ame_rep: AME model fitting routine for replicated relational data

In amen: Additive and Multiplicative Effects Models for Networks and Relational Data

AME model fitting routine for replicated relational data

Description

An MCMC routine providing a fit to an additive and multiplicative effects (AME) regression model to replicated relational data of various types.

Usage

ame_rep(Y,Xdyad=NULL, Xrow=NULL, Xcol=NULL, family, R=0, rvar = !(family=="rrl"),
cvar = TRUE, dcor = !symmetric, nvar=TRUE,  
intercept=!is.element(family,c("rrl","ord")),
symmetric=FALSE,
odmax=rep(max(apply(Y>0,c(1,3),sum,na.rm=TRUE)),nrow(Y[,,1])), seed = 1,
nscan = 10000, burn = 500, odens = 25, plot=TRUE, print = TRUE, gof=TRUE)

Arguments

Y	an n x n x T array of relational matrix, where the third dimension correponds to replicates (over time, for example). See family below for various data types.
Xdyad	an n x n x pd x T array of covariates
Xrow	an n x pr x T array of nodal row covariates
Xcol	an n x pc x T array of nodal column covariates
family	character: one of "nrm","bin","ord","cbin","frn","rrl" - see the details below
R	integer: dimension of the multiplicative effects (can be zero)
rvar	logical: fit row random effects (asymmetric case)?
cvar	logical: fit column random effects (asymmetric case)?
dcor	logical: fit a dyadic correlation (asymmetric case)?
nvar	logical: fit nodal random effects (symmetric case)?
intercept	logical: fit model with an intercept?
symmetric	logical: Is the sociomatrix symmetric by design?
odmax	a scalar integer or vector of length n giving the maximum number of nominations that each node may make - used for "frn" and "cbin" families
seed	random seed
nscan	number of iterations of the Markov chain (beyond burn-in)
burn	burn in for the Markov chain
odens	output density for the Markov chain
plot	logical: plot results while running?
print	logical: print results while running?
gof	logical: calculate goodness of fit statistics?

Details

This command provides posterior inference for parameters in AME models of independent replicated relational data, assuming one of six possible data types/models:

"nrm": A normal AME model.

"bin": A binary probit AME model.

"ord": An ordinal probit AME model. An intercept is not identifiable in this model.

"cbin": An AME model for censored binary data. The value of 'odmax' specifies the maximum number of links each row may have.

"frn": An AME model for fixed rank nomination networks. A higher value of the rank indicates a stronger relationship. The value of 'odmax' specifies the maximum number of links each row may have.

"rrl": An AME model based on the row ranks. This is appropriate if the relationships across rows are not directly comparable in terms of scale. An intercept, row random effects and row regression effects are not estimable for this model.

Value

BETA	posterior samples of regression coefficients
VC	posterior samples of the variance parameters
APM	posterior mean of additive row effects a
BPM	posterior mean of additive column effects b
U	posterior mean of multiplicative row effects u
V	posterior mean of multiplicative column effects v (asymmetric case)
UVPM	posterior mean of UV
ULUPM	posterior mean of ULU (symmetric case)
L	posterior mean of L (symmetric case)
EZ	estimate of expectation of Z matrix
YPM	posterior mean of Y (for imputing missing values)
GOF	observed (first row) and posterior predictive (remaining rows) values of four goodness-of-fit statistics

Author(s)

Peter Hoff, Yanjun He

Examples

data(YX_bin_long) 
fit<-ame_rep(YX_bin_long$Y,YX_bin_long$X,burn=5,nscan=5,odens=1,family="bin")
# you should run the Markov chain much longer than this

amen documentation built on May 29, 2024, 9:58 a.m.