Generalised Linear MULTILEVEL Models for HIERARCHICAL data sets Differences from Program 8.1 by Congdon: 1) the level-2 model is a linear regression with covariate w_i 2) the random intercept and random impact at borough level are given independent univariate normal priors. The bivariate Normal specification is available however commented. model { # precision for residual variability for (j in 1:T) { gamm[j] ~ dnorm(0,tau.gam)} tau.gam ~ dgamma(1.0E-3,1.0E-3); sigma.gam <- 1/sqrt(tau.gam) # variable intercepts and slopes for (i in 1:N) { # beta[i,1:M] ~ dmnorm(mubet[i,1:M], Omega[,]) beta1[i] ~ dnorm(mubet1[i], tau.b1) beta2[i]~ dnorm(mubet2[i], tau.b2) # mubet[i,1]<-gam11+gam12*w[i] # mubet[i,2]<-gam21+gam22*w[i] mubet1[i]<-gam11+gam12*w[i] mubet2[i]<-gam21+gam22*w[i] } # Omega[1:M,1:M] ~ dwish(R[,], 2); # R[1,1] <- 0.01; R[1,2] <- 0.0; R[2,1] <- 0.0; R[2,2] <- 0.01; tau.b1 ~ dgamma(2,1); #tau.b1 ~ dgamma(2,100); sigma.b1 <- 1/sqrt(tau.b1) tau.b2 ~ dgamma(2,1); #tau.b2 ~ dgamma(2,100); sigma.b2 <- 1/sqrt(tau.b2) gam11 ~ dnorm(0,1.0E-1); gam12 ~ dnorm(0,1.0E-1); gam21 ~ dnorm(0,1.0E-1); gam22 ~ dnorm(0,1.0E-1); #corr1.2 <- Sigma2[1,2] / (Sig[1]*Sig[2]) #for (i in 1 : M) { # Sig[i] <- sqrt(Sigma2[i,i]) #for (j in 1 : M) { Sigma2[i, j] <- inverse(Omega[ , ], i, j) # } } # sampling model x.bar <- mean(x[]); for (j in 1:T) { O[j] ~ dpois(mu[j]) #log(mu[j] )<- log(E[j]) + beta[borough[j],1] + # beta[borough[j],2]*(x[j] - x.bar) + gamm[j]; log(mu[j] )<- log(E[j]) + beta1[borough[j]] + beta2[borough[j]]*(x[j] - x.bar) + gamm[j]; dev[j] <- O[j]*log(O[j]/mu[j])-(O[j]-mu[j]) } # fit tot.dev <- 2*sum(dev[]) } Inits list(beta = structure(.Data=c(0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1, 0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1, 0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1, 0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1, 0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1, 0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1, 0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1, 0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1),.Dim=c(33,2)), gam11=0,gam12=0,gam21=0,gam22=0,tau.gam=1, Omega = structure(.Data= c(0.01, 0, 0, 0.01),.Dim=c(2,2))) list(beta = structure(.Data=c(1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1),.Dim=c(33,2)), gam11=1,gam12=1,gam21=1,gam22=1,tau.gam=.1, Omega = structure(.Data= c(0.1, 0, 0, 0.1),.Dim=c(2,2))) list( gam11=0,gam12=0,gam21=0,gam22=0,tau.gam=1, tau.b1=1, tau.b2=1) list( gam11=1,gam12=1,gam21=1,gam22=1,tau.gam=.1, tau.b1=0.1, tau.b2=0.1) Data list( N = 33, # number of boros # M = 2, T = 758, # total number of wards O = c( 13.0, 40.0, 37.0, 30.0, 42.0, 42.0, 37.0, 62.0, 29.0, 39.0, 48.0, 39.0, 41.0, 15.0, 39.0, 13.0, 35.0, 52.0, 61.0, 51.0, 64.0, 73.0, 59.0, 56.0, 62.0, 54.0, 70.0, 57.0, 66.0, 54.0, 63.0, 50.0, 81.0, 50.0, 64.0, 59.0, 62.0, 59.0, 64.0, 79.0, 19.0, 13.0, 38.0, 27.0, 44.0, 28.0, 47.0, 40.0, 16.0, 49.0, 39.0, 42.0, 43.0, 12.0, 25.0, 50.0, 49.0, 41.0, 37.0, 53.0, 47.0, 25.0, 46.0, 33.0, 40.0, 37.0, 34.0, 36.0, 31.0, 23.0, 26.0, 32.0, 45.0, 29.0, 20.0, 13.0, 27.0, 22.0, 39.0, 41.0, 36.0, 50.0, 44.0, 30.0, 21.0, 19.0, 27.0, 36.0, 13.0, 27.0, 23.0, 34.0, 31.0, 21.0, 41.0, 55.0, 28.0, 82.0, 69.0, 86.0, 36.0, 35.0, 36.0, 11.0, 42.0, 33.0, 59.0, 40.0, 43.0, 38.0, 47.0, 39.0, 24.0, 51.0, 69.0, 62.0, 74.0, 39.0, 37.0, 31.0, 27.0, 32.0, 21.0, 15.0, 25.0, 24.0, 25.0, 29.0, 20.0, 12.0, 14.0, 28.0, 23.0, 8.0, 40.0, 24.0, 33.0, 16.0, 26.0, 56.0, 19.0, 15.0, 36.0, 15.0, 36.0, 15.0, 50.0, 28.0, 49.0, 33.0, 50.0, 49.0, 36.0, 81.0, 29.0, 46.0, 41.0, 54.0, 51.0, 50.0, 49.0, 32.0, 41.0, 30.0, 36.0, 35.0, 44.0, 35.0, 62.0, 47.0, 45.0, 55.0, 21.0, 55.0, 53.0, 55.0, 53.0, 51.0, 36.0, 53.0, 65.0, 27.0, 43.0, 64.0, 55.0, 41.0, 60.0, 59.0, 44.0, 46.0, 56.0, 25.0, 23.0, 42.0, 46.0, 49.0, 33.0, 27.0, 28.0, 23.0, 33.0, 38.0, 30.0, 35.0, 38.0, 34.0, 44.0, 19.0, 22.0, 39.0, 22.0, 25.0, 27.0, 25.0, 44.0, 27.0, 30.0, 29.0, 39.0, 18.0, 32.0, 35.0, 16.0, 33.0, 51.0, 41.0, 27.0, 36.0, 21.0, 34.0, 26.0, 22.0, 21.0, 24.0, 6.0, 18.0, 31.0, 15.0, 32.0, 28.0, 20.0, 38.0, 30.0, 41.0, 35.0, 28.0, 41.0, 26.0, 10.0, 24.0, 16.0, 26.0, 31.0, 42.0, 18.0, 30.0, 2.0, 33.0, 10.0, 15.0, 16.0, 35.0, 24.0, 30.0, 