tnam is used to fit (temporal) network
autocorrelation models. The function tnamdata can be used alternatively to
create a data frame containing all the data ready for estimation.
This may be useful when a non-standard model should be estimated,
like a tobit model or a model with zero inflation, for example. Both functions accept a formula containing several model terms.
The model terms are themselves functions which can be called
separately. For example, one model term is called netlag.
This model term can be part of the formula handed over to the
tnam function, or netlag can be called directly
in order to create a single variable. This help page describes the different model terms available in
(temporal) network autocorrelation models. See the
tnam help page for details on the model.attribsim(y, attribute, match = FALSE, lag = 0,
normalization = c("no", "row", "column"), center = FALSE,
coefname = NULL)centrality(networks, type = c("indegree", "outdegree", "freeman",
"betweenness", "flow", "closeness", "eigenvector",
"information", "load", "bonpow"), directed = TRUE, lag = 0,
rescale = FALSE, center = FALSE, coefname = NULL, ...)
cliquelag(y, networks, k.min = 2, k.max = Inf, directed = TRUE,
lag = 0, normalization = c("no", "row", "column"),
center = FALSE, coefname = NULL)
clustering(networks, directed = TRUE, lag = 0, center = FALSE,
coefname = NULL, ...)
covariate(y, lag = 0, exponent = 1, center = FALSE,
coefname = NULL)
degreedummy(networks, deg = 0, type = c("indegree", "outdegree",
"freeman"), reverse = FALSE, directed = TRUE, lag = 0,
center = FALSE, coefname = NULL, ...)
interact(x, y, lag = 0, center = FALSE, coefname = NULL)
netlag(y, networks, lag = 0, pathdist = 1, decay = pathdist^-1,
normalization = c("no", "row", "column", "complete"),
reciprocal = FALSE, center = FALSE, coefname = NULL, ...)
structsim(y, networks, lag = 0, method = c("euclidean",
"minkowski", "jaccard", "binary", "hamming"), center = FALSE,
coefname = NULL, ...)
weightlag(y, networks, lag = 0, normalization = c("no", "row",
"column"), center = FALSE, coefname = NULL)
y. Based on this attribute, the similarity between nodes i and j will be calculated, and the resulting similarity matrix is used to weight the y variable. pathdist, the decay argument specifies the relative importance. By default, a geometric decay is used, that is, the behavior of nodes at path distance 2 is counted only half as much as the behavior of adjacent nodes. Alternatively, if both are equally important, it is possible to write pathdist = c(1, 2) and decay = c(1, 1).deg = 2) or degree range (e.g., deg = 1:3).exponent = 2 creates a squared variable. This may be helpful for modeling non-linear effects or for modeling a quadratic behavior shape.match = FALSE, a similarity matrix is computed by subtracting node j's attribute value from node i's attribute value, standardizing the resulting distance between 0 and 1, and converting it into a similarity by subtracting it from 1. This similarity matrix is used as a weight matrix to compute a spatial lag. If match = TRUE is specified, the weight matrix contains values of 1 whenever node i and j have the same attribute value and 0 otherwise."euclidean", "minkowski", "jaccard", "binary", and "hamming"."no" for switching off normalization, "row" for row normalization of the weight matrix, "column" for column normalization of the weight matrix, and "complete" for complete normalization.
If "no" is selected, this corresponds to the total similarity or the sum of all influences of tied alters.
If "row" is selected, this corresponds to the average alter effect. If i is the row node and j is the column node, row normalization computes the peer influence of j on i as a fraction of i's overall number of outgoing ties (i.e., i's row sum or outdegree centrality). The theoretical intuition is that other nodes' influences on i are not cumulative; i rather perceives the average influence of his or her peers. Note that row normalization does not necessarily entail that the values are standardized between 0 and 1.
If "column" is selected, this corresponds to the peer influence of node j on node i as a fraction of the number of incoming ties j has (i.e., j's column sum or indegree centrality). This captures the theoretical effect that j may distribute his or her influence among many nodes, in which case j's influence on i is relatively weak. Thus the "exerted influence of j on i decreases with the number of actors j influences" (Leenders 2002). Note that column normalization does not necessarily entail that the values are standardized between 0 and 1.
