model {
for (i in 1:N) {
for (j in 1:T) {
Y[i,j] ~ dnorm(mu[i,j], tau)
mu[i,j] <- alpha[i,1] + alpha[i,2]*(x[j] - mean(x[]))
## cross-product statistics
XY[i,j] <- Y[i,j]*(x[j] - mean(x[]))
XX[i,j] <- (x[j] - mean(x[]))*(x[j] - mean(x[]))
## posterior predictive
## N(0,1) under null
resid[i,j] <- (Y[i,j] - mu[i,j])*sqrt(tau)
resid2[i,j] <- resid[i,j]*resid[i,j]
}
X2[i] <- sum(resid2[i,]) # X2_T under null
chi.sqr[i] ~ dchisqr(T) # comparison under null
P.resid[i] <- step(X2[i] - chi.sqr[i])
# prior for intercept and gradient
alpha[i,1:2] ~ dmnorm(mu.alpha[],R[,])
# replicated intercept and gradient
alpha.pred[i,1:2] ~ dmnorm(mu.alpha[],R[,])
# summary statistics for intercept and gradient
alpha.est[i,1] <- mean(Y[i, ])
alpha.est[i,2] <- sum(XY[i,])/sum(XX[i,])
## precision of intercept estimates
alpha.est.prec[i,1] <- tau*T
## precision of gradient estimates
alpha.est.prec[i,2] <- tau*sum(XX[i,])
alpha.est.pred[i,1] ~ dnorm(alpha.pred[i,1],
alpha.est.prec[i,1])
alpha.est.pred[i,2] ~ dnorm(alpha.pred[i,2],
alpha.est.prec[i,2])
P.alpha[i,1] <- step(alpha.est[i,1] -
alpha.est.pred[i,1])
P.alpha[i,2] <- step(alpha.est[i,2] -
alpha.est.pred[i,2])
}
mu.alpha[1] ~ dunif(-1000,1000)
mu.alpha[2] ~ dunif(-1000,1000)
R[1:2,1:2] ~ dwish(Omega[,],2)
Omega[1,1] <- 1;
Omega[1,2] <- 0;
Omega[2,1] <- 0;
Omega[2,2] <- 1
tau ~ dgamma(0.001,0.001)
sigma <- 1/tau
}
Inits:
list(mu.alpha = c(0,0), tau=1,
alpha = structure(
.Data = c(100,6,100,6,100,6,100,6,100,6,
100,6,100,6,100,6,100,6,100,6,
100,6,100,6,100,6,100,6,100,6,
100,6,100,6,100,6,100,6,100,6,
100,6,100,6,100,6,100,6,100,6,
100,6,100,6,100,6,100,6,100,6),
.Dim = c(30, 2)),
R = structure(.Data = c(1,0,0,1), .Dim = c(2, 2)))
Data:
list(x = c(8.0, 15.0, 22.0, 29.0, 36.0), N = 30, T = 5,
Y = structure(
.Data = c(151, 199, 246, 283, 320,
145, 199, 249, 293, 354,
147, 214, 263, 312, 328,
155, 200, 237, 272, 297,
135, 188, 230, 280, 323,
159, 210, 252, 298, 331,
141, 189, 231, 275, 305,
159, 201, 248, 297, 338,
177, 236, 285, 350, 376,
134, 182, 220, 260, 296,
160, 208, 261, 313, 352,
143, 188, 220, 273, 314,
154, 200, 244, 289, 325,
171, 221, 270, 326, 358,
163, 216, 242, 281, 312,
160, 207, 248, 288, 324,
142, 187, 234, 280, 316,
156, 203, 243, 283, 317,
157, 212, 259, 307, 336,
152, 203, 246, 286, 321,
154, 205, 253, 298, 334,
139, 190, 225, 267, 302,
146, 191, 229, 272, 302,
157, 211, 250, 285, 323,