24.0, 17.0, 31.0, 37.0, 26.0, 26.0, 32.0, 29.0, 28.0, 29.0, 18.0, 28.0, 26.0, 45.0, 20.0, 28.0, 22.0, 37.0, 26.0, 17.0, 34.0, 49.0, 40.0, 18.0, 43.0, 25.0, 18.0, 34.0, 21.0, 22.0, 32.0, 36.0, 28.0, 26.0, 30.0, 17.0, 23.0, 30.0, 12.0, 24.0, 18.0, 20.0, 23.0, 20.0, 18.0, 41.0, 32.0, 27.0, 23.0, 16.0, 44.0, 36.0, 38.0, 26.0, 33.0, 39.0, 38.0, 22.0, 23.0, 24.0, 12.0, 33.0, 50.0, 18.0, 23.0, 19.0, 22.0, 37.0, 41.0, 46.0, 34.0, 48.0, 26.0, 28.0, 41.0, 40.0, 43.0, 18.0, 35.0, 36.0, 34.0, 46.0, 37.0, 30.0, 38.0, 34.0, 49.0, 29.0, 55.0, 39.0, 32.0, 44.0, 36.0, 26.0, 34.0, 33.0, 22.0, 40.0, 17.0, 43.0, 35.0, 35.0, 59.0, 60.0, 35.0, 25.0, 58.0, 57.0, 50.0, 52.0, 33.0, 61.0, 31.0, 51.0, 22.0, 45.0, 48.0, 46.0, 37.0, 30.0, 26.0, 32.0, 30.0, 26.0, 31.0, 29.0, 44.0, 32.0, 35.0, 29.0, 24.0, 28.0, 34.0, 45.0, 15.0, 31.0, 47.0, 26.0, 39.0, 45.0, 29.0, 20.0, 32.0, 29.0, 31.0, 27.0, 27.0, 34.0, 39.0, 36.0, 50.0, 43.0, 40.0, 29.0, 53.0, 38.0, 28.0, 31.0, 45.0, 32.0, 43.0, 23.0, 49.0, 45.0, 51.0, 42.0, 29.0, 22.0, 46.0, 24.0, 26.0, 51.0, 9.0, 26.0, 12.0, 36.0, 26.0, 33.0, 46.0, 40.0, 36.0, 29.0, 23.0, 35.0, 26.0, 25.0, 34.0, 20.0, 36.0, 2.0, 16.0, 18.0, 16.0, 30.0, 9.0, 25.0, 23.0, 20.0, 14.0, 16.0, 8.0, 15.0, 12.0, 18.0, 11.0, 51.0, 32.0, 25.0, 45.0, 22.0, 17.0, 26.0, 24.0, 37.0, 12.0, 26.0, 18.0, 17.0, 25.0, 28.0, 16.0, 24.0, 25.0, 46.0, 19.0, 15.0, 24.0, 29.0, 35.0, 46.0, 41.0, 42.0, 41.0, 43.0, 44.0, 67.0, 46.0, 42.0, 35.0, 46.0, 40.0, 33.0, 46.0, 33.0, 50.0, 33.0, 21.0, 38.0, 35.0, 50.0, 39.0, 21.0, 21.0, 33.0, 47.0, 39.0, 45.0, 34.0, 35.0, 39.0, 42.0, 35.0, 47.0, 27.0, 32.0, 28.0, 28.0, 26.0, 45.0, 21.0, 21.0, 31.0, 55.0, 32.0, 47.0, 45.0, 31.0, 31.0, 26.0, 27.0, 25.0, 46.0, 17.0, 30.0, 22.0, 38.0, 53.0, 32.0, 46.0, 30.0, 48.0, 35.0, 52.0, 27.0, 29.0, 36.0, 15.0, 40.0, 33.0, 36.0, 22.0, 46.0, 33.0, 49.0, 29.0, 26.0, 45.0, 41.0, 20.0, 25.0, 27.0, 41.0, 41.0, 49.0, 30.0, 59.0, 18.0, 37.0, 48.0, 30.0, 65.0, 50.0, 36.0, 58.0, 41.0, 59.0, 43.0, 46.0, 48.0, 70.0, 47.0, 62.0, 48.0, 60.0, 33.0, 51.0, 42.0, 59.0, 60.0, 35.0, 46.0, 31.0, 34.0, 17.0, 29.0, 37.0, 39.0, 48.0, 21.0, 25.0, 58.0, 49.0, 28.0, 27.0, 55.0, 