terms.ergmm {latentnet} | R Documentation |
Model terms that can be used in an ergmm
formula and
their parameter names.
The latentnet
package itself allows only
dyad-independent terms. In the formula for the model, the model terms are various function-like
calls, some of which require arguments, separated by +
signs.
Latent Space Effects
euclidean(d, G=0, var.mul=1/8, var=NULL, var.df.mul=1, var.df=NULL,
mean.var.mul=1, mean.var=NULL, pK.mul=1, pK=NULL)
(Negative)
Euclidean distance model term, with
optional clustering.
Adds a term to the model equal to the negative Eucledean distance
-dist(Z[i],Z[j]), where Z[i] and Z[j]
are the positions of their respective actors in an unobserved social
space. These positions may optionally have a finite spherical
Gaussian mixture clustering structure. This term was previously
called latent
which now fits negative Euclidean latent
space model with a warning.
The parameters are as follows:
d
The dimension of the latent space.
G
The number of groups (0 for no clustering).
var.mul
In the absence of var
, this
argument will be used as a scaling factor for a
function of average cluster size and latent space dimension to
set var
. To set it in the prior
argument to ergmm
, use Z.var.mul
.
var
If given, the scale
parameter for the scale-inverse-chi-squared prior distribution of the within-cluster
variance. To set it in the prior
argument to ergmm
, use
Z.var
.
var.df.mul
In the absence of var.df
, this
argument is the multiplier for the square root of average
cluster size, which serves in place of var.df
. To set it in the prior
argument to ergmm
, use
Z.var.df.mul
.
var.df
The degrees of freedom
parameter for the scale-inverse-chi-squared prior distribution of the within-cluster
variance. To set it in the prior
argument to ergmm
, use
Z.var.df
.
mean.var.mul
In the absence of mean.var
,
the multiplier for a function of number of vertices and latent space
dimension to set mean.var
. To set it in the
prior
argument to ergmm
, use Z.mean.var.mul
.
mean.var
The variance of
the spherical Gaussian prior distribution of the cluster means. To set it in the
prior
argument to ergmm
, use
Z.mean.var
.
pK.mul
In the absence of pK
, this argument
is the multiplier for the square root of the average cluster size,
which is used as pK
. To set it in
the prior
argument to ergmm
, use Z.pK
.
pK
The parameter of the Dirichilet prior
distribution of cluster assignment probabilities. To set it in
the prior
argument to ergmm
, use Z.pK
.
The following parameters are associated with this term:
Z
Numeric matrix with rows being latent space positions.
Z.K
(when \code{G}>0)Integer vector of cluster assignments.
Z.mean
(when \code{G}>0)Numeric matrix with rows being cluster means.
Z.var
(when \code{G}>0)Depending on the model, either a numeric vector with within-cluster variances or a numeric scalar with the overal latent space variance.
Z.pK
(when \code{G}>0)Numeric vector of probabilities of a vertex being in a particular cluster.
bilinear(d, G=0, var.mul=1/8, var=NULL, var.df.mul=1, var.df=NULL,
mean.var.mul=1, mean.var=NULL, pK.mul=1, pK=NULL)
Bilinear latent model term, with optional clustering. Adds a term to the model equal to the inner product of the latent positions: sum(Z[i]*Z[j]), where Z[i] and Z[j] are the positions of their respective actors in an unobserved social space. These positions may optionally have a finite spherical Gaussian mixture clustering structure. Note: For a bilinear latent space effect, two actors being closer in the clustering sense does not necessarily mean that the expected value of a tie between them is higher. Thus, a warning is printed when this model is combined with clustering. The parameters are as follows:
d
The dimension of the latent space.
G
The number of groups (0 for no clustering).
var.mul
In the absence of var
, this
argument will be used as a scaling factor for a
function of average cluster size and latent space dimension to
set var
. To set it in the prior
argument to ergmm
, use Z.var.mul
.
var
If given, the scale
parameter for the scale-inverse-chi-squared prior distribution of the within-cluster
variance. To set it in the prior
argument to ergmm
, use
Z.var
.
var.df.mul
In the absence of var.df
, this
argument is the multiplier for the square root of average
cluster size, which serves in place of var.df
. To set it in the prior
argument to ergmm
, use
Z.var.df.mul
.
var.df
The degrees of freedom
parameter for the scale-inverse-chi-squared prior distribution of the within-cluster
variance. To set it in the prior
argument to ergmm
, use
Z.var.df
.
mean.var.mul
In the absence of mean.var
,
the multiplier for a function of number of vertices and latent space
dimension to set mean.var
. To set it in the
prior
argument to ergmm
, use Z.mean.var.mul
.
mean.var
The variance of
the spherical Gaussian prior distribution of the cluster means. To set it in the
prior
argument to ergmm
, use
Z.mean.var
.
pK.mul
In the absence of pK
, this argument
is the multiplier for the square root of the average cluster size,
which is used as pK
. To set it in
the prior
argument to ergmm
, use Z.pK
.
pK
The parameter of the Dirichilet prior
distribution of cluster assignment probabilities. To set it in
the prior
argument to ergmm
, use Z.pK
.
The following parameters are associated with this term:
Z
Numeric matrix with rows being latent space positions.
Z.K
(when \code{G}>0)Integer vector of cluster assignments.
Z.mean
(when \code{G}>0)Numeric matrix with rows being cluster means.
Z.var
(when \code{G}>0)Depending on the model, either a numeric vector with within-cluster variances or a numeric scalar with the overal latent space variance.