132, 185, 237, 286, 331,
160, 207, 257, 303, 345,
169, 216, 261, 295, 333,
157, 205, 248, 289, 316,
137, 180, 219, 258, 291,
153, 200, 244, 286, 324),
.Dim = c(30,5)))
node mean sd MC error 2.5% median 97.5% start sample
P.alpha[1,1] 0.423 0.494 0.002084 0.0 0.0 1.0 1001 50000
P.alpha[1,2] 0.3992 0.4897 0.002263 0.0 0.0 1.0 1001 50000
P.alpha[2,1] 0.6431 0.4791 0.002189 0.0 1.0 1.0 1001 50000
P.alpha[2,2] 0.9589 0.1984 8.727E-4 0.0 1.0 1.0 1001 50000
P.alpha[3,1] 0.755 0.4301 0.001995 0.0 1.0 1.0 1001 50000
P.alpha[3,2] 0.7291 0.4444 0.001867 0.0 1.0 1.0 1001 50000
P.alpha[4,1] 0.24 0.4271 0.001955 0.0 0.0 1.0 1001 50000
P.alpha[4,2] 0.0435 0.204 0.001032 0.0 0.0 1.0 1001 50000
P.alpha[5,1] 0.218 0.4129 0.001902 0.0 0.0 1.0 1001 50000
P.alpha[5,2] 0.787 0.4094 0.001823 0.0 1.0 1.0 1001 50000
P.alpha[6,1] 0.6917 0.4618 0.002198 0.0 1.0 1.0 1001 50000
P.alpha[6,2] 0.4904 0.4999 0.002446 0.0 0.0 1.0 1001 50000
P.alpha[7,1] 0.1616 0.368 0.00172 0.0 0.0 1.0 1001 50000
P.alpha[7,2] 0.3339 0.4716 0.002196 0.0 0.0 1.0 1001 50000
P.alpha[8,1] 0.658 0.4744 0.002123 0.0 1.0 1.0 1001 50000
P.alpha[8,2] 0.6826 0.4655 0.002121 0.0 1.0 1.0 1001 50000
P.alpha[9,1] 0.9969 0.05541 2.338E-4 1.0 1.0 1.0 1001 50000
P.alpha[9,2] 0.9605 0.1949 8.522E-4 0.0 1.0 1.0 1001 50000
P.alpha[10,1] 0.05134 0.2207 9.796E-4 0.0 0.0 1.0 1001 50000
P.alpha[10,2] 0.2389 0.4264 0.002025 0.0 0.0 1.0 1001 50000
P.alpha[11,1] 0.8651 0.3417 0.001579 0.0 1.0 1.0 1001 50000
P.alpha[11,2] 0.8963 0.3049 0.001321 0.0 1.0 1.0 1001 50000
P.alpha[12,1] 0.1551 0.362 0.001634 0.0 0.0 1.0 1001 50000
P.alpha[12,2] 0.4483 0.4973 0.002003 0.0 0.0 1.0 1001 50000
P.alpha[13,1] 0.4936 0.5 0.002394 0.0 0.0 1.0 1001 50000
P.alpha[13,2] 0.4833 0.4997 0.002241 0.0 0.0 1.0 1001 50000
P.alpha[14,1] 0.9628 0.1892 8.804E-4 0.0 1.0 1.0 1001 50000
P.alpha[14,2] 0.8506 0.3565 0.001657 0.0 1.0 1.0 1001 50000
P.alpha[15,1] 0.507 0.5 0.002254 0.0 1.0 1.0 1001 50000
P.alpha[15,2] 0.06122 0.2397 0.001099 0.0 0.0 1.0 1001 50000
P.alpha[16,1] 0.5774 0.494 0.002298 0.0 1.0 1.0 1001 50000
P.alpha[16,2] 0.2942 0.4557 0.001915 0.0 0.0 1.0 1001 50000
P.alpha[17,1] 0.2277 0.4194 0.00199 0.0 0.0 1.0 1001 50000
P.alpha[17,2] 0.5694 0.4952 0.002468 0.0 1.0 1.0 1001 50000
P.alpha[18,1] 0.4363 0.4959 0.002321 0.0 0.0 1.0 1001 50000
P.alpha[18,2] 0.2441 0.4295 0.001855 0.0 0.0 1.0 1001 50000
P.alpha[19,1] 0.7875 0.4091 0.001933 0.0 1.0 1.0 1001 50000
