model { for (i in 1:n) { mu[i] <- alpha + b.sex*sex[i] + b.age*age[i] # Regression function bp[i] ~ dnorm(mu[i],tau) # Normal likelihood terms for each data point } alpha ~ dnorm(0.0,1.0E-4) b.sex ~ dnorm(0.0,1.0E-4) b.age ~ dnorm(0.0,1.0E-4) tau <- 1/(sigma*sigma) # Prior for tau as function of sigma sigma ~ dunif(0,20) # Prior directly on sigma for (i in 1:n) { # Linear regression model for missing ages age.mu[i] <- alpha.age + beta.bp*bp[i] age[i] ~ dnorm(age.mu[i], tau.age) } alpha.age ~ dnorm(0.0,1.0E-4) beta.bp ~ dnorm(0.0,1.0E-4) tau.age <- 1/(sigma.age*sigma.age) sigma.age ~ dunif(0,20) } # Data list( sex = c(0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1), age = c(NA, NA, NA, 40, 67, 43, 61, 34, 51, 58, 54, 31, 49, 45, 66, 48, 41, 47, 53, 62, 60, 33, 44, 70, 56, 69, 35, 36, 68, 38), bp = c(143, 132, 88, 98, 177, 102, 154, 83, 131, 150, 131, 69, 111, 114, 170, 117, 96, 116, 131, 158, 156, 75, 111, 184, 141, 182, 74, 87, 183, 89), n=30) # Inits list(alpha=50, b.sex=1, b.age=4, sigma=1, alpha.age =40, beta.bp = 0, sigma.age= 10) Results: node mean sd MC error 2.5% median 97.5% start sample age[1] 56.31 0.9419 0.004311 54.46 56.31 58.17 5001 50000 age[2] 52.38 0.9399 0.004776 50.53 52.39 54.22 5001 50000 age[3] 37.78 0.9666 0.007956 35.88 37.78 39.68 5001 50000 alpha -23.99 3.595 0.09631 -31.19 -23.96 -17.0 5001 50000 alpha.age 8.154 0.9265 0.0222 6.315 8.158 10.01 5001 50000 b.age 2.959 0.06495 0.001743 2.834 2.959 3.089 5001 50000 b.sex 1.348 1.545 0.0174 -1.723 1.351 4.373 5001 50000 beta.bp 0.3359 0.007113 1.705E-4 0.3216 0.3359 0.3501 5001 50000 mu[1] 142.7 2.783 0.0121 137.2 142.6 148.1 5001 50000 mu[2] 132.4 2.794 0.01241 126.9 132.4 137.9 5001 50000 mu[3] 87.82 2.853 0.02268 82.19 87.83 93.44 5001 50000 mu[4] 94.38 1.308 0.027 91.79 94.39 96.96 5001 50000 mu[5] 174.3 1.333 0.02133 171.7 174.3 176.9 5001 50000 mu[6] 104.6 1.139 0.007668 102.3 104.6 106.8 5001 50000 mu[7] 156.5 1.109 0.01153 154.4 156.5 158.7 5001 50000 mu[8] 77.98 1.386 0.02234 75.22 77.98 80.7 5001 50000 mu[9] 128.3 1.147 0.008969 126.0 128.3 130.5 5001 50000 mu[10] 147.7 1.035 0.007355 145.6 147.7 149.7 5001 50000 mu[11] 137.2 1.209 0.01374 134.8 137.2 139.5 5001 50000 mu[12] 67.75 1.748 0.04248 64.26 67.76 71.18 5001 50000 mu[13] 121.0 1.025 0.01206 119.0 121.0 123.0 5001 50000 mu[14] 109.2 1.122 0.01855 107.0 109.2 111.4 5001 50000 mu[15] 171.3 1.29 0.01965 168.8 171.3 173.9 5001 50000 mu[16] 119.4 1.116 0.005173 117.2 119.4 121.6 5001 50000 mu[17] 97.34 1.267 0.02529 94.83 97.35 99.84 5001 50000 mu[18] 116.4 1.113 0.004584 114.2 116.4 118.6 5001 50000 mu[19] 132.9 0.9876 0.00664 130.9 132.9 134.8 5001 50000 mu[20] 159.5 1.14 0.01309 157.3 159.5 161.7 5001 50000 mu[21] 154.9 1.408 0.02386 152.2 154.9 157.7 5001 50000 mu[22] 73.67 1.643 0.03902 70.41 73.68 76.9 5001 50000 mu[23] 107.6 1.127 0.006343 105.3 107.6 109.8 5001 50000 mu[24] 183.2 1.471 0.02642 180.3 183.2 186.1 5001 50000 mu[25] 141.7 1.004 0.005645 139.7 141.7 143.7 5001 50000 mu[26] 180.2 1.423 0.02471 177.4 180.2 183.0 5001 50000 mu[27] 80.94 1.348 0.02064 78.25 80.95 83.59 5001 50000 mu[28] 83.9 1.313 0.01894 81.28 83.9 86.47 5001 50000 mu[29] 178.6 1.774 0.03765 175.1 178.6 182.1 5001 50000 mu[30] 89.81 1.249 0.01558 87.33 89.82 92.26 5001 50000 sigma 3.885 0.579 0.003988 2.948 3.815 5.208 5001 50000 sigma.age 1.307 0.1886 0.001215 1.002 1.284 1.739 5001 50000