23.0, 33.0, 45.0, 23.0, 49.0, 28.0, 16.0, 24.0, 28.0, 34.0, 63.0, 43.0, 28.0, 38.0, 51.0, 34.0, 26.0, 46.0, 55.0, 34.0, 28.0, 52.0, 40.0, 38.0, 41.0, 40.0, 26.0, 47.0, 33.0, 34.0, 21.0, 40.0, 29.0, 31.0, 18.0, 21.0, 28.0, 35.0, 11.0, 26.0, 26.0, 56.0, 33.0, 31.0, 24.0, 17.0, 43.0, 15.0, 50.0, 41.0, 21.0, 11.0, 30.0, 28.0, 31.0, 20.0, 33.0, 37.0, 28.0, 16.0, 44.0, 37.0, 36.0, 32.0, 20.0, 36.0, 41.0, 38.0, 43.0, 32.0, 45.0, 36.0, 45.0, 49.0, 47.0, 41.0, 51.0, 50.0, 29.0, 40.0, 41.0, 32.0, 72.0, 41.0, 40.0, 60.0, 66.0, 47.0, 51.0, 45.0, 58.0, 46.0, 48.0, 54.0, 41.0, 47.0, 42.0, 49.0, 21.0, 51.0, 47.0, 42.0, 57.0, 41.0, 24.0, 28.0, 55.0, 29.0, 41.0, 35.0, 52.0, 68.0, 50.0, 51.0, 26.0, 65.0, 16.0, 35.0, 12.0, 23.0, 20.0, 37.0, 46.0, 18.0, 40.0, 23.0, 9.0, 23.0, 36.0, 29.0, 28.0, 43.0, 41.0, 28.0, 29.0, 15.0, 13.0, 45.0, 28.0), E = c( 23.7, 29.6, 30.3, 37.3, 40.5, 39.0, 30.5, 44.7, 27.5, 29.2, 41.2, 44.6, 35.5, 12.7, 32.9, 20.3, 27.5, 47.1, 48.2, 39.4, 69.4, 64.8, 58.2, 58.8, 46.0, 61.1, 60.4, 68.0, 65.6, 65.7, 71.6, 71.2, 75.4, 61.1, 80.4, 70.8, 63.7, 74.4, 60.7, 66.1, 25.1, 17.8, 41.3, 27.5, 40.5, 50.4, 50.7, 46.0, 25.2, 45.4, 43.5, 50.1, 40.4, 15.4, 38.4, 37.5, 42.8, 48.6, 41.1, 53.3, 47.5, 27.7, 46.5, 27.2, 41.9, 38.6, 29.0, 37.6, 23.7, 29.0, 18.3, 30.0, 37.3, 27.9, 19.9, 17.2, 36.9, 23.3, 36.1, 24.3, 27.5, 52.8, 33.0, 21.1, 28.1, 19.0, 20.1, 31.3, 16.0, 33.3, 22.3, 38.1, 25.7, 24.9, 35.4, 62.4, 28.4, 76.3, 66.5, 83.6, 39.2, 32.0, 51.8, 20.1, 45.0, 41.9, 75.0, 50.2, 37.8, 37.5, 51.3, 38.6, 29.2, 71.0, 69.0, 62.1, 78.0, 47.5, 44.4, 50.1, 43.2, 29.0, 27.7, 18.0, 21.1, 23.9, 28.2, 23.3, 23.0, 21.5, 28.7, 27.7, 22.6, 23.0, 41.3, 26.6, 32.9, 22.1, 32.2, 45.0, 22.1, 19.3, 28.6, 22.2, 34.3, 17.4, 51.7, 37.9, 46.5, 33.8, 46.4, 55.8, 51.8, 66.7, 21.9, 42.9, 35.3, 46.8, 41.7, 58.0, 57.8, 28.3, 50.3, 36.3, 38.9, 45.5, 46.4, 35.5, 55.5, 47.6, 42.5, 58.3, 26.6, 52.1, 42.9, 47.3, 51.2, 45.7, 33.3, 55.3, 49.2, 39.7, 47.4, 37.7, 27.3, 50.6, 48.4, 55.2, 48.7, 42.2, 45.9, 28.8, 29.5, 45.9, 37.5, 46.0, 36.8, 29.1, 24.7, 25.7, 32.7, 34.9, 25.8, 31.6, 28.6, 44.0, 29.0, 32.9, 32.5, 35.2, 29.7, 29.5, 27.5, 35.8, 