Z.pK
(when \code{G}>0)Numeric vector of probabilities of a vertex being in a particular cluster.
Actor-specific effects
rsender(var=1, var.df=3)
Random sender effect. Adds a random sender effect to the model, with normal prior centered around 0 and a variance that is estimated. Can only be used on directed networks. The parameters are as follows:
var
The scale
parameter for the scale-inverse-chi-squared prior distribution
of the sender effect variance. To set it in the prior
argument to ergmm
, use
sender.var
.
var.df
The degrees of freedom
parameter for the scale-inverse-chi-squared prior distribution
of the sender effect variance. To set it in the prior
argument to ergmm
, use
sender.var.df
.
The following parameters are associated with this term:
sender
Numeric vector of values of each vertex's random sender effect.
sender.var
Random sender effect's variance.
rreceiver(var=1, var.df=3)
Random receiver effect. Adds a random receiver effect to the model, with normal prior centered around 0 and a variance that is estimated. Can only be used on directed networks. The parameters are as follows:
var
The scale
parameter for the scale-inverse-chi-squared prior distribution
of the receiver effect variance. To set it in the prior
argument to ergmm
, use
receiver.var
.
var.df
The degrees of freedom
parameter for the scale-inverse-chi-squared prior distribution
of the receiver effect variance. To set it in the prior
argument to ergmm
, use
receiver.var.df
.
The following parameters are associated with this term:
receiver
Numeric vector of values of each vertex's random receiver effect.
receiver.var
Random receiver effect's variance.
rsociality(var=1, var.df=3)
Random sociality effect. Adds a random sociality effect to the model, with normal prior centered around 0 and a variance that is estimated. Can be used on either a directed or an undirected network. The parameters are as follows:
var
The scale
parameter for the scale-inverse-chi-squared prior distribution
of the sociality effect variance. To set it in the prior
argument to ergmm
, use
sociality.var
.
var.df
The degrees of freedom
parameter for the scale-inverse-chi-squared prior distribution
of the sociality effect variance. To set it in the prior
argument to ergmm
, use
sociality.var.df
.
The following parameters are associated with this term:
sociality
Numeric vector of values of each vertex's random sociality effect.
sociality.var
Random sociality effect's variance.
Fixed Effects
Each coefficient for a fixed effect covariate has a normal prior whose
mean and variance are set by the mean
and var
parameters
of the term. For those formula terms that add more than one covariate,
a vector can be given for mean and variance. If not, the vectors given
will be repeated until the needed length is reached.
Each parameter in this section adds one element to beta
vector.
latentcov(x, attrname=NULL, mean=0, var=9)
Edge covariates for the
latent model.
x
is either a matrix of
covariates on each pair of vertices, a network, or an edge attribute on g
;
if the latter, optional argument
attrname
provides the name of the edge attribute to
use for edge values. latentcov
can be called more
than once, to model the effects of multiple covariates. Note that
some covariates can be more conveniently specified using the
following terms.
absdiff(attrname, mean=0, var=9)
Absolute Difference.
attrname
is a character string giving the
name of an attribute in the network's vertex attribute list. This
term adds a covariate with the value
abs(attrname(i)-attrname(j))
for all edges.
nodematch(attrname, diff=FALSE, mean=0, var=9)
Uniform Homophily
and Differential Homophily. attrname
is a
character string giving the name of an attribute in the
network's vertex attribute list. When diff=FALSE
,
this term adds one covariate with the value
attrname(i)==attrname(j)
. When diff=TRUE
,
p covariates are added to the model, where p is the
number of unique values of the attrname
attribute.
The kth such covariate has the value attrname(i) == attrname(j) == value(k)
, where
value(k)
is the kth smallest unique value of the
attrname
attribute.
sendercov(attrname, force.factor=FALSE, mean=0, var=9)
Sender covariate effect.
attrname
is a character string giving the name of an
attribute in the network's vertex attribute list.
If the attribute is numeric, This term adds one covariate
to the model equaling attrname(i)
. If the attribute is not
numeric or force.factor==TRUE
, this term adds p-1
covariates to the model,
where p is the number of unique values of attrname
.
The kth such covariate has the value attrname(i) == value(k+1)
, where
value(k)
is the kth smallest unique value of the
attrname
attribute. This term only makes
sense if g
is directed.
receivercov(attrname, force.factor=FALSE, mean=0, var=9)
Receiver covariate effect.
attrname
is a character string giving the name of an
attribute in the network's vertex attribute list.
If the attribute is numeric, This term adds one covariate
to the model equaling attrname(j)
. If the attribute is not
numeric or force.factor==TRUE
, this term adds p-1
covariates to the model,
where p is the number of unique values of attrname
.
The kth such covariate has the value attrname(j) == value(k+1)
, where
value(k)
is the kth smallest unique value of the
attrname
attribute. This term only makes
sense if g
is directed.
socialitycov(attrname, force.factor=FALSE, mean=0, var=9)
Sociality covariate effect.
attrname
is a character string giving the name of an
attribute in the network's vertex attribute list.
If the attribute is numeric, This term adds one covariate
to the model equaling attrname(i)+attrname(j)
. If the attribute is not
numeric or force.factor==TRUE
, this term adds p-1
covariates to the model,
where p is the number of unique values of attrname
.
The kth such covariate has the value attrname(i) ==
value(k+1) + attrname(j) == value(k+1)
, where
value(k)
is the kth smallest unique value of the
attrname
attribute. This term makes sense whether or not
g
is directed.