure).

Usage

draw_Metropolis_multiple(
  theta,
  first.partitions,
  presence.tables,
  nodes,
  effects,
  objects,
  burnin,
  thining,
  num.steps,
  neighborhood = c(0.7, 0.3, 0),
  numgroups.allowed,
  numgroups.simulated,
  sizes.allowed,
  sizes.simulated,
  return.all.partitions = FALSE,
  verbose = FALSE
)

Arguments

Value

A list

Examples

# define an arbitrary set of n = 6 nodes with attributes, and an arbitrary covariate matrix
n <- 6 
nodes <- data.frame(label = c("A","B","C","D","E","F"),
                    gender = c(1,1,2,1,2,2),
                    age = c(20,22,25,30,30,31)) 
friendship <- matrix(c(0, 1, 1, 1, 0, 0,
                       1, 0, 0, 0, 1, 0,
                       1, 0, 0, 0, 1, 0,
                       1, 0, 0, 0, 0, 0,
                       0, 1, 1, 0, 0, 1,
                       0, 0, 0, 0, 1, 0), 6, 6, TRUE) 

# specify whether nodes are present at different points of time
presence.tables <- matrix(c(1, 1, 1, 1, 1, 1,
                            0, 1, 1, 1, 1, 1,
                            1, 0, 1, 1, 1, 1), 6, 3)

# choose effects to be included in the estimated model
effects_multiple <- list(names = c("num_groups","same","diff","tie","inertia_1"),
                objects = c("partitions","gender","age","friendship","partitions"),
                objects2 = c("","","","",""))
objects_multiple <- list()
objects_multiple[[1]] <- list(name = "friendship", object = friendship)

# set parameter values for each of these effects
parameters <- c(-0.2,0.2,-0.1,0.5,1)

# set a starting point for the simulation
first.partitions <- matrix(c(1, 1, 2, 2, 2, 3,
                             NA, 1, 1, 2, 2, 2,
                             1, NA, 2, 3, 3, 1), 6, 3) 


# generate the simulated sample
nsteps <- 50
sample <- draw_Metropolis_multiple(theta = parameters, 
                                   first.partitions = first.partitions,
                                   nodes = nodes, 
                                   presence.tables = presence.tables,
                                   effects = effects_multiple, 
                                   objects = objects_multiple, 
                                   burnin = 100, 
                                   thining = 100, 
                                   num.steps = nsteps, 
                                   neighborhood = c(0,1,0), 
                                   numgroups.allowed = 1:n,
                                   numgroups.simulated = 1:n,
                                   sizes.allowed = 1:n,
                                   sizes.simulated = 1:n,
                                   return.all.partitions = TRUE)

Draw Metropolis single

Description

Function to sample the model with a Markov chain (single partition procedure).

Usage

draw_Metropolis_single(
  theta,
  first.partition,
  nodes,
  effects,
  objects,
  burnin,
  thining,
  num.steps,
  neighborhood = c(0.7, 0.3, 0),
  numgroups.allowed = NULL,
  numgroups.simulated = NULL,
  sizes.allowed = NULL,
  sizes.simulated = NULL,
  return.all.partitions = FALSE
)

Arguments

Value

A list

Examples

# define an arbitrary set of n = 6 nodes with attributes, and an arbitrary covariate matrix
n <- 6 
nodes <- data.frame(label = c("A","B","C","D","E","F"),
                    gender = c(1,1,2,1,2,2),
                    age = c(20,22,25,30,30,31)) 
friendship <- matrix(c(0, 1, 1, 1, 0, 0,
                       1, 0, 0, 0, 1, 0,
                       1, 0, 0, 0, 1, 0,
                       1, 0, 0, 0, 0, 0,
                       0, 1, 1, 0, 0, 1,
                       0, 0, 0, 0, 1, 0), 6, 6, TRUE)

# choose the effects to be included (see manual for all effect names)
effects <- list(names = c("num_groups","same","diff","tie"),
objects = c("partition","gender","age","friendship"))
objects <- list()
objects[[1]] <- list(name = "friendship", object = friendship)