P.alpha[19,2] 0.6738 0.4688 0.002136 0.0 1.0 1.0 1001 50000
P.alpha[20,1] 0.4694 0.4991 0.00233 0.0 0.0 1.0 1001 50000
P.alpha[20,2] 0.392 0.4882 0.002152 0.0 0.0 1.0 1001 50000
P.alpha[21,1] 0.663 0.4727 0.002101 0.0 1.0 1.0 1001 50000
P.alpha[21,2] 0.6755 0.4682 0.001997 0.0 1.0 1.0 1001 50000
P.alpha[22,1] 0.1106 0.3137 0.001352 0.0 0.0 1.0 1001 50000
P.alpha[22,2] 0.2487 0.4322 0.00185 0.0 0.0 1.0 1001 50000
P.alpha[23,1] 0.1594 0.366 0.00176 0.0 0.0 1.0 1001 50000
P.alpha[23,2] 0.1853 0.3886 0.00182 0.0 0.0 1.0 1001 50000
P.alpha[24,1] 0.5711 0.4949 0.002071 0.0 1.0 1.0 1001 50000
P.alpha[24,2] 0.2716 0.4448 0.00191 0.0 0.0 1.0 1001 50000
P.alpha[25,1] 0.2836 0.4507 0.001975 0.0 0.0 1.0 1001 50000
P.alpha[25,2] 0.9289 0.2569 0.00125 0.0 1.0 1.0 1001 50000
P.alpha[26,1] 0.7914 0.4063 0.001772 0.0 1.0 1.0 1001 50000
P.alpha[26,2] 0.7715 0.4199 0.00182 0.0 1.0 1.0 1001 50000
P.alpha[27,1] 0.7982 0.4013 0.001688 0.0 1.0 1.0 1001 50000
P.alpha[27,2] 0.2762 0.4471 0.001961 0.0 0.0 1.0 1001 50000
P.alpha[28,1] 0.5136 0.4998 0.002303 0.0 1.0 1.0 1001 50000
P.alpha[28,2] 0.243 0.4289 0.00188 0.0 0.0 1.0 1001 50000
P.alpha[29,1] 0.0425 0.2017 8.804E-4 0.0 0.0 1.0 1001 50000
P.alpha[29,2] 0.1437 0.3508 0.001649 0.0 0.0 1.0 1001 50000
P.alpha[30,1] 0.4651 0.4988 0.002067 0.0 0.0 1.0 1001 50000
P.alpha[30,2] 0.4559 0.4981 0.002458 0.0 0.0 1.0 1001 50000
P.resid[1] 0.4074 0.4913 0.002362 0.0 0.0 1.0 1001 50000
P.resid[2] 0.4588 0.4983 0.002278 0.0 0.0 1.0 1001 50000
P.resid[3] 0.9992 0.02756 1.26E-4 1.0 1.0 1.0 1001 50000
P.resid[4] 0.6535 0.4759 0.002147 0.0 1.0 1.0 1001 50000
P.resid[5] 0.3198 0.4664 0.002236 0.0 0.0 1.0 1001 50000
P.resid[6] 0.4475 0.4972 0.002138 0.0 0.0 1.0 1001 50000
P.resid[7] 0.4759 0.4994 0.002065 0.0 0.0 1.0 1001 50000
P.resid[8] 0.191 0.3931 0.00186 0.0 0.0 1.0 1001 50000
P.resid[9] 0.9505 0.217 9.948E-4 0.0 1.0 1.0 1001 50000
P.resid[10] 0.2958 0.4564 0.002058 0.0 0.0 1.0 1001 50000
P.resid[11] 0.3532 0.478 0.00224 0.0 0.0 1.0 1001 50000
P.resid[12] 0.4141 0.4926 0.002265 0.0 0.0 1.0 1001 50000
P.resid[13] 0.2377 0.4257 0.001863 0.0 0.0 1.0 1001 50000
P.resid[14] 0.6142 0.4868 0.002064 0.0 1.0 1.0 1001 50000
P.resid[15] 0.7484 0.434 0.001837 0.0 1.0 1.0 1001 50000
P.resid[16] 0.2805 0.4492 0.001844 0.0 0.0 1.0 1001 50000
P.resid[17] 0.2894 0.4535 0.002019 0.0 0.0 1.0 1001 50000
P.resid[18] 0.3193 0.4662 0.001961 0.0 0.0 1.0 1001 50000