42.9, 31.3, 23.7, 36.9, 30.9, 24.5, 29.8, 34.3, 32.9, 33.7, 47.9, 47.1, 26.8, 39.5, 32.6, 34.7, 29.5, 13.5, 21.1, 35.7, 8.6, 18.5, 38.2, 14.0, 34.9, 29.3, 19.0, 21.1, 22.2, 33.4, 38.4, 18.3, 29.1, 29.5, 9.5, 16.8, 13.3, 22.9, 26.0, 25.2, 23.4, 32.2, 11.8, 28.8, 17.3, 14.6, 15.2, 29.1, 27.7, 34.6, 20.2, 19.8, 26.7, 30.0, 27.2, 28.3, 28.9, 29.7, 22.0, 18.3, 18.7, 30.2, 23.8, 42.9, 17.2, 34.5, 29.7, 33.2, 24.7, 17.2, 30.5, 37.2, 28.4, 11.9, 35.1, 19.9, 20.6, 27.2, 20.6, 21.7, 30.0, 32.8, 22.5, 17.7, 16.8, 20.4, 17.0, 25.4, 24.6, 20.8, 22.3, 20.2, 20.0, 19.8, 22.7, 28.3, 28.6, 36.4, 29.4, 19.9, 42.8, 31.2, 35.8, 26.6, 36.9, 24.0, 27.6, 24.1, 30.5, 25.2, 16.9, 35.3, 40.8, 25.0, 21.5, 16.8, 25.3, 36.5, 34.2, 42.2, 33.4, 59.1, 35.7, 32.9, 39.6, 48.5, 48.1, 41.7, 30.2, 38.4, 38.1, 30.3, 48.4, 43.5, 39.9, 36.5, 40.1, 38.7, 57.9, 38.5, 32.3, 42.1, 38.0, 30.3, 31.1, 27.5, 26.4, 35.7, 31.2, 46.1, 38.7, 37.8, 54.8, 55.4, 43.3, 35.1, 49.9, 46.1, 44.8, 52.9, 25.6, 42.9, 31.2, 52.2, 27.3, 38.3, 50.8, 35.7, 24.5, 30.5, 34.6, 34.6, 24.5, 35.3, 22.0, 32.4, 52.2, 31.0, 35.0, 27.1, 27.7, 28.7, 33.5, 55.5, 30.0, 47.9, 50.7, 32.7, 40.6, 43.8, 29.1, 21.6, 27.5, 24.9, 24.6, 27.3, 32.7, 26.4, 41.9, 33.3, 49.3, 38.0, 39.3, 31.6, 44.4, 40.4, 24.9, 24.4, 41.5, 32.5, 41.3, 38.6, 37.6, 42.4, 35.0, 46.0, 37.6, 32.7, 42.7, 28.0, 24.1, 42.3, 17.2, 30.2, 15.5, 29.1, 28.7, 34.8, 36.6, 39.8, 30.7, 36.0, 26.5, 36.9, 20.2, 23.6, 36.2, 27.7, 27.1, 12.9, 27.5, 25.3, 23.9, 22.7, 16.5, 24.3, 22.0, 36.1, 28.3, 19.9, 12.8, 23.8, 22.9, 27.8, 25.9, 47.4, 24.0, 23.8, 42.8, 23.5, 34.3, 29.6, 25.5, 34.2, 23.5, 37.0, 22.7, 22.5, 23.4, 28.3, 29.2, 36.6, 29.2, 37.6, 22.1, 21.2, 24.3, 36.2, 34.0, 39.3, 44.8, 39.7, 35.0, 44.9, 33.6, 47.9, 38.4, 38.3, 32.7, 40.3, 38.2, 34.3, 49.3, 42.5, 46.3, 31.4, 27.1, 43.2, 32.1, 41.3, 40.1, 24.0, 23.1, 37.8, 49.7, 38.3, 50.3, 34.1, 33.2, 27.3, 29.0, 30.3, 37.8, 37.4, 35.4, 26.0, 30.8, 30.3, 43.8, 30.9, 28.8, 28.5, 47.8, 38.3, 38.1, 33.4, 35.0, 43.1, 26.3, 29.8, 20.1, 37.1, 17.3, 39.4, 21.1, 41.4, 41.8, 37.2, 43.5, 28.8, 46.6, 43.2, 47.6, 27.7, 40.3, 38.9, 17.3, 25.5, 30.1, 28.1, 25.4, 37.3, 28.7, 44.6, 38.7, 