# set parameter values for each of these effects
parameters <- c(-0.2, 0.2, -0.1, 0.5)


# generate simulated sample, by setting the desired additional parameters for the 
# Metropolis sampler and choosing a starting point for the chain (first.partition)
nsteps <- 100
sample <- draw_Metropolis_single(theta = parameters, 
                                 first.partition = c(1,1,2,2,3,3), 
                                 nodes = nodes, 
                                 effects = effects, 
                                 objects = objects, 
                                 burnin = 100, 
                                 thining = 10, 
                                 num.steps = nsteps, 
                                 neighborhood = c(0,1,0), 
                                 numgroups.allowed = 1:n,
                                 numgroups.simulated = 1:n,
                                 sizes.allowed = 1:n,
                                 sizes.simulated = 1:n,
                                 return.all.partitions = TRUE)


# or: simulate an estimated model
partition <- c(1,1,2,2,2,3) # the partition already defined for the (previous) estimation
nsimulations <- 1000
simulations <- draw_Metropolis_single(theta = estimation$results$est, 
                                      first.partition = partition, 
                                      nodes = nodes, 
                                      effects = effects, 
                                      objects = objects, 
                                      burnin = 100, 
                                      thining = 20, 
                                      num.steps = nsimulations, 
                                      neighborhood = c(0,1,0), 
                                      sizes.allowed = 1:n,
                                      sizes.simulated = 1:n,
                                      return.all.partitions = TRUE)

Estimate ERPM

Description

Function to estimate a given model for a given observed partition. All options of the algorithm can be specified here.

Usage

estimate_ERPM(
  partition,
  nodes,
  objects,
  effects,
  startingestimates,
  gainfactor = 0.1,
  a.scaling = 0.8,
  r.truncation.p1 = -1,
  r.truncation.p2 = -1,
  burnin = 30,
  thining = 10,
  length.p1 = 100,
  min.iter.p2 = NULL,
  max.iter.p2 = NULL,
  multiplication.iter.p2 = 100,
  num.steps.p2 = 6,
  length.p3 = 1000,
  neighborhood = c(0.7, 0.3, 0),
  fixed.estimates = NULL,
  numgroups.allowed = NULL,
  numgroups.simulated = NULL,
  sizes.allowed = NULL,
  sizes.simulated = NULL,
  double.averaging = FALSE,
  inv.zcov = NULL,
  inv.scaling = NULL,
  parallel = FALSE,
  parallel2 = FALSE,
  cpus = 1,
  verbose = FALSE
)

Arguments

Value

A list with the outputs of the three different phases of the algorithm

Examples

# define an arbitrary set of n = 6 nodes with attributes, and an arbitrary covariate matrix
n <- 6 
nodes <- data.frame(label = c("A","B","C","D","E","F"),
                    gender = c(1,1,2,1,2,2),
                    age = c(20,22,25,30,30,31)) 
friendship <- matrix(c(0, 1, 1, 1, 0, 0,
                       1, 0, 0, 0, 1, 0,
                       1, 0, 0, 0, 1, 0,
                       1, 0, 0, 0, 0, 0,
                       0, 1, 1, 0, 0, 1,
                       0, 0, 0, 0, 1, 0), 6, 6, TRUE)

# choose the effects to be included (see manual for all effect names)
effects <- list(names = c("num_groups","same","diff","tie"),
                objects = c("partition","gender","age","friendship"))
objects <- list()
objects[[1]] <- list(name = "friendship", object = friendship)

# define observed partition
partition <- c(1,1,2,2,2,3)


# estimate
startingestimates <- c(-2,0,0,0)
estimation <- estimate_ERPM(partition, 
                            nodes, 
                            objects, 
                            effects, 
                            startingestimates = startingestimates, 
                            burnin = 100, 
                            thining = 20,
                            length.p1 = 500, # number of samples in phase 1
                            multiplication.iter.p2 = 20, # iterations in phase 2
                            num.steps.p2 = 4, # number of phase 2 subphases
                            length.p3 = 1000) # number of samples in phase 3

