rem (version 1.1.1)

triadStat: Calculate triad statistics

Description

Calculate the endogenous network statistic triads that measures the tendency for events to close open triads.

Usage

triadStat(data, time, sender, target, halflife, 
    weight = NULL, 
    eventtypevar = NULL, 
    eventtypevalues = NULL, 
    eventattributevar = NULL,
    eventattributeAI = NULL, 
    eventattributeBI = NULL,
    eventattributeAB = NULL, 
    variablename = 'triad', 
    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.

sender

A string (or factor or numeric) variable that represents the sender of the event.

target

A string (or factor or numeric) variable that represents the target of the event.

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 determins after how long a period the event weight should be halved. E.g. if

weight

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

eventtypevar

An optional dummy variable that represents the type of the event. Use eventtypevalues to specify how the eventtypevar should be used to filter past events. Specifying the eventtypevar is needed to calculate effects o

eventtypevalues

Two string values that represent the type of the past events. The first string value represents the eventtype that exists for all past events that include the current sender (either as sender or target) and a third actor. The second value represents the e

eventattributevar

An optional string (or factor or numeric) variable that can be used to filter past and current events. Use eventattributeAI, eventattributeBI or eventattributeAB to specify which past events should be filtered and by

eventattributeAI

An optional value used to specify how paste events should be filtered depending on their attribute. Each distinct edge that form a triad can be filtered. eventattributeAI refers to the past event involving the current sender (a) and a third a

eventattributeBI

see eventattributeAI.

eventattributeAB

see eventattributeAI.

variablename

An optional value (or values) with the name the triad statistic variable should be given. To be used if returnData = TRUE.

returnData

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

showprogressbar

TRUE/FALSE. To be implemented.

Details

The triadStat()-function calculates an endogenous statistic that measures whether events have a tendency to form closing triads.

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 $b \in B$ 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 triad effect, the past events $G_t$ are filtered to include only events where the current event closes an open triad in the past.

$$triad(G_t , a , b) = \sqrt{\sum_{i \in A} w_t(a, i) \cdot w_t(i, b)}$$

An exponential decay function is used to model the effect of time on the endogenous statistics. The further apart the past event is from the present event, the less weight is given to this event. The halflife parameter in the triadStat()-function determines at which rate the weights of past events should be reduced. Therefore, if the one (or more) of the two events in the triad have occurred further in the past, less weight is given to this triad because it becomes less likely that the sender and target actors reacted to each other in the way the triad assumes.

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
sender <- c('TUN', 'UNK', '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', 'UNK', 'IRN')
target <- c('BNG', 'RUS', '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', 'IRN', 'CHN')
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)
important <- sample(c('important', 'not important'), 33,
                    replace = TRUE)

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

# 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 triad statistic
dt$triad <- triadStat(data = dt, time = dt$time, 
                      sender = dt$sender, target = dt$target, 
                      halflife = 2)

# calculate friend-of-friend statistic
dt$triad.fof <- triadStat(data = dt, time = dt$time, 
                          sender = dt$sender, target = dt$target, 
                          halflife = 2, eventtypevar = dt$type, 
                          eventtypevalues = c('cooperation',
                                              'cooperation'))

# calculate friend-of-enemy statistic
dt$triad.foe <- triadStat(data = dt, time = dt$time, 
                          sender = dt$sender, target = dt$target, 
                          halflife = 2, eventtypevar = dt$type, 
                          eventtypevalues = c('conflict',
                                              'cooperation'))

# calculate enemy-of-friend statistic
dt$triad.eof <- triadStat(data = dt, time = dt$time, 
                          sender = dt$sender, target = dt$target, 
                          halflife = 2, eventtypevar = dt$type, 
                          eventtypevalues = c('cooperation',
                                              'conflict'))

# calculate enemy-of-enemy statistic
dt$triad.eoe <- triadStat(data = dt, time = dt$time, 
                          sender = dt$sender, target = dt$target, 
                          halflife = 2, eventtypevar = dt$type, 
                          eventtypevalues = c('conflict',
                                              'conflict'))