amen (version 1.0)

rZ_cbin_fc: Simulate Z given fixed rank nomination data

Description

Simulates a random latent matrix Z given its expectation, dyadic correlation and censored binary nomination data

Usage

rZ_cbin_fc(Z, EZ, rho, Y, odmax, odobs)

Arguments

Z

a square matrix, the current value of Z

EZ

expected value of Z

rho

dyadic correlation

Y

square matrix of ranked nomination data

odmax

a scalar or vector giving the maximum number of nominations for each individual

odobs

observed outdegree

Value

• a square matrix, the new value of Z

Details

simulates Z under the constraints (1) Y[i,j]=1, Y[i,k]=0 => Z[i,j]>Z[i,k] , (2) Y[i,j]=1 => Z[i,j]>0 , (3) Y[i,j]=0 & odobs[i] Z[i,j]

Examples

## The function is currently defined as
function(Z,EZ,rho,Y,odmax,odobs)
{
  # simulates Z under the constraints
  # (1)  Y[i,j] > Y[i,k]              => Z[i,j]>Z[i,k]
  # (2)  Y[i,j]>0                     => Z[i,j]>0
  # (3)  Y[i,j]=0 & odobs[i]<odmax[i] => Z[i,j]<0

  sz<-sqrt(1-rho^2)
  ut<-upper.tri(EZ)
  lt<-lower.tri(EZ)

  for(y in sample(0:1))
  {
    if(y==1)
    {
      ub<- Inf
      lbm<-matrix(pmax(apply(Z-(Y!=0)*(Inf^(Y!=0)),1,max,na.rm=TRUE),0),
                  nrow(Z),nrow(Z))
    }

    if(y==0)
    {
      lb<- -Inf
      ubm<-matrix(apply(Z+(Y!=1)*(Inf^(Y!=1)),1,min,na.rm=TRUE),nrow(Z),
                  nrow(Z))
      ubm[ odobs<odmax ] <- 0
    }

    up<- ut & Y==y
    if(y==0)  { ub<-ubm[up] }
    if(y==1)  { lb<-lbm[up] }
    ez<- EZ[up] + rho*( t(Z)[up]  - t(EZ)[up] )
    Z[up]<-ez+sz*qnorm(runif(sum(up),pnorm((lb-ez)/sz),pnorm((ub-ez)/sz)))

    up<- lt & Y==y
    if(y==0)  { ub<-ubm[up] }
    if(y==1)  { lb<-lbm[up] }
    ez<- EZ[up] + rho*( t(Z)[up]  - t(EZ)[up] )
    Z[up]<-ez+sz*qnorm(runif(sum(up),pnorm((lb-ez)/sz),pnorm((ub-ez)/sz)))
  }

  #diag(Z)<-rnorm(nrow(Z),diag(EZ),1)
  Z[is.na(Y)]<- rnorm(sum(is.na(Y)),EZ[is.na(Y)],1)
  Z
}