# get results table
estimation

Estimate log likelihood

Description

Function to estimate the log likelihood of a model for an observed partition

Usage

estimate_logL(
  partition,
  nodes,
  effects,
  objects,
  theta,
  theta_0,
  M,
  num.steps,
  burnin,
  thining,
  neighborhoods = c(0.7, 0.3, 0),
  numgroups.allowed = NULL,
  numgroups.simulated = NULL,
  sizes.allowed = NULL,
  sizes.simulated = NULL,
  logL_0 = NULL,
  parallel = FALSE,
  cpus = 1,
  verbose = FALSE
)

Arguments

Value

List with the log likelihood , AIC, lambda and the draws

Examples

# estimate the log-likelihood and AIC of an estimated model (e.g. useful to compare two models)

# define an arbitrary set of n = 6 nodes with attributes, and an arbitrary covariate matrix
n <- 6
nodes <- data.frame(label = c("A","B","C","D","E","F"),
                    gender = c(1,1,2,1,2,2),
                    age = c(20,22,25,30,30,31)) 
friendship <- matrix(c(0, 1, 1, 1, 0, 0,
                       1, 0, 0, 0, 1, 0,
                       1, 0, 0, 0, 1, 0,
                       1, 0, 0, 0, 0, 0,
                       0, 1, 1, 0, 0, 1,
                       0, 0, 0, 0, 1, 0), 6, 6, TRUE)

# choose the effects to be included (see manual for all effect names)
effects <- list(names = c("num_groups","same","diff","tie"),
objects = c("partition","gender","age","friendship"))
objects <- list()
objects[[1]] <- list(name = "friendship", object = friendship)

# define observed partition 
partition <- c(1,1,2,2,2,3)
# (an exemplary estimation is internally stored in order to save time)

# first: estimate the ML estimates of a simple model with only one parameter 
# for number of groups (this parameter should be in the model!)
likelihood_function <- function(x){ exp(x*max(partition)) / compute_numgroups_denominator(n,x)}
curve(likelihood_function, from=-2, to=0)
parameter_base <- optimize(likelihood_function, interval=c(-2, 0), maximum=TRUE)
parameters_basemodel <- c(parameter_base$maximum,0,0,0)


# estimate logL and AIC
logL_AIC <- estimate_logL(partition,
                          nodes,
                          effects, 
                          objects,
                          theta = estimation$results$est,
                          theta_0 = parameters_basemodel,
                          M = 3,
                          num.steps = 200,
                          burnin = 100,
                          thining = 20)
logL_AIC$logL
logL_AIC$AIC

Estimate ERPM for multiple observations

Description

Function to estimate a given model for given observed (multiple) partitions. All options of the algorithm can be specified here.

Usage

estimate_multipleERPM(
  partitions,
  presence.tables,
  nodes,
  objects,
  effects,
  startingestimates,
  gainfactor = 0.1,
  a.scaling = 0.8,
  r.truncation.p1 = -1,
  r.truncation.p2 = -1,
  burnin = 30,
  thining = 10,
  length.p1 = 100,
  min.iter.p2 = NULL,
  max.iter.p2 = NULL,
  multiplication.iter.p2 = 200,
  num.steps.p2 = 6,
  length.p3 = 1000,
  neighborhood = c(0.7, 0.3, 0),
  fixed.estimates = NULL,
  numgroups.allowed = NULL,
  numgroups.simulated = NULL,
  sizes.allowed = NULL,
  sizes.simulated = NULL,
  double.averaging = FALSE,
  inv.zcov = NULL,
  inv.scaling = NULL,
  parallel = FALSE,
  parallel2 = FALSE,
  cpus = 1,
  verbose = FALSE
)

Arguments

Value

A list with the outputs of the three different phases of the algorithm

Examples

# define an arbitrary set of n = 6 nodes with attributes, and an arbitrary covariate matrix
n <- 6 
nodes <- data.frame(label = c("A","B","C","D","E","F"),
                    gender = c(1,1,2,1,2,2),
                    age = c(20,22,25,30,30,31)) 
friendship <- matrix(c(0, 1, 1, 1, 0, 0,
                       1, 0, 0, 0, 1, 0,
                       1, 0, 0, 0, 1, 0,
                       1, 0, 0, 0, 0, 0,
                       0, 1, 1, 0, 0, 1,
                       0, 0, 0, 0, 1, 0), 6, 6, TRUE) 

