rem (version 1.1.2)

degreeStat: Calculate (in/out)-degree statistics

Description

Calculate the endogenous network statistic indegree/outdegree for relational event models. indegree/outdegree measures the senders' tendency to be involved in events (sender activity, sender out- or indegree) or the tendency of events to surround a specific target (target popularity, target in- or outdegree)

Usage

degreeStat(data, time, degreevar, halflife, 
    weight = NULL, 
    eventtypevar = NULL, 
    eventtypevalue = "valuematch", 
    eventattributevar = NULL,
    eventattributevalue = "valuematch", 
    degree.on.other.var = NULL,
    variablename = "degree", 
    returnData = FALSE, 
    showprogressbar = FALSE)

Arguments

data

A data frame containing all the variables.

time

Numeric variable that represents the event sequence. The variable has to be sorted in ascending order.

degreevar

A string (or factor or numeric) variable that represents the sender or target of the event. The degree statistic will calculate how often in the past, a given sender or target has been active by counting the number of events in the past where the degreevar is repeated. See details for more information on which variable to chose as degreevar for one- and two-mode networks.

halflife

A numeric value that is used in the decay function. The vector of past events is weighted by an exponential decay function using the specified halflife. The halflife parameter determines after how long a period the event weight should be halved. E.g. if halflife = 5, the weight of an event that occurred 5 units in the past is halved. Smaller halflife values give more importance to more recent events, while larger halflife values should be used if time does not affect the sequence of events that much.

weight

An optional numeric variable that represents the weight of each event. If weight = NULL each event is given an event weight of 1.

eventtypevar

An optional variable that represents the type of the event. Use eventtypevalue to specify how the eventtypevar should be used to filter past events.

eventtypevalue

An optional value (or set of values) used to specify how paste events should be filtered depending on their type. eventtypevalue = "valuematch" indicates that only past events that have the same type should be used to calculate the degree statistic. eventtypevalue = "valuemix" indicates that past and present events of specific types should be used for the degree statistic. All the possible combinations of the eventtypevar-values will be used. E.g. if eventtypevar contains two unique values "a" and "b", 4 degree statistics will be calculated. The first variable calculates the degree effect where the present event is of type "a" and all the past events are of type "b". The next variable calculates the degree statistic for present events of type "b" and past events of type "a". Additionally, a variable is calculated, where present events as well as past events are of type "a" and a fourth variable calculates the degree statistic for events with type "b" (i.e. valuematch on value "b"). eventtypevalue = c("..", "..") is similar to the "nodemix"-option, all different combinations of the values specified in eventtypevalue are used to create the degree statistics.

eventattributevar

An optional variable that represents an attribute of the event. It can be a sender attribute, a target attribute, time or dyad attribute. Use eventattributevalue to specify how the eventattributevar should be used.

eventattributevalue

An optional value (or set of values) used to specify how paste events should be filtered depending on their attribute. Similar to eventtypevalue. eventattributevalue = "valuematch" indicates that only past events that have the same attribute should be used to calculate the degree statistic. eventtypevalue = "valuemix" indicates that past and present events of specific attributes should be used for the degree statistic. All the possible combinations of the eventattributevar-values will be used. eventtypevalue = c("..", "..") is similar to the "valuemix"-option, all different combinations of the values specified in eventtypevalue are used to create degree statistics.

degree.on.other.var

A string (or factor or numeric) variable that represents the sender or target of the event. It can be used to calculate target-outdegree or sender-indegree statistics in one-mode networks. For the sender indegree statistic, fill the sender variable into the degreevar and the target variable into the degree.on.other.var. For the target-outdegree statistic, fill the target variable into the degreevar and the sender variable into the degree.on.other.var.

variablename

An optional value (or values) with the name the degree statistic variable should be given. Default "degree" is used. To be used if returnData = TRUE or multiple degree statistics are calculated.

returnData

TRUE/FALSE. Set to FALSE by default. The new variable(s) are bound directly to the data.frame provided and the data frame is returned in full.

showprogressbar

TRUE/FALSE. To be implemented.

Details

The degreeStat()-function calculates an endogenous statistic that measures whether events have a tendency to include either the same sender or the same target over the entire event sequence.

The effect is calculated as follows.

$$G_t = G_t(E) = (A, B, w_t), $$

\(G_t\) represents the network of past events and includes all events \(E\). These events consist each of a sender \(a \in A\) and a target \(b \in B\) (in one-mode networks \(A = B\)) and a weight function \(w_t\):

$$ w_t(i, j) = \sum_{e:a = i, b = j} | w_e | \cdot e^{-(t-t_e)\cdot\frac{ln(2)}{T_{1/2}}} \cdot \frac{ln(2)}{T_{1/2}}, $$

where \(w_e\) is the event weight (usually a constant set to 1 for each event), \(t\) is the current event time, \(t_e\) is the past event time and \(T_{1/2}\) is a halflife parameter.

