amen (version 1.0)

ame: AME model fitting routine

Description

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

Usage

ame(Y, Xdyad=NULL, Xrow=NULL, Xcol=NULL, rvar = !(model=="rrl") ,
cvar = TRUE, dcor = TRUE, R = 0, model="nrm",
intercept=!is.element(model,c("rrl","ord")),
odmax=rep(max(apply(Y>0,1,sum,na.rm=TRUE)),nrow(Y)), seed = 1, nscan =
50000, burn = 500, odens = 25, plot=TRUE, print = TRUE, gof=TRUE)

Arguments

Y

an n x n square relational matrix of relations. See model below for various data types.

Xdyad

an n x n x pd array of covariates

Xrow

an n x pr matrix of nodal row covariates

Xcol

an n x pc matrix of nodal column covariates

rvar

logical: fit row random effects?

cvar

logical: fit column random effects?

dcor

logical: fit a dyadic correlation?

R

integer: dimension of the multiplicative effects (can be zero)

model

character: one of "nrm","bin","ord","cbin","frn","rrl" - see the details below

intercept

logical: fit model with an intercept?

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" models

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?

Value

• BETA
  posterior samples of regression coefficients
• SABR
  posterior samples of Cov(a,b) and the dyadic correlation
• 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
• UVPM
  posterior mean of UV
• 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

Details

This command provides posterior inference for parameters in AME models of 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.

Examples

data(YX_frn)
fit<-ame(YX_frn$Y,YX_frn$X,burn=5,nscan=5,odens=1,model="frn")
# you should run the Markov chain much longer than this