# specify whether nodes are present at different points of time
presence.tables <- matrix(c(1, 1, 1, 1, 1, 1,
                            0, 1, 1, 1, 1, 1,
                            1, 0, 1, 1, 1, 1), 6, 3)

# choose effects to be included in the estimated model
effects_multiple <- list(names = c("num_groups","same","diff","tie","inertia_1"),
                objects = c("partitions","gender","age","friendship","partitions"),
                objects2 = c("","","","",""))
objects_multiple <- list()
objects_multiple[[1]] <- list(name = "friendship", object = friendship)

# define the observation
partitions <- matrix(c(1, 1, 2, 2, 2, 3,
                       NA, 1, 1, 2, 2, 2,
                       1, NA, 2, 3, 3, 1), 6, 3) 


# estimate
startingestimates <- c(-2,0,0,0,0)
estimation <- estimate_multipleERPM(partitions,
                                    presence.tables,          
                                    nodes, 
                                    objects_multiple, 
                                    effects_multiple, 
                                    startingestimates = startingestimates, 
                                    burnin = 100, 
                                    thining = 50,
                                    gainfactor = 0.6,
                                    length.p1 = 200, 
                                    multiplication.iter.p2 = 20, 
                                    num.steps.p2 = 4, 
                                    length.p3 = 1000) 

# get results table
estimation

Exact estimates number of groups

Description

This function finds the best estimate for a model only including the statistics of number of groups. It does a grid search for a vector of potential parameters, for all numbers of groups.

Usage

exactestimates_numgroups(num.nodes, pmin, pmax, pinc)

Arguments

Value

a list

Function to enumerate all possible partitions for a given n

Description

Function to enumerate all possible partitions for a given n

Usage

find_all_partitions(n)

Arguments

Value

matrix where each line corresponds to a possible partition

Examples

n <- 6
all_partitions <- find_all_partitions(n)

Grid - search burnin single

Description

Function that can be used to find a good length for the burn-in of the Markov chain for a given model and differents sets of transitions in the chain (the neighborhoods). For each neighborhood, it draws a chain and calculates the mean statistics for different burn-ins.

Usage

gridsearch_burnin_single(
  partition,
  theta,
  nodes,
  effects,
  objects,
  num.steps,
  neighborhoods,
  numgroups.allowed,
  numgroups.simulated,
  sizes.allowed,
  sizes.simulated,
  parallel = FALSE,
  cpus = 1
)

Arguments

Value

all simulations

Grid - search burnin thining multiple

Description

Function that simulates the Markov chain for a given model and several sets of transitions (the neighborhoods), for multiple partitions. For each neighborhood, it calculates the autocorrelation of statistics for different thinings and the average statistics for different burn-ins. Then the best neighborhood can be selected along with good values for burn-in and thining

Usage

gridsearch_burninthining_multiple(
  partitions,
  presence.tables,
  theta,
  nodes,
  effects,
  objects,
  num.steps,
  neighborhoods,
  numgroups.allowed,
  numgroups.simulated,
  sizes.allowed,
  sizes.simulated,
  max.thining,
  parallel = FALSE,
  cpus = 1
)

Arguments

Value

list

Grid - search burnin thining single

Description

Function that simulates the Markov chain for a given model and several sets of transitions (the neighborhoods), for a single partition. For each neighborhood, it calculates the autocorrelation of statistics for different thinings and the average statistics for different burn-ins. Then the best neighborhood can be selected along with good values for burn-in and thining

Usage

gridsearch_burninthining_single(
  partition,
  theta,
  nodes,
  effects,
  objects,
  num.steps,
  neighborhoods,
  numgroups.allowed,
  numgroups.simulated,
  sizes.allowed,
  sizes.simulated,
  max.thining,
  parallel = FALSE,
  cpus = 1
)

Arguments

Value

list

Grid - search thining single

Description

Function that can be used to find a good length for the thining of the Markov chain for a given model and differents sets of transitions in the chain (the neighborhoods). For each neighborhood, it draws a chain and calculates the autocorrelation of statistics for different thinings.