For the degree effect, the past events \(G_t\) are filtered to include only events where the senders or targets are identical to the current sender or target.

$$sender-outdegree(G_t , a , b) = \sum_{j \in B} w_t(a, j)$$

$$target-indegree(G_t , a , b) = \sum_{i \in A} w_t(i, b)$$

$$sender-indegree(G_t , a , b) = \sum_{i \in A} w_t(i, a)$$

$$target-outdegree(G_t , a , b) = \sum_{j \in B} w_t(b, j)$$

Depending on whether the degree statistic is measured on the sender variable or the target variable, either activity or popularity effects are calculated.

For one-mode networks: Four distinct statistics can be calculated: sender-indegree, sender-outdegree, target-indegree or target-outdegree. The sender-indegree measures how often the current sender was targeted by other senders in the past (i.e. how popular were current senders). The sender-outedegree measures how often the current sender was involved in an event, where they were also marked as sender (i.e. how active the current sender has been in the past). The target-indegree statistic measures how often the current targets were targeted in the past (i.e. how popular were current targets). And the target-outdegree measures how often the current targets were senders in the past (i.e. how active were current targets in the past).

For two-mode networks: Two distinct statistics can be calculated: sender-outdegree and target-indegree. Sender-outdegree measures how often the current sender has been involved in an event in the past (i.e. how active the sender has been up until now). The target-indegree statistic measures how often the current target has been involved in an event in the past (i.e. how popular a given target has been before the current event).

An exponential decay function is used to model the effect of time on the endogenous statistics. Each past event that contains the same sender or the same target (depending on the variable specified in degreevar) and fulfills additional filtering options (specified via event type or event attributes) is weighted with an exponential decay. The further apart the past event is from the present event, the less weight is given to this event. The halflife parameter in the degreeStat()-function determines at which rate the weights of past events should be reduced.

The eventtypevar- and eventattributevar-options help filter the past events more specifically. How they are filtered depends on the eventtypevalue- and eventattributevalue-option.

See Also

rem-package

Examples

# create some data with 'sender', 'target' and a 'time'-variable
# (Note: Data used here are random events from the Correlates of War Project)
sender <- c('TUN', 'NIR', 'NIR', 'TUR', 'TUR', 'USA', 'URU', 
            'IRQ', 'MOR', 'BEL', 'EEC', 'USA', 'IRN', 'IRN', 
            'USA', 'AFG', 'ETH', 'USA', 'SAU', 'IRN', 'IRN',
            'ROM', 'USA', 'USA', 'PAN', 'USA', 'USA', 'YEM', 
            'SYR', 'AFG', 'NAT', 'NAT', 'USA')
target <- c('BNG', 'ZAM', 'JAM', 'SAU', 'MOM', 'CHN', 'IRQ', 
            'AFG', 'AFG', 'EEC', 'BEL', 'ITA', 'RUS', 'UNK',
            'IRN', 'RUS', 'AFG', 'ISR', 'ARB', 'USA', 'USA',
            'USA', 'AFG', 'IRN', 'IRN', 'IRN', 'AFG', 'PAL',
            'ARB', 'USA', 'EEC', 'BEL', 'PAK')
time <- c('800107', '800107', '800107', '800109', '800109', 
          '800109', '800111', '800111', '800111', '800113',
          '800113', '800113', '800114', '800114', '800114', 
          '800116', '800116', '800116', '800119', '800119',
          '800119', '800122', '800122', '800122', '800124', 
          '800125', '800125', '800127', '800127', '800127', 
          '800204', '800204', '800204')
type <- sample(c('cooperation', 'conflict'), 33,
               replace = TRUE)

# combine them into a data.frame
dt <- data.frame(sender, target, time, type)

# create event sequence and order the data
dt <- eventSequence(datevar = dt$time, dateformat = '%y%m%d', 
                    data = dt, type = 'continuous', 
                    byTime = 'daily', returnData = TRUE,
                    sortData = TRUE)

# calculate sender-outdegree statistic
dt$sender.outdegree <- degreeStat(data = dt,
                                  time = dt$time, 
                                  degreevar = dt$sender, 
                                  halflife = 2, 
                                  returnData = FALSE)

# plot sender-outdegree over time
library('ggplot2')
ggplot(dt, aes ( event.seq.cont, sender.outdegree) ) +
  geom_point()+ geom_smooth() 

# calculate sender-indegree statistic
dt$sender.indegree <- degreeStat(data = dt,
                                  time = dt$time, 
                                  degreevar = dt$sender,
                                  degree.on.other.var = dt$target,
                                  halflife = 2, 
                                  returnData = FALSE)

# calculate target-indegree statistic
dt$target.indegree <- degreeStat(data = dt,
                                  time = dt$time, 
                                  degreevar = dt$target, 
                                  halflife = 2, 
                                  returnData = FALSE)

# calculate target-outdegree statistic
dt$target.outdegree <- degreeStat(data = dt,
                                 time = dt$time, 
                                 degreevar = dt$target,
                                 degree.on.other.var = dt$sender,
                                 halflife = 2, 
                                 returnData = FALSE)

# calculate target-indegree with typematch
dt$target.indegree.tm <- degreeStat(data = dt,
                                    time = dt$time, 
                                    degreevar = dt$target, 
                                    halflife = 2, 
                                    eventtypevar = dt$type, 
                                    eventtypevalue = 'valuematch',
                                    returnData = FALSE)