21.5, 37.4, 42.2, 21.4, 26.0, 19.3, 30.5, 30.1, 38.9, 22.3, 48.5, 20.9, 26.2, 40.0, 26.4, 52.0, 56.9, 45.2, 50.8, 38.7, 64.6, 39.5, 45.8, 55.9, 55.7, 41.7, 57.0, 36.4, 50.9, 49.4, 38.8, 47.3, 41.3, 55.4, 31.3, 42.0, 41.2, 29.7, 28.0, 41.4, 42.1, 42.0, 39.0, 23.6, 49.3, 47.4, 45.3, 34.9, 39.2, 45.3, 33.7, 44.1, 41.0, 26.1, 41.2, 21.3, 24.3, 23.0, 36.0, 34.0, 41.5, 35.8, 20.7, 29.5, 38.3, 36.9, 27.5, 38.0, 45.9, 24.9, 23.1, 41.3, 48.9, 38.4, 35.9, 43.3, 32.2, 37.3, 31.0, 25.4, 25.8, 33.5, 29.3, 36.3, 24.7, 23.3, 32.2, 28.1, 10.5, 25.0, 26.9, 47.8, 25.0, 28.0, 24.9, 28.8, 50.3, 23.2, 37.2, 43.6, 19.7, 16.0, 34.1, 27.2, 26.1, 19.8, 29.4, 33.6, 25.6, 19.1, 42.2, 35.0, 34.0, 38.1, 27.6, 31.7, 40.9, 30.2, 36.0, 22.7, 35.7, 29.8, 28.7, 38.7, 37.2, 33.9, 44.2, 62.3, 36.1, 37.3, 38.3, 32.1, 67.5, 28.5, 40.1, 45.9, 55.3, 42.1, 36.7, 37.2, 42.0, 41.5, 44.1, 52.3, 32.5, 45.0, 27.8, 49.7, 24.8, 54.9, 41.8, 44.5, 48.8, 34.9, 32.7, 25.4, 60.4, 37.4, 39.8, 44.4, 44.0, 57.3, 46.5, 46.8, 32.6, 64.8, 21.3, 38.5, 25.2, 23.8, 33.5, 47.3, 42.0, 30.6, 33.8, 34.5, 22.1, 29.5, 34.9, 40.5, 38.2, 37.5, 34.2, 55.4, 34.4, 16.5, 21.2, 39.2, 29.3), x = c( 2.42, 2.39, 2.38, 2.44, 2.14, 2.15, 2.35, 2.38, 2.43, 2.45, 2.32, 2.03, 2.43, 2.32, 2.43, 2.21, 2.40, 2.38, 2.42, 2.35, 2.23, 2.01, 2.49, 2.33, 2.45, 2.10, 2.31, 2.11, 2.24, 2.16, 2.12, 2.33, 1.99, 2.03, 2.27, 2.11, 2.21, 2.17, 2.38, 2.24, 1.92, 1.99, 2.12, 1.89, 1.82, 1.87, 1.94, 1.96, 2.15, 2.13, 1.99, 2.08, 2.21, 1.87, 1.88, 2.29, 2.10, 1.86, 2.00, 2.12, 2.02, 2.28, 1.90, 2.30, 2.31, 2.17, 2.37, 2.45, 2.60, 2.35, 2.44, 2.44, 2.25, 2.30, 2.46, 2.44, 2.10, 2.52, 2.24, 2.42, 2.52, 2.23, 2.22, 2.43, 2.21, 2.53, 2.47, 2.53, 2.54, 2.18, 2.09, 2.29, 2.40, 2.49, 2.34, 1.75, 1.78, 2.01, 1.75, 1.88, 2.07, 2.03, 1.82, 1.83, 1.98, 1.95, 1.88, 1.96, 2.13, 2.19, 2.24, 2.11, 2.35, 1.78, 2.11, 2.15, 2.22, 1.90, 1.73, 1.89, 2.42, 2.37, 2.67, 2.64, 2.50, 2.49, 2.55, 2.34, 2.42, 2.31, 2.26, 2.51, 2.54, 2.20, 2.43, 2.59, 2.49, 2.62, 2.54, 2.59, 2.45, 2.57, 2.65, 2.42, 2.44, 2.44, 2.29, 2.19, 2.24, 2.12, 2.36, 2.04, 2.08, 2.29, 2.40, 1.93, 2.00, 1.97, 2.32, 2.15, 1.96, 2.25, 1.91, 1.80, 