Temporally-Sensitive Terms used in Exponential Family Random Graph Models
Unlike ordinary ergm-terms, which take only a single
network as an argument, the terms documented here also take into
account the "ages" of extant ties in the network: the time elapsed since
their formation.
As implemented, many of these terms cannot be used to "drive" the process
of network evolution, but they can be used as target statistics to
infer the terms that do. More concretely, they may appear in
targets= or monitor= formulas of
stergm, simulate.stergm, or
summary.formula (with an ERGM formula), but they may
not appear in their formation= and
dissolution= formulas. These terms are marked with
"(target-only)".
All terms listed here are binary.
tergm packagedegrange.mean.age(from, to=+Inf, byarg=NULL, emptyval=0)
(target-only)Average age of ties incident on nodes having
degree in a given range:
The from and to arguments are vectors of distinct
integers or +Inf, for to. If one of the vectors has
length 1, it is recycled to the length of the other. Otherwise, they
must have the same length. This term adds one
network statistic to the model for each element of from (or to); the ith
such statistic equals the average, among all ties incident on nodes
with degree greater than or equal to
from[i] but strictly less than to[i], of the amount of time elapsed
since the tie's formation. The optional argument
by is a character string giving the name of an attribute in the
network's vertex attribute list. If specified, then separate degree
statistics are calculated for nodes having each separate
value of the attribute.
Because this average is undefined for a network that does not have
any actors with degree in the specified range, the
argument emptyval can be used to specify the value returned
if this is the case. This is, technically, an arbitrary value, but it should
not have a substantial effect unless a non-negligible fraction of
networks at the parameter configuration of interest has no actors
with specified degree.
degree.mean.age(d, by=NULL,
emptyval=0) (target-only)Average age of ties incident
on nodes having a given degree:
The d argument is a vector of distinct integers. This term adds one
network statistic to the model for each element in d; the ith
such statistic equals the average, among all ties incident on nodes
with degree exactly d[i], of the amount of time elapsed
since the tie's formation. The optional argument
by is a character string giving the name of an attribute in the
network's vertex attribute list. If specified, then separate degree
statistics are calculated for nodes having each separate
value of the attribute.
Because this average is undefined for a network that does not have
any actors with degree d[i], the
argument emptyval can be used to specify the value returned
if this is the case. This is, technically, an arbitrary value, but it should
not have a substantial effect unless a non-negligible fraction of
networks at the parameter configuration of interest has no actors
with specified degree.
edges.ageinterval(from, to=+Inf) (dissolution- and target-only)Number of edges
with age falling into a specified range:
This term counts the number of edges in the network for
which the time elapsed since formation is greater than or equal to
from but strictly less than to. In other words, it
is in the semiopen interval [from, to). from and
to may be scalars, vectors of the same length, or one of
them must have length one, in which case it is recycled.
When used in the dissolution formula of a STERGM, it can be used to model a non-Markovian dissolution process, controlling the hazard function in the interval directly.
edge.ages (target-only)Sum of ages of extant ties: This term adds one statistic equaling sum, over all ties present in the network, of the amount of time elapsed since formation.
Unlike mean.age, this statistic is well-defined on
an empty network. However, if used as a target, it appears to
produce highly biased dissolution parameter estimates if the goal
is to get an intended average duration.
edgecov.ages(x, attrname=NULL) (target-only)Weighted sum of ages of extant
ties:
This term adds one statistic equaling sum, over all ties
present in the network, of the amount of time elapsed since
formation, multiplied by a dyadic covariate. See the help for the
edgecov term for details for
specifying the covariate.
"Weights" can be negative.
Unlike edgecov.mean.age, this statistic is well-defined on
an empty network. However, if used as a target, it appears to
produce highly biased dissolution parameter estimates if the goal
is to get an intended average duration.
edgecov.mean.age(x, attrname=NULL,
emptyval=0) (target-only)Weighted average age of an extant
tie:
This term adds one statistic equaling the average, over all ties
present in the network, of the amount of time elapsed since
formation, weighted by a (nonnegative) dyadic covariate. See the help for the
edgecov term for details for
specifying the covariate.
The behavior when there are negative weights is undefined.
Because this average is undefined for an empty network (or a
network all of whose extant edges have been weighted 0), the
argument emptyval can be used to specify the value returned
if this is the case. This is, technically, an arbitrary value, but it should
not have a substantial effect unless a non-negligible fraction of
networks at the parameter configuration of interest is empty
and/or if only a few dyads have nonzero weights.
mean.age(emptyval=0) (target-only)Average age of an extant tie: This term adds one statistic equaling the average, over all ties present in the network, of the amount of time elapsed since formation.
Because this average is undefined for an empty network, the
argument emptyval can be used to specify the value returned
if it is. This is, technically, an arbitrary value, but it should
not have a substantial effect unless a non-negligible fraction of
networks at the parameter configuration of interest is empty.
Handcock M. S., Hunter D. R., Butts C. T., Goodreau S. G., Krivitsky P. N. and Morris M. (2012). _Fit, Simulate and Diagnose Exponential-Family Models for Networks_. Version 3.1. Project home page at <URL: https://statnet.org>, <URL: CRAN.R-project.org/package=ergm>.
Krivitsky, P.N. (2012). Modeling of Dynamic Networks based on Egocentric Data with Durational Information. Pennsylvania State University Department of Statistics Technical Report, 2012(2012-01). https://web.archive.org/web/20170830053722/https://stat.psu.edu/research/technical-report-files/2012-technical-reports/TR1201A.pdf
Krivitsky, P.N. (2012). Modeling Tie Duration in ERGM-Based Dynamic Network Models. Pennsylvania State University Department of Statistics Technical Report, 2012(2012-02).
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