Indegree (indeg())

indeg(network, isTwoMode = FALSE, weighted = FALSE, window = Inf,
     ignoreRep = FALSE, type = c("alter", "ego"), transformFun = identity)

\[\begin{align} r(i, t, x) &= \begin{cases} \sum_{j}{I(x(t)_{ji}>0)} & \text{unweighted}\\ \sum_{j}{x(t)_{ji}} & \text{weighted} \end{cases} && \text{ego type}\\ s(i,j, t, x) &= \begin{cases} \sum_{l}{I(x(t)_{lj}>0)} & \text{unweighted}\\ \sum_{l}{x(t)_{lj}} & \text{weighted} \end{cases} && \text{alter type} \end{align}\]

• DyNAM-Rate model: tendency of actor \(i\) to create an event when \(i\) has a high incoming degree in a covariate network (‘ego’ type).
• DyNAM-choice model: tendency to create an event \(i\rightarrow j\) when \(j\) has a high incoming degree in a covariate network (‘alter’ type).
• REM model: tendency to create an event \(i\rightarrow j\) when either \(i\) or \(j\) has a high incoming degree in a covariate network. The argument type allows to choose whether to use the indegree effect for sender \(i\) (type = "ego") or for receiver j (type = "alter").
• DyNAM-choice_coordination: the effects compute the total degree in a covariate network (‘alter’ type). Note: The effect statistic correspond to the total degree for an undirected network as define when using defineNetwork(net, directed = FALSE).

The degree can be transform with .

Outdegree (outdeg())

outdeg(network, isTwoMode = FALSE, weighted = FALSE, window = Inf,
       ignoreRep = FALSE, type = c("alter", "ego"), transformFun = identity)  

\[\begin{align} r(i, t, x) &= \begin{cases} \sum_{j}{I(x(t)_{ij}>0)} & \text{unweighted}\\ \sum_{j}{x(t)_{ij}} & \text{weighted} \end{cases} && \text{ego type}\\ s(i,j, t, x) &= \begin{cases} \sum_{l}{I(x(t)_{jl}>0)} & \text{unweighted}\\ \sum_{l}{x(t)_{jl}} & \text{weighted} \end{cases} && \text{alter type} \end{align}\]

• DyNAM-Rate model: tendency of actor \(i\) to create an event when \(i\) has a high outgoing degree in a covariate network (‘ego’ type).
• DyNAM-choice model: tendency to create an event \(i\rightarrow j\) when \(j\) has a high outgoing degree in a covariate network (‘alter’ type).
• REM model: tendency to create an event \(i\rightarrow j\) when either \(i\) or \(j\) has a high outgoing degree in a covariate network. The argument type allows to choose whether to use the outdegree effect for sender \(i\) (type = "ego") or for receiver \(j\) (type = "alter").

Node embeddedness transitivity (nodeTrans())

nodeTrans(network, isTwoMode = FALSE, window = Inf, ignoreRep = FALSE,
          type = c("alter", "ego"), transformFun = identity)  

\[\begin{align} r(i, t, x) &= \sum_{jk}{I(x(t)_{ik}>0)I(x(t)_{kj}>0)I(x(t)_{ij}>0)} && \text{ego type}\\ s(i,j, t, x) &= \sum_{kl}{I(x(t)_{jk}>0)I(x(t)_{kl}>0)I(x(t)_{jl}>0)} && \text{alter type} \end{align}\]

Embeddedness in transitive structures as a source node.

• DyNAM-Rate model: tendency of actor \(i\) to create an event when \(i\) is embeddeded in more transitive structures as the source \(i\rightarrow k \rightarrow j \leftarrow i\) in a covariate network (‘ego’ type).
• DyNAM-choice model: tendency to create an event \(i\rightarrow j\) when \(j\) is embeddeded in more transitive structures as the source \(j\rightarrow k \rightarrow l \leftarrow j\) in a covariate network (‘alter’ type).
• REM model: tendency to create an event \(i\rightarrow j\) when either \(i\) or \(j\) are embeddeded in more transitive structures as the source in a covariate network. The argument type allows to choose whether to use the node embeddedness transitivity effect for sender \(i\) (type = "ego") or for receiver \(j\) (type = "alter").