2.27, 2.09, 2.26, 2.26, 2.29, 2.23, 2.36, 1.90, 2.22, 2.28, 2.16, 2.44, 2.33, 2.29, 2.38, 2.24, 2.44, 2.27, 2.29, 2.33, 2.36, 2.19, 2.15, 2.17, 2.28, 2.27, 2.38, 2.40, 2.36, 2.31, 2.17, 2.33, 2.16, 2.31, 2.35, 2.25, 2.18, 2.21, 2.35, 2.10, 2.21, 1.71, 2.16, 1.89, 2.11, 2.23, 2.06, 2.14, 2.34, 1.96, 2.23, 2.22, 2.30, 1.96, 2.21, 2.17, 2.31, 2.14, 1.99, 2.07, 1.87, 1.90, 2.26, 2.00, 2.05, 2.08, 2.24, 2.53, 2.31, 2.18, 2.39, 2.35, 2.18, 1.88, 1.99, 2.38, 2.44, 2.41, 2.37, 2.35, 2.28, 2.31, 2.37, 1.93, 2.52, 2.14, 2.27, 2.39, 2.36, 2.50, 2.24, 2.39, 2.02, 2.24, 2.19, 2.11, 2.31, 2.36, 2.35, 2.23, 2.47, 2.49, 2.51, 2.52, 2.42, 2.50, 2.48, 2.55, 2.60, 2.37, 2.56, 2.43, 2.56, 2.57, 2.39, 2.52, 2.51, 2.51, 2.51, 2.44, 2.49, 2.51, 2.57, 2.50, 2.49, 2.46, 2.52, 2.55, 2.44, 2.34, 2.55, 2.48, 2.26, 2.39, 2.53, 2.41, 2.47, 2.48, 2.14, 2.44, 2.39, 2.35, 2.36, 2.31, 2.36, 2.47, 2.58, 2.44, 2.12, 2.27, 2.37, 2.35, 2.36, 2.26, 2.27, 2.37, 2.40, 2.44, 2.26, 2.34, 2.32, 2.23, 2.43, 2.41, 2.45, 2.43, 2.39, 2.42, 2.37, 2.41, 2.38, 2.15, 2.14, 2.29, 2.26, 2.17, 2.00, 1.94, 2.16, 2.28, 2.05, 2.29, 2.08, 1.98, 2.22, 2.22, 2.28, 2.15, 2.07, 2.25, 2.25, 1.98, 2.18, 1.88, 2.17, 2.15, 1.93, 1.96, 1.61, 2.03, 1.74, 1.98, 2.29, 1.97, 2.00, 1.96, 2.30, 2.36, 2.02, 2.06, 2.15, 1.95, 1.93, 2.04, 2.14, 2.02, 1.88, 2.29, 2.33, 2.14, 2.04, 2.14, 2.24, 2.33, 2.27, 2.05, 2.03, 2.24, 2.29, 2.27, 2.26, 2.11, 2.26, 1.92, 2.10, 2.13, 2.21, 1.93, 2.18, 2.30, 2.08, 2.37, 2.21, 2.24, 2.19, 2.37, 2.30, 2.27, 2.20, 2.41, 2.28, 2.30, 2.26, 2.27, 2.39, 2.35, 2.19, 2.26, 2.35, 2.38, 2.37, 2.18, 2.39, 2.31, 2.37, 2.16, 2.37, 2.47, 2.54, 2.47, 2.45, 2.54, 2.43, 2.48, 2.48, 2.46, 2.42, 2.51, 2.50, 2.49, 2.40, 2.45, 2.47, 2.44, 2.53, 2.52, 2.52, 2.48, 2.57, 2.59, 2.36, 2.34, 2.57, 2.55, 2.46, 2.54, 2.61, 2.44, 2.36, 2.46, 2.35, 2.25, 2.49, 2.41, 2.37, 2.49, 2.55, 2.51, 2.09, 2.17, 2.10, 2.24, 2.15, 2.11, 2.05, 2.27, 2.07, 2.15, 1.84, 2.40, 2.14, 1.94, 2.27, 2.30, 2.07, 2.18, 2.21, 2.02, 2.53, 2.57, 2.37, 2.42, 2.50, 2.42, 2.40, 2.30, 2.53, 2.51, 2.52, 2.39, 2.44, 2.55, 2.35, 2.21, 2.40, 2.37, 2.21, 2.43, 2.42, 2.53, 2.40, 2.36, 2.25, 2.21, 