Semiparametric Factor and Regression Models for Symmetric Relational Data

Description

Estimation of the parameters in a model for symmetric relational data (e.g., the above-diagonal part of a square matrix), using a model-based eigenvalue decomposition and regression. Missing data is accomodated, and a posterior mean for missing data is calculated under the assumption that the data are missing at random. The marginal distribution of the relational data can be arbitrary, and is fit with an ordered probit specification. See Hoff (2007) <arXiv:0711.1146> for details on the model.

Details

Author(s)

Peter Hoff <peter.hoff@duke.edu>

References

Hoff (2007) “Modeling homophily and stochastic equivalence in symmetric relational data”

Examples

data(YX_Friend)

fit<-eigenmodel_mcmc(Y=YX_Friend$Y,X=YX_Friend$X,R=2,S=50,burn=50)

# in general you should run the Markov chain longer than 50 scans

plot(fit)


# people familiar with MCMC might want to implement 
# their own Markov chains: 

Y<-YX_Friend$Y
X<-YX_Friend$X

eigenmodel_setup(R=2)

for(s in 1:50) {   # you should run your chain longer than 50 scans

    Z<-rZ_fc() 
    UL<-rUL_fc()
    b<-rb_fc()  

                 }


#fit_Gen<-eigenmodel_mcmc(Y=Y_Gen,R=3,S=10000)

#fit_Pro<-eigenmodel_mcmc(Y=Y_Pro,R=3,S=10000)

Computes a matrix from its eigenvalue decomposition

Description

Computes a matrix from its eigenvalue decomposition

Usage

ULU(UL)

Arguments

Value

an n x n matrix

Author(s)

Peter Hoff

Computes a sociomatrix of regression effects

Description

Computes a sociomatrix of regression effects

Usage

XB(X, b)

Arguments

Value

an n x n matrix

Author(s)

Peter Hoff

Sex, race and friendship data from a 12th grade classroom

Description

A list in which Y encodes the presence of a friendship tie between 90 12th graders. The array X indicates pairs of the same sex and of the same race.

Source

http://www.cpc.unc.edu/projects/addhealth/design

Examples

data(YX_Friend)

Relations between words in the 1st chapter of Genesis

Description

The i,j th entry of this matrix is the numerical count of the number of times word i was next to word j in the first chapter of Genesis.

Examples

data(Y_Gen)

Butland's protein-protein interaction data

Description

Butland's protein-protein interaction data

References

Butland et al (2005) “Interaction network containing conserved and essential protein complexes in Escherichia coli”

Examples

data(Y_Pro)

Impute missing values of a sociomatrix

Description

Impute missing values of a sociomatrix

Usage

Y_impute()

Details

Imputes missing values of a sociomatrix from a matrix of latent variables and an ordered-probit specification.

Value

symmetric matrix

Author(s)

Peter Hoff

Adds lines between nodes to an existing plot of nodes

Description

Adds lines between nodes to an existing plot of nodes

Usage

addlines(U, Y, col = "green", lwd = 1, lty = 1)

Arguments

Author(s)

Peter Hoff

Approximate the posterior distribution of parameters in an eigenmodel

Description

Construct approximate samples from the posterior distribution of the parameters and latent variables in an eigenmodel for symmetric relational data.

Usage

eigenmodel_mcmc(Y, X = NULL, R = 2, S = 1000, seed = 1, Nss = min(S,
  1000), burn = 100)

Arguments

Value

a list with the following components:

Author(s)

Peter Hoff

Examples

data(YX_Friend)

fit<-eigenmodel_mcmc(Y=YX_Friend$Y,X=YX_Friend$X,R=2,S=50,burn=50)

# in general you  should run the Markov chain longer than 50 scans

plot(fit)

#fit<-eigenmodel_mcmc(Y=Y_Gen,R=3,S=10000)

#fit<-eigenmodel_mcmc(Y=Y_Pro,R=3,S=10000)

Setup constants and starting values for an eigenmodel fit

Description

Setup constants and starting values for an eigenmodel fit

Usage

eigenmodel_setup(R = 0, seed = 1, em_env = .GlobalEnv)

Arguments

Author(s)

Peter Hoff

Plot the output of an eigenmodel fit

Description

A graphical display of MCMC output and posterior estimates of model parameters in an eigenmodel fit. Includes 95 percent quantile-based posterior confidence intervals of regression coefficients.

Usage

## S3 method for class 'eigenmodel_post'
plot(x, ...)

Arguments

Author(s)

Peter Hoff

Sample UL from its full conditional distribution

Description

Samples the components of a reduced rank approximating matrix from their full conditional distributions

Usage

rUL_fc(E = Z - XB(X, b))

Arguments

Value

A list with the following components:

Author(s)

Peter Hoff

Sample from the full conditional distribution of the probit latent variables

Description

Sample from the full conditional distribution of the latent variables in the ordered probit model

Usage

rZ_fc(EZ = XB(X, b) + ULU(UL), MH = TRUE)

Arguments

Value

a symmetric matrix

Author(s)

Peter Hoff

Sample from the full conditional distribution of the regression coefficients

Description

Sample from the full conditional distribution of the regression coefficients in an eigenmodel

Usage

rb_fc(E = Z - ULU(UL))

Arguments

Value

a p x 1 vector

Author(s)

Peter Hoff

Sample from the multivariate normal distribution

Description

Sample from the multivariate normal distribution

Usage

rmvnorm(mu, Sig2)

Arguments

Value

a p x 1 vector

Author(s)

Peter Hoff

Examples

rmvnorm( c(0,0,0),diag(rep(3,1)) )