The statistic can be transform with , there is not weighted version for this effect.

Ego attribute (ego())

ego(attribute, isTwoMode = FALSE)

\[\begin{align} r(i, t, z) &= z(t)_i \end{align}\]

• DyNAM-Rate model: tendency of actors to be more active when they score high on an attribute.
• REM model: tendency to create an event \(i\rightarrow j\) when \(i\) has a high score on an attribute.

Alter attribute (alter())

alter(attribute, isTwoMode = FALSE)

\[\begin{align} s(i, j, t, z) &= z(t)_j \end{align}\]

• DyNAM-choice/DyNAM-choice_coordination model: tendency to create an event \(i\rightarrow j\) when \(j\) score high on an attribute.
• REM model: tendency to create an event \(i\rightarrow j\) when \(j\) has a high score on an attribute.

Tertius (tertius())

tertius(network, attribute, isTwoMode = FALSE, window = Inf,
        ignoreRep = FALSE, type = c("alter", "ego"), transformFun = identity,
        aggregateFun = function(x) mean(x, na.rm = TRUE))

\[\begin{align} r(i, t, x, z) &= \frac{\sum_{j:~x(t)_{ji} > 0}{z(t)_j}}{\sum_{j}{I(x(t)_{ji} > 0)}} && \text{ego type}\\ s(i,j, t, x, z) &= \frac{\sum_{k:~x(t)_{kj} > 0}{z(t)_k}}{\sum_{k}{I(x(t)_{kj} > 0)}} && \text{alter type} \end{align}\]

• DyNAM-Rate submodel: tendency of actor \(i\) to create an event when \(i\) has a high aggregate (aggregateFun) value of its in-neighbors (\(\forall j:~ x[j, i] > 0\)) in a covariate network (‘ego’ type).
• DyNAM-choice/choice_coordination submodels: tendency to create an event \(i\rightarrow j\) when \(j\) has a high aggregate (aggregateFun) value of its in-neighbors (\(\forall k:~ x[k, j] > 0\)) in a covariate network (‘alter’ type).
• REM model: tendency to create an event \(i\rightarrow j\) when either \(i\) or \(j\) has a high aggregate (aggregateFun) value of its in-neighbors in a covariate network. The argument type allows to choose whether to use the tertius effect for sender \(i\) (type = "ego") or for receiver \(j\) (type = "alter").

Note: When a node does not have in-neighbors, the tertius effect is impute as the average of the aggregate values of nodes with in-neighbors.

Tie (tie())

tie(network, weighted = FALSE, window = Inf, ignoreRep = FALSE,
    transformFun = identity) 

\[\begin{equation} s(i,j, t, x) = \begin{cases} I(x(t)_{ij}>0) & \text{unweighted}\\ x(t)_{ij} & \text{weighted} \end{cases} \end{equation}\]

Tendency to create an event \(i\rightarrow j\) if the tie \(i\rightarrow j\) exists in a covariate network. Parameter weighted can be set to TRUE if the value in the covariate network for the dyad \(i\rightarrow j\) is to be taken as a statistic. It can be transformed by using transformFun (This might make sense when weighted = TRUE).