2.34, 2.24, 2.39, 2.42, 2.55, 2.35, 2.49, 2.32, 2.36, 2.27, 2.35, 2.28, 2.52, 2.41, 2.20, 2.36, 2.11, 2.32, 2.16, 2.39, 2.37, 2.34, 2.36, 2.01, 2.29, 2.21, 2.20, 2.23, 2.26, 2.26, 2.36, 2.06, 2.01, 2.09, 2.34, 2.26, 2.27, 2.13, 2.32, 2.28, 2.12, 2.11, 2.47, 2.35, 2.44, 2.47, 2.41, 2.38, 2.35, 2.24, 2.39, 2.44, 2.41, 2.41, 2.39, 2.48, 2.46, 2.46, 2.46, 2.47, 2.46, 2.35, 2.47, 2.42, 2.34, 2.46, 2.22, 1.98, 2.19, 1.96, 2.08, 1.98, 2.22, 2.06, 2.13, 2.06, 2.27, 2.20, 2.34, 2.02, 1.79, 2.08, 2.05, 2.19, 2.17, 2.29, 1.96, 2.17, 2.14, 2.05, 2.18, 2.17, 2.15, 2.15, 2.19, 2.09, 2.14, 2.14, 2.25, 2.15, 2.25, 2.34, 2.08, 2.16, 2.08, 2.09, 2.58, 2.30, 2.46, 2.36, 2.47, 2.56, 2.54, 2.55, 2.50, 2.59, 2.31, 2.52, 2.40, 2.52, 2.56, 2.64, 2.44, 2.52, 2.50, 2.52, 2.17, 2.28, 2.50, 2.46, 2.38, 1.96, 2.27, 2.02, 1.85, 2.07, 1.92, 1.75, 1.90, 2.12, 1.96, 2.05, 2.40, 2.42, 2.24, 2.00, 2.18, 2.25, 2.04, 2.14, 2.14, 2.27, 1.32, 2.01, 1.98, 2.18, 2.57, 2.48, 2.60, 2.52, 2.39, 2.60, 2.55, 2.58, 2.43, 2.49, 2.58, 2.65, 2.55, 2.58, 2.68, 2.61, 2.62, 2.74, 2.62, 2.40, 2.47, 2.21, 2.10, 1.89, 2.33, 2.33, 2.04, 2.21, 2.34, 2.39, 2.41, 2.12, 2.35, 2.46, 2.34, 2.34, 2.38, 2.18, 2.35, 2.29, 2.42, 2.31, 2.31, 2.32, 2.30, 2.40, 2.47, 2.33, 2.19, 2.30, 2.43, 2.43, 2.47, 2.32, 2.35, 2.26, 2.25, 2.28, 2.39, 2.36, 2.32, 2.60, 2.58, 2.47, 2.57, 2.52, 2.56, 2.63, 2.40, 2.56, 2.50, 2.37, 2.60, 2.41, 2.45, 2.45, 2.59, 2.59, 2.47, 2.52, 2.55, 2.45, 2.57, 2.61), borough = c( 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33), w=c(0,1,0,0,1,0,0,1,0,1, 0,1,1,0,1,0,1,0,1,0, 1,1,0,0,1,1,0,1,0,1,1,0,0) ) node mean sd MC error 2.5% median 97.5% start sample gam11 -0.06166 0.07383 0.004361 -0.1964 -0.0636 0.08509 401 1200 gam12 0.05625 0.1037 0.00568 -0.1474 0.05804 0.261 401 1200 gam21 0.613 0.1337 0.009941 0.3368 0.6162 0.8745 401 1200 gam22 0.1247 0.1853 0.01359 -0.2222 0.1242 0.4777 401 1200 sigma.b1 0.2919 0.03752 0.001376 0.23 0.2886 0.3786 401 1200 sigma.b2 0.4316 0.07524 0.004797 0.3113 0.4255 0.6029 401 1200 sigma.gam 0.08047 0.0109 0.001365 0.06005 0.08149 0.09997 401 1200 tot.dev 789.4 37.44 3.724 717.1 789.2 859.8 401 1200