terms.ergmm {latentnet}R Documentation

Model Terms for Latent Space Random Graph Model

Description

Model terms that can be used in an ergmm formula and their parameter names.

Model Terms

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.

See Also

ergmm


[Package latentnet version 2.4-1 Index]