If "complete" is selected, this captures the peer influence of node j on node i as a fraction of all nodes' cumulative outcome values (including non-tied dyads; except i's own outcome value). In other words, complete normalization corresponds to the actual exposure of i to the influence of his or her tied alters j over the the exposure i could receive if i were tied to all other nodes in the network. If a decay <= 1 is used and if only direct friends are considered, this effectively standardizes the influence scores between 0 and 1.pathdist = 1 is used, this computes the sum of the behavior of adjacent nodes. If pathdist = 2 is specified, this computes the effect of indirect paths of length 2 ("friends of friends"). If pathdist = 1:2 is set, both directly connected nodes' behavior and the behavior of nodes at a path distance of 2 from the focal node are counted. Arbitrary (sets of) path distances can be used. See also the decay argument.reciprocal = TRUE is specified, only the behavior of nodes to which a reciprocal relation exists is counted (that is, a link in both directions).deg = 0 and reverse = FALSE are specified, resulting values of 1 indicate that a node has no connections, whereas the combination deg = 0 and reverse = TRUE results in the value 1 representing nodes which have a degree of at least 1."indegree", "outdegree", "freeman", "betweenness", "flow", "closeness", "eigenvector", "information", "load", and "bonpow".y. Either a vector or a list of vectors or another model term (this is the preferred way).attribsim model term computes a similarity matrix
based on the attribute argument and uses this similarity
matrix to construct a spatial lag by multiplying the similarity
matrix and the outcome vector y. The intuition behind
this model term is that node i's behavior may be influenced
by node j's behavior if nodes i and j are similar on another
dimension. For example, if i and j both smoke while k does not
smoke, j's alcohol consumption may affect i's alcohol
consumption to a larger extent than node k's alcohol
consumption. In this example, the y outcome variable
is alcohol consumption and the attribute argument is
smoking. If match = FALSE, the absolute similarity
between i and j is computed by subtracting j's attribute value
from i's attribute value and taking the absolute value to
construct the similarity matrix. If match = TRUE, the
function computes a matrix containing values of 1 if i and j
have the same attribute value and 0 otherwise. A scenario where
the attribsim model term makes sense is degree
assortativity: if i and j have the same degree centrality, they
may be inclined to learn from each other's behavior, even in
the absence of a direct connection between them.centrality model term computes a centrality index
for the nodes in a network or matrix. This can capture important
structural effects because being central often implies certain
constraints or opportunities more peripheral nodes do not have.
For example, central nodes in a network of employees might be
able to perform better.cliquelag model term computes a clique co-membership
matrix and multiplies this matrix with the outcome variable. The
intuition behind this is that in some settings individuals may
be influenced to a particularly strong extent by peers in the
same cliques. A clique is defined as a maximal connected
subgraph of size k. For example, a deviant behavior of a person
may be conditioned by the deviant behavior of the person's
friends -- but only if these friends are tied to each other as
well so that a clique among these persons exists. A minimal and
a maximal k may be defined, where k is the size
of the cliques. In the clique co-membership matrix, all cliques
with k.min <= k <= k.max are included.clustering model term computes the local clustering
coefficient, which is also known as transitivity. This index
has high values if the direct neighborhood of a node is densely
interconnected. For example, if one's friends are friends with
each other, this may have repercussions on ego's behavior.covariate model term adds an exogenous nodal
covariate to the model. For example, when performance of
employees is modeled, a covariate could be seniority of these
employees. It is possible to add lagged covariates to model
the effect of past nodal attributes on current behavior.
Similarly, this model term can be used to add autoregressive
terms, that is, the effect of previous behavior on current
behavior.degreedummy model term controls for specific degree
centralities or ranges of degree centrality. For example,
do nodes with a degree of 0 (isolates) show different behavior
than nodes who are connected? Or do nodes with a degree
centrality larger than three exert different behavior?interact model term adds an interaction effect
between two other model terms by multiplying the result
vectors of these two model terms. When using interaction
terms, centering the result is recommended. Note that only
the interaction term is created; the main effects must be
introduced to the model using the other model terms.netlag model term captures the autocorrelation
inherent in networks. For example, when political actors
are members of a policy network, their success of achieving
policy outcomes is not independent from each other. Most
likely, being connected to policy winners increases the
success rate. In many settings, indirect effects may be
important as well: how does the behavior of my friends'
friends affect my own behavior? In some contexts,
spatio-temporal lags are useful: how does the past behavior
of my friends affect my current behavior? The netlag
model term is designed for binary networks because things
like indirect effects, restriction to reciprocal dyads,
decay of indirect relations etc. is possible. For weighted
networks, the weightlag term is recommended. If no
other arguments are specified and loops are absent and a
binary matrix is used, both model terms produce the same
results.structsim model term computes the structural
similarity with other nodes in the network and multiplies
this similarity matrix with the outcome variable. The
intuition is that behavior is sometimes affected by
comparison with structurally similar nodes. For example,
a worker may be impressed by the performance of other
workers who are embedded in the same team or who report
to the same bosses. As with the other model terms, temporal
lags are possible.weightlag model term captures spatial
autocorrelation in weighted networks. For example, the
GDP per capita of a country may be affected by the
GDP of proximate other countries or by the GDP of trade
partners. In these cases, indirect contacts etc. do not
make any sense, therefore the distinction between the
weightlag and the netlag model term. The
weight matrix is multiplied by the outcome variable,
possibly after row or column normalization.