Inertia (inertia())

inertia(network, weighted = FALSE, window = Inf, transformFun = identity)  

\[\begin{equation} s(i,j, t, x) = \begin{cases} I(x(t)_{ij}>0) & \text{unweighted}\\ x(t)_{ij} & \text{weighted} \end{cases} \end{equation}\]

Usually used as the “intercept” for the choice submodel, inertia is the tendency to create an event \(i\rightarrow j\) if the event \(i\rightarrow j\) happened before. It can be interpreted as the differential tendency to update existing ties rather than creating new ones. Thus, inertia is similar to tie, but defined on the network to which the dependent events relate. Parameter weighted can be set to TRUE if the count of past events \(i\rightarrow j\) is to be taken as a statistic. It can be transformed by using transformFun (this might make sense when weighted = TRUE). Note: inertia can never be used in combination with a ignoreRep = TRUE parameter as this would replace all positive statistics with zeros.

Tie reciprocation (recip())

recip(network, weighted = FALSE, window = Inf, ignoreRep = FALSE,
      transformFun = identity) 

\[\begin{equation} s(i,j, t, x) = \begin{cases} I(x(t)_{ji}>0) & \text{unweighted}\\ x(t)_{ji} & \text{weighted} \end{cases} \end{equation}\]

Effect of a tie j->i on event \(i\rightarrow j\). Recip cannot be used with binary = T in undirected dependent network

Tendency to create an event \(i\rightarrow j\) if one or several \(j\rightarrow i\) happened before. Parameter weighted can be set to TRUE if the count/weight of \(j\rightarrow i\) events/ties is to be taken as a statistic. It can be transformed by using transformFun (this might make sense when weighted = TRUE). This effect cannot be used for two-mode networks and for DyNAM-choice_coordination submodel.

Same value in attribute (same())

same(attribute)

\[\begin{equation} s(i,j, t, z) = I(z(t)_i = z(t)_j) \end{equation}\]

Homophily (same value). The tendency of an event \(i\rightarrow j\) to happen if actors i and j have the same attribute value. This effect cannot be used for two-mode networks and for the DyNAM-rate submodel.

Differences in attribute (diff())

diff(attribute, transformFun = abs)

\[\begin{equation} s(i,j, t, z) = |z(t)_i - z(t)_j| \end{equation}\]

Heterophily. The tendency of an event \(i\rightarrow j\) to happen if actors i and j have different attribute values (high absolute differences regarding attribute if transformFun = abs). This effect cannot be used for two-mode networks.

Similarity in attribute (sim())

sim(attribute, transformFun = abs)

\[\begin{equation} s(i,j, t, z) = -|z(t)_i - z(t)_j| \end{equation}\]

Homophily (similar value). The tendency of an event \(i\rightarrow j\) to happen if actors i and j have similar attribute values (low absolute differences regarding attribute if transformFun = abs). This effect cannot be used for two-mode networks.

Ego Alter interaction (egoAlterInt())

egoAlterInt(attribute = list(attribute1, attribute2)) 

\[\begin{equation} s(i,j, t, z^{(1)}, z^{(2)}) = z(t)_i^{(1)} * z(t)_j^{(2)} \end{equation}\]

In a model that includes an alter effect using attribute2, the ego alter interaction helps to study the tendency to create an event \(i \rightarrow j\) when \(j\) score high on attribute2 moderated by the score of ego on attribute1.

Tertius difference (tertiusDiff())

tertiusDiff(network, attribute, isTwoMode = FALSE, weighted = FALSE,
            window = Inf, ignoreRep = FALSE, transformFun = abs,
            aggregateFun = function(x) mean(x, na.rm = TRUE)) 

\[\begin{equation} s(i,j, t, x, z) = \left|\frac{z(t)_i - \sum_{k:~x(t)_{kj} > 0}{z(t)_k}}{ \sum_{k}{I(x(t)_{kj} > 0)}}\right| \end{equation}\]

The tendency to create an event \(i\rightarrow j\) when \(i\) has a similar value as \(j\) aggregate (aggregateFun) value of its in-neighbors (\(\forall j:~ x[j, i] > 0\)). Note: When the node \(j\) does not have in-neighbors, its value is imputed by the average of the similarities computed for the pairs \(i\), \(k\) for all \(k\) that has at least one in-neighbor.