Usage

gridsearch_thining_single(
  partition,
  theta,
  nodes,
  effects,
  objects,
  num.steps,
  neighborhoods,
  numgroups.allowed,
  numgroups.simulated,
  sizes.allowed,
  sizes.simulated,
  burnin,
  max.thining,
  parallel = FALSE,
  cpus = 1
)

Arguments

Value

all simulations

Statistics on the size of groups in a partition

Description

This function computes the average or the standard deviation of the size of groups in a partition.

Usage

group_size(partition, stat)

Arguments

Value

A number corresponding to the correlation coefficient if the attribute is numerical or the correlation ratio if the attribute is categorical.

Examples

p <- c(1,2,2,3,3,4,4,4,5)
group_size(p,'avg')
group_size(p,'sd')

Intra class correlation

Description

This function computes the intra class correlation correlation of attributes for 2 randomly drawn individuals in the same group.

Usage

icc(partition, attribute)

Arguments

Value

A number corresponding to the ICC

Examples

p <- c(1,2,2,3,3,4,4,4,5)
at <- c(3,5,23,2,1,0,3,9,2)
icc(p, at)

Number of individuals having an attribute

Description

This function computes the total number of individuals being in a category of an attribute in a partition. It also computes the sum of the proportion in each group of individuals being in a category.

Usage

number_categories(partition, attribute, stat, category)

Arguments

Value

The statisic chosen in stat depending on the value of category. If category = 'all', returns a vector.

Examples

p <- c(1,2,2,3,3,4,4,4,5)
at <- c(1,0,0,0,1,1,0,0,1)
number_categories(p,at,'avg','all')

Same pairs of individuals in a partition

Description

This function computes the number of ties.

Usage

number_ties(partition, dyadic_attribute, stat)

Arguments

Value

The statisic chosen in stat

Examples

p <- c(1,2,2,3,3,4)
v <- c(0,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0)
at <- matrix(v,6,6, byrow = TRUE)
number_ties(p,at,'avg_pergroup')

Function to replace the ids of the group without forgetting an id and put in the first appearance order for example: ⁠[2 1 1 4 2]⁠ becomes ⁠[1 2 2 3 1]⁠

Description

Function to replace the ids of the group without forgetting an id and put in the first appearance order for example: ⁠[2 1 1 4 2]⁠ becomes ⁠[1 2 2 3 1]⁠

Usage

order_groupids(partition)

Arguments

Value

a vector (partition)

Exemplary outcome objects for the ERPM Package

Description

These are exemplary outcome objects for the ERPM package and can be used in order not to run all precedent functions and thus save time. The following products are provided:

Format

estimation An results object created by the function estimate_ERPM().

Core function for Phase 1

Description

Core function for Phase 1

Usage

phase1(
  startingestimates,
  inv.zcov,
  inv.scaling,
  z.phase1,
  z.obs,
  nodes,
  effects,
  objects,
  r.truncation.p1,
  length.p1,
  fixed.estimates,
  verbose = FALSE
)

Arguments

Value

estimated parameters after phase 1

Plot average sizes

Description

Function to plot the average size of a random partition depending on the number of nodes

Usage

plot_averagesizes(nmin, nmax, ninc)

Arguments

Value

a vector

Plot likelihood of number groups

Description

Function to plot the log-likelihood of the model with a single statistic (number of groups) depending on the parameter value for this statistic

Usage

plot_numgroups_likelihood(m.obs, num.nodes, pmin, pmax, pinc)

Arguments

Value

a vector

Visualization of partition

Description

This function plot the groups of a partition

Usage

plot_partition(
  partition,
  title = NULL,
  group.color = NULL,
  attribute.color = NULL,
  attribute.shape = NULL
)

Arguments

Value

A plot of the partition

Examples

p <- c(1,1,1,2,2,2,2,3,3,3,4,4,4,4,4,4)
attr1 <- c(1,0,0,1,0,0,1,0,1,0,1,1,1,1,1,2)
attr2 <- c(1,1,1,1,0,0,3,0,1,0,1,1,1,1,1,2)
plot_partition(p,attribute.color = attr1, attribute.shape = attr2)