P.resid[19] 0.7902 0.4072 0.001819 0.0 1.0 1.0 1001 50000
P.resid[20] 0.4443 0.4969 0.002249 0.0 0.0 1.0 1001 50000
P.resid[21] 0.421 0.4937 0.002285 0.0 0.0 1.0 1001 50000
P.resid[22] 0.389 0.4875 0.002236 0.0 0.0 1.0 1001 50000
P.resid[23] 0.3519 0.4776 0.002093 0.0 0.0 1.0 1001 50000
P.resid[24] 0.5902 0.4918 0.002062 0.0 1.0 1.0 1001 50000
P.resid[25] 0.3999 0.4899 0.002165 0.0 0.0 1.0 1001 50000
P.resid[26] 0.198 0.3985 0.00176 0.0 0.0 1.0 1001 50000
P.resid[27] 0.4457 0.497 0.002451 0.0 0.0 1.0 1001 50000
P.resid[28] 0.6589 0.4741 0.002103 0.0 1.0 1.0 1001 50000
P.resid[29] 0.2439 0.4295 0.001919 0.0 0.0 1.0 1001 50000
P.resid[30] 0.2216 0.4153 0.001782 0.0 0.0 1.0 1001 50000
X2[1] 3.861 1.73 0.00791 1.963 3.367 8.467 1001 50000
X2[2] 4.484 2.547 0.0114 1.62 3.821 11.05 1001 50000
X2[3] 24.03 3.756 0.02262 17.39 23.78 32.16 1001 50000
X2[4] 6.135 2.363 0.01082 3.288 5.531 12.36 1001 50000
X2[5] 3.267 2.301 0.01115 0.8389 2.61 9.267 1001 50000
X2[6] 4.193 1.808 0.008305 2.188 3.683 9.055 1001 50000
X2[7] 4.424 1.799 0.008365 2.384 3.924 9.167 1001 50000
X2[8] 2.195 1.727 0.007285 0.5136 1.661 6.864 1001 50000
X2[9] 12.02 2.554 0.01316 8.158 11.63 18.15 1001 50000
X2[10] 3.059 1.902 0.01007 1.144 2.478 8.209 1001 50000
X2[11] 3.547 1.928 0.008393 1.528 2.977 8.706 1001 50000
X2[12] 3.964 1.873 0.00863 1.927 3.422 8.916 1001 50000
X2[13] 2.584 1.686 0.007174 0.8894 2.074 7.089 1001 50000
X2[14] 5.577 1.931 0.008528 3.252 5.092 10.63 1001 50000
X2[15] 7.282 2.582 0.01183 4.031 6.664 13.86 1001 50000
X2[16] 2.965 1.861 0.007617 1.061 2.407 7.924 1001 50000
X2[17] 3.019 1.875 0.008794 1.099 2.46 7.99 1001 50000
X2[18] 3.263 1.845 0.008046 1.331 2.716 8.158 1001 50000
X2[19] 7.542 1.937 0.009697 4.886 7.16 12.41 1001 50000
X2[20] 4.165 1.752 0.007779 2.204 3.673 8.827 1001 50000
X2[21] 3.978 1.767 0.007942 2.04 3.476 8.751 1001 50000
X2[22] 3.768 1.819 0.008523 1.82 3.238 8.653 1001 50000
X2[23] 3.468 1.8 0.007778 1.563 2.941 8.294 1001 50000
X2[24] 5.404 1.961 0.008565 3.063 4.889 10.54 1001 50000
X2[25] 4.054 2.772 0.01353 0.8602 3.352 11.04 1001 50000
X2[26] 2.273 1.751 0.007676 0.5643 1.738 6.951 1001 50000
X2[27] 4.285 2.177 0.01013 1.892 3.669 9.972 1001 50000
X2[28] 6.074 1.983 0.00909 3.621 5.592 11.25 1001 50000
X2[29] 2.674 1.863 0.008367 0.8385 2.11 7.65 1001 50000
X2[30] 2.473 1.706 0.0069 0.787 1.953 7.057 1001 50000