tergm-terms {btergm} | R Documentation |
Temporal dependencies for TERGMs
Description
Network statistics that span multiple time points.
Transform a covariate using a function of time.
Usage
timecov(
covariate,
minimum = 1,
maximum = length(covariate),
transform = function(t) 1 + (0 * t) + (0 * t^2),
onlytime = FALSE
)
Arguments
covariate |
The list of networks or matrices for which to create a time
covariate. This can be the list of networks on the left-hand side of the
formula, in which case a time trend is created as a covariate list of
matrices, or it can be a list of networks or matrices that is used as a
dyadic covariate on the right-hand side of the formula, in which case an
interaction effect between the time trend and the covariate is created. If
used as a model term inside a formula, |
minimum , maximum |
For time steps below the |
transform |
In the default case, edges are modeled as being linearly
increasingly important over time (i.e., a linear time trend). By tweaking
the |
onlytime |
If |
Details
In addition to the ERGM user terms that can be estimated within a single network (see ergm-terms), the btergm package provides additional model terms that can be used within a formula. These additional statistics span multiple time periods and are therefore called "temporal dependencies." Examples include memory terms (i.e., positive autoregression, dyadic stability, edge innovation, or edge loss), delayed reciprocity or mutuality, and time covariates (i.e., functions of time or interactions with time):
delrecip(mutuality = FALSE, lag = 1)
The
delrecip
term checks for delayed reciprocity. For example, if nodej
is tied to nodei
att = 1
, does this lead to a reciprocation of that tie back fromi
toj
att = 2
? Ifmutuality = TRUE
is set, this extends not only to ties, but also non-ties. That is, ifi
is not tied toj
att = 1
, will this lead toj
not being tied toi
att = 2
, in addition to positively reciprocal patterns over time? Thelag
argument controls the size of the temporal lag: withlag = 1
, reciprocity over one consecutive time period is checked. Note that aslag
increases, the number of time steps on the dependent variable decreases.memory(type = "stability", lag = 1)
Memory terms control for the impact of a previous network on the current network. Four different types of memory terms are available: positive autoregression (
type = "autoregression"
) checks whether previous ties are carried over to the current network; dyadic stability (type = "stability"
) checks whether both edges and non-edges are stable between the previous and the current network; edge loss (type = "loss"
) checks whether ties in the previous network have been dissolved and no longer exist in the current network; and edge innovation (type = "innovation"
) checks whether previously unconnected nodes have the tendency to become tied in the current network. Thelag
argument accepts integer values and controls whether the comparison is made with the previous network (lag = 1
), the pre-previous network (lag = 2
) etc. Note that aslag
increases, the number of time steps on the dependent variable decreases.timecov(x = NULL, minimum = 1, maximum = NULL, transform = function(t) t)
The
timecov
model term checks for linear or non-linear time trends with regard to edge formation. Optionally, this can be combined with a covariate to create an interaction effect between a dyadic covariate and time in order to test whether the importance of a covariate increases or decreases over time. In the default case, edges modeled as being linearly increasingly important over time. By tweaking thetransform
function, arbitrary functional forms of time can be tested. For example,transform = sqrt
(for a geometrically decreasing time effect),transform = function(x) x^2
(for a geometrically increasing time effect),transform = function(t) t
(for a linear time trend) or polynomial functional forms (e.g.,0 + (1 * t) + (1 * t^2)
) can be used. For time steps below theminimum
value and above themaximum
value, the time covariate is set to 0. These arguments can be used to create step-wise, discrete effects, for example to use a value of 0 up to an external event and 1 from that event onwards in order to control for influences of external events.
The timecov
model term checks for linear or non-linear time trends
with regard to edge formation. Optionally, this can be combined with a
covariate to create an interaction effect between a dyadic covariate and time
in order to test whether the importance of a covariate increases or decreases
over time. The function can either be used in a formula with
btergm
, mtergm
, or tbergm
, or it
can be executed directly for manual inclusion of the results as a covariate.
Functions
-
timecov()
: Time trends and temporal covariate interactions
References
Leifeld, Philip, Skyler J. Cranmer and Bruce A. Desmarais (2017): Temporal Exponential Random Graph Models with btergm: Estimation and Bootstrap Confidence Intervals. Journal of Statistical Software 83(6): 1-36. doi:10.18637/jss.v083.i06.