bilinear-ergmTerm {latentnet}

Bilinear (inner-product) latent space, with optional clustering

Description

Adds a term to the model equal to the inner product of the latent positions: Z_i \cdot 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.

Important: This term works in latentnet's ergmm() only. Using it in ergm() will result in an error.

Usage

# binary: 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)

# valued: 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)

Arguments

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.

Details

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.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None