Print results of bayesian estimation (beta version)

Description

Print results of bayesian estimation (beta version)

Usage

## S3 method for class 'results.bayesian.erpm'
print(x, ...)

Arguments

Value

a data frame

Print estimation results

Description

Print estimation results

Usage

## S3 method for class 'results.list.erpm'
print(x, ...)

Arguments

Value

a data frame

Print results of estimation of phase 3

Description

Print results of estimation of phase 3

Usage

## S3 method for class 'results.p3.erpm'
print(x, ...)

Arguments

Value

a data frame

Proportion of isolates

Description

This function computes the proportion of individuals not joining others.

Usage

proportion_isolate(partition)

Arguments

Value

A number corresponding to proportion of individuals alone.

Examples

p <- c(1,2,2,3,3,4,4,4,5)
proportion_isolate(p)

Range of attribute in groups

Description

This function computes the sum or the average range of an attribute for groups in a partition.

Usage

range_attribute(partition, attribute, stat)

Arguments

Value

The statisic chosen in stat

Examples

p <- c(1,2,2,3,3,4,4,4,5)
at <- c(3,5,23,2,1,0,3,9,2)
range_attribute(p,at,'avg_pergroup')

Phase 1 wrapper for multiple observations

Description

Phase 1 wrapper for multiple observations

Usage

run_phase1_multiple(
  partitions,
  startingestimates,
  z.obs,
  presence.tables,
  nodes,
  effects,
  objects,
  burnin,
  thining,
  gainfactor,
  a.scaling,
  r.truncation.p1,
  length.p1,
  neighborhood,
  fixed.estimates,
  numgroups.allowed,
  numgroups.simulated,
  sizes.allowed,
  sizes.simulated,
  parallel = FALSE,
  cpus = 1,
  verbose = FALSE
)

Arguments

Value

a list

Phase 1 wrapper for single observation

Description

Phase 1 wrapper for single observation

Usage

run_phase1_single(
  partition,
  startingestimates,
  z.obs,
  nodes,
  effects,
  objects,
  burnin,
  thining,
  gainfactor,
  a.scaling,
  r.truncation.p1,
  length.p1,
  neighborhood,
  fixed.estimates,
  numgroups.allowed,
  numgroups.simulated,
  sizes.allowed,
  sizes.simulated,
  parallel = TRUE,
  cpus = 1,
  verbose = FALSE
)

Arguments

Value

a list

Phase 2 wrapper for multiple observation

Description

Phase 2 wrapper for multiple observation

Usage

run_phase2_multiple(
  partitions,
  estimates.phase1,
  inv.zcov,
  inv.scaling,
  z.obs,
  presence.tables,
  nodes,
  effects,
  objects,
  burnin,
  thining,
  num.steps,
  gainfactors,
  r.truncation.p2,
  min.iter,
  max.iter,
  multiplication.iter,
  neighborhood,
  fixed.estimates,
  numgroups.allowed,
  numgroups.simulated,
  sizes.allowed,
  sizes.simulated,
  double.averaging,
  parallel = FALSE,
  cpus = 1,
  verbose = FALSE
)

Arguments

Value

a list

Phase 2 wrapper for single observation

Description

Phase 2 wrapper for single observation

Usage

run_phase2_single(
  partition,
  estimates.phase1,
  inv.zcov,
  inv.scaling,
  z.obs,
  nodes,
  effects,
  objects,
  burnin,
  thining,
  num.steps,
  gainfactors,
  r.truncation.p2,
  min.iter,
  max.iter,
  multiplication.iter,
  neighborhood,
  fixed.estimates,
  numgroups.allowed,
  numgroups.simulated,
  sizes.allowed,
  sizes.simulated,
  double.averaging,
  parallel = FALSE,
  cpus = 1,
  verbose = FALSE
)

