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Three different ways can be modeled in which a triadic combination can be made between
the dyadic covariate and the network. In the explanation, the dyadic covariate is regarded
as a weighted network (which will be reduced to a non-weighted network if wij only assumes
the values 0 and 1). By way of exception, the dyadic covariate is not centered in these three
effects (to make it better interpretable as a network). In the text and the pictures, an arrow
with the letter W represents a tie according to the weighted network W .
33. W W => X
P closure of covariate,
snet
(x)
=
i33
j6=h xij wih whj ;
this refers to the closure of W − W two-paths; each W − W twoW
W
path i → h → j is weighted by the product wih whj and the sum of
these product weights measures the strength of the tendency toward
closure of these W − W twopaths by a tie.
h
•
.. ..
........... .....
...
...
...
..
.
...
.
...
...
...
..
.
.
...
...
.
............
..
.
.
.
.
...................................................
W
W
•
•
i
j
Since the dyadic covariates are represented by square arrays and not by edgelists, this will
be a relatively time-consuming effect if the number of nodes is large.
34. W X => X
Pclosure of covariate,
snet
(x)
=
i34
j6=h xij wih xhj ;
this refers to the closure of mixed W − X two-paths; each W − X
W
two-path i → h → j is weighted by wih and the sum of these weights
measures the strength of the tendency toward closure of these mixed
W − X twopaths by a tie;
35. XW => X
Pclosure of covariate,
snet
i35 (x) =
j6=h xij xih whj ;
this refers to the closure of mixed X − W two-paths; each X − W
W
two-path i → h → j is weighted by whj and the sum of these weights
measures the strength of the tendency toward closure of these mixed
X − W twopaths by a tie.
h
•
.. ..
.......... .....
...
...
...
...
.
...
..
...
...
.
...
.
...
...
.
.
.
...........
.
..
...
....................................................
W
•
•
i
j
h
•
.. ..
......... ...
... ....
...
...
...
...
..
...
...
...
.
.
...
...
.
....
..
.........
.
..
...
....................................................
W
•
•
i
j
For actor-dependent covariates vj (recall that these are centered internally by SIENA) as well as
for dependent behavior variables (for notational simplicity here also denoted vj ; these variables
also are centered), the following effects are available:
36. covariate-alter or covariate-related popularity, defined by the sum of the covariate over all
actors to whom
i has a tie,
P
snet
(x)
=
x
i36
j ij vj ;
37. covariate squared - alter or squared covariate-related popularity, defined by the sum of the
squared centered covariate over all actors to whom i has a tie, (not included if the variable
has range P
less than 2)
snet
(x)
=
i37
j xij vj ;
38. covariate-ego or covariate-related activity, defined by i’s out-degree weighted by his covariate
value,
snet
i38 (x) = vi xi+ ;
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