Calculate the endogenous network statistic triads
that measures the tendency for events to close open triads.
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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 
eventtypevar 
An optional dummy variable that represents the type of the event. Use 
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 eventtype for all past events that include the target (either as sender or target) as well as the third actor.
An example: Let the 
eventattributevar 
An optional string (or factor or numeric) variable that can be used to filter past and current events. Use 
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. 
eventattributeBI 
see 
eventattributeAB 
see 
variablename 
An optional value (or values) with the name the triad
statistic variable should be given. To be used if 
returnData 

showprogressbar 

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) = ∑_{e:a = i, b = j}  w_e  * exp^{(tt_e)* (ln(2)/T_{1/2})} * (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) = (∑_{i in A} w_t(a, i) * w_t(i, b))^(1/2)
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.
Laurence Brandenberger laurence.brandenberger@eawag.ch
rempackage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64  # 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$target,
halflife = 2)
# calculate friendoffriend statistic
dt$triad.fof < triadStat(data = dt, time = dt$time,
sender = dt$sender, target = dt$target,
halflife = 2, eventtypevar = dt$type,
eventtypevalues = c('cooperation',
'cooperation'))
# calculate friendofenemy statistic
dt$triad.foe < triadStat(data = dt, time = dt$time,
sender = dt$sender, target = dt$target,
halflife = 2, eventtypevar = dt$type,
eventtypevalues = c('conflict',
'cooperation'))
# calculate enemyoffriend statistic
dt$triad.eof < triadStat(data = dt, time = dt$time,
sender = dt$sender, target = dt$target,
halflife = 2, eventtypevar = dt$type,
eventtypevalues = c('cooperation',
'conflict'))
# calculate enemyofenemy 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'))

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