Arguments

Value

a list

Phase 3 wrapper for multiple observation

Description

Phase 3 wrapper for multiple observation

Usage

run_phase3_multiple(
  partitions,
  estimates.phase2,
  z.obs,
  presence.tables,
  nodes,
  effects,
  objects,
  burnin,
  thining,
  a.scaling,
  length.p3,
  neighborhood,
  numgroups.allowed,
  numgroups.simulated,
  sizes.allowed,
  sizes.simulated,
  fixed.estimates,
  parallel = FALSE,
  cpus = 1,
  verbose = FALSE
)

Arguments

Value

a list

Phase 3 wrapper for single observation

Description

Phase 3 wrapper for single observation

Usage

run_phase3_single(
  partition,
  estimates.phase2,
  z.obs,
  nodes,
  effects,
  objects,
  burnin,
  thining,
  a.scaling,
  length.p3,
  neighborhood,
  numgroups.allowed,
  numgroups.simulated,
  sizes.allowed,
  sizes.simulated,
  fixed.estimates,
  parallel = FALSE,
  cpus = 1,
  verbose = FALSE
)

Arguments

Value

a list

Same pairs of individuals in a partition

Description

This function computes the total number, the average number having the same value of a categorical variable and the number of individuals a partition.

Usage

same_pairs(partition, attribute, stat)

Arguments

Value

The statistic chosen in stat

Examples

p <- c(1,2,2,3,3,4,4,4,5)
at <- c(0,1,1,1,1,0,0,0,0)
same_pairs(p,at,'avg_pergroup')

Similar pairs of individuals in a partition

Description

This function computes the total number, the average number having the close values of a numerical variable and the number of individuals a partition.

Usage

similar_pairs(partition, attribute, stat, threshold)

Arguments

Value

The statisic chosen in stat

Examples

p <- c(1,2,2,3,3,4,4,4,5)
at <- c(3,5,23,2,1,0,3,9,2)
similar_pairs(p,at,1,'avg_pergroup')

Simulate burn in single

Description

Function that can be used to find a good length for the burn-in of the Markov chain for a given model and a given set of transitions in the chain (the neighborhood). It draws a chain and calculates the mean statistics for different burn-ins.

Usage

simulate_burnin_single(
  partition,
  theta,
  nodes,
  effects,
  objects,
  num.steps,
  neighborhood,
  numgroups.allowed,
  numgroups.simulated,
  sizes.allowed,
  sizes.simulated
)

Arguments

Value

A list with list the draws, the moving.means and the moving means smoothed

Simulate burnin thining multiple

Description

Function that simulates the Markov chain for a given model and a set of transitions (the neighborhood), for multiple partitions. It calculates the autocorrelation of statistics for different thinings and the average statistics for different burn-ins.

Usage

simulate_burninthining_multiple(
  partitions,
  presence.tables,
  theta,
  nodes,
  effects,
  objects,
  num.steps,
  neighborhood,
  numgroups.allowed,
  numgroups.simulated,
  sizes.allowed,
  sizes.simulated,
  max.thining,
  verbose = FALSE
)

Arguments

Value

A list

Simulate burnin thining single

Description

Function that simulates the Markov chain for a given model and a set of transitions (the neighborhood), for a single partition. It calculates the autocorrelation of statistics for different thinings and the average statistics for different burn-ins.

Usage

simulate_burninthining_single(
  partition,
  theta,
  nodes,
  effects,
  objects,
  num.steps,
  neighborhood,
  numgroups.allowed,
  numgroups.simulated,
  sizes.allowed,
  sizes.simulated,
  max.thining,
  verbose = FALSE
)

Arguments

Value

A list

Simulate thining single

Description

Function that can be used to find a good length for the thining of the Markov chain for a given model and a set of transitions in the chain (the neighborhood). It draws a chain and calculates the autocorrelation of statistics for different thinings.

Usage

simulate_thining_single(
  partition,
  theta,
  nodes,
  effects,
  objects,
  num.steps,
  neighborhood,
  numgroups.allowed,
  numgroups.simulated,
  sizes.allowed,
  sizes.simulated,
  burnin,
  max.thining,
  verbose = FALSE
)

Arguments

Value

A list