原文链接：http://tecdat.cn/?p=6894

加载和格式化数据

rm(list=ls())   ls()  ## [1] "s" "Y"  dim(Y)  ## [1] 1106   31  dim(s)  ## [1] 1106    2  ns   <- nrow(Y)      plot(s,axes=FALSE,xlab="",ylab="",main="Monitor locations")

 abline(75,0,col=2)

 abline(75,0,col=2)

在JAGS中指定模型

Ozone_model <- "model{       # Likelihood          # Random effects     for(i in 1:ns){      alpha i] ~ dnorm(0, )     }     for(j in 1:nt){      gamma j] ~ dnorm(0, )     }       # Priors     mu   ~ dnorm(0,0.01)          # Output the parameters of interest     sigma2[1] <- 1/taue   ]      pct[1]    <- sigma2[1]/sum(sigma2[])        pct[2]    <- sigma2[2]/sum(sigma2[])        pct[3]    <- sigma2[3]/sum(sigma2[])         }"

模型

dat    <- list(Y=Y,ns=ns,nt=nt)  model1 <- jags.model(textConnection(Ozone_model),inits=init,data = dat, n.chains=1)  ## Compiling model graph  ##    Resolving undeclared variables  ##    Allocating nodes  ##    Graph Size: 69733  ##   ## Initializing model

   summary(samp)

##   ## Iterations = 10001:30000  ## Thinning interval = 1   ## Number of chains = 1   ## Sample size per chain = 20000   ##   ## 1. Empirical mean and standard deviation for each variable,  ##    plus standard error of the mean:  ##   ##                Mean       SD  Naive SE Time-series SE  ## gamma[1]   0.792641 0.646869 4.574e-03      3.521e-02  ## gamma[2]  -0.005295 0.640672 4.530e-03      3.552e-02  ## gamma[3]   1.637455 0.644532 4.558e-03      3.664e-02  ## gamma[4]  -0.193925 0.648253 4.584e-03      3.685e-02  ## gamma[5]  -3.486456 0.647315 4.577e-03      3.761e-02  ## gamma[6]  -3.208898 0.652157 4.611e-03      3.784e-02  ## gamma[7]  -4.598029 0.646555 4.572e-03      3.636e-02  ## gamma[8]  -1.152366 0.646559 4.572e-03      3.740e-02  ## gamma[9]   2.394293 0.646956 4.575e-03      3.715e-02  ## gamma[10]  0.487923 0.644625 4.558e-03      3.733e-02  ## gamma[11]  0.460761 0.644827 4.560e-03      3.636e-02  ## gamma[12]  0.833041 0.651137 4.604e-03      3.649e-02  ## gamma[13] -1.580735 0.651594 4.607e-03      3.672e-02  ## gamma[14] -1.585905 0.647296 4.577e-03      3.760e-02  ## gamma[15] -1.587356 0.647281 4.577e-03      3.744e-02  ## gamma[16] -2.748602 0.644203 4.555e-03      3.740e-02  ## gamma[17] -5.031267 0.647277 4.577e-03      3.710e-02  ## gamma[18] -4.176877 0.648933 4.589e-03      3.655e-02  ## gamma[19] -1.315643 0.648456 4.585e-03      3.730e-02  ## gamma[20]  1.023326 0.648118 4.583e-03      3.502e-02  ## gamma[21]  2.319419 0.652453 4.614e-03      3.625e-02  ## gamma[22]  4.252081 0.642283 4.542e-03      3.672e-02  ## gamma[23]  1.674201 0.648382 4.585e-03      3.726e-02  ## gamma[24]  3.226205 0.649139 4.590e-03      3.647e-02  ## gamma[25]  3.795414 0.650599 4.600e-03      3.717e-02  ## gamma[26]  5.847544 0.653161 4.619e-03      3.616e-02  ## gamma[27]  0.240722 0.651784 4.609e-03      3.609e-02  ## gamma[28] -0.792185 0.649085 4.590e-03      3.542e-02  ## gamma[29]  1.314577 0.648981 4.589e-03      3.578e-02  ## gamma[30]  2.312463 0.643270 4.549e-03      3.774e-02  ## gamma[31]  1.366669 0.645759 4.566e-03      3.719e-02  ## pct[1]     0.560401 0.011415 8.072e-05      8.779e-05  ## pct[2]     0.413958 0.011479 8.117e-05      9.040e-05  ## pct[3]     0.025641 0.007074 5.002e-05      9.037e-05  ## sigma[1]  12.948830 0.051492 3.641e-04      3.837e-04  ## sigma[2]  11.130828 0.250331 1.770e-03      1.933e-03  ## sigma[3]   2.746672 0.378729 2.678e-03      4.721e-03  ##   ## 2. Quantiles for each variable:  ##   ##               2.5%      25%       50%      75%    97.5%  ## gamma[1]  -0.49380  0.36017  0.791847  1.22949  2.05602  ## gamma[2]  -1.29551 -0.42523  0.001094  0.42257  1.22885  ## gamma[3]   0.37334  1.20738  1.636656  2.06665  2.89512  ## gamma[4]  -1.48133 -0.61898 -0.193318  0.23839  1.07346  ## gamma[5]  -4.77636 -3.91313 -3.479185 -3.05709 -2.23466  ## gamma[6]  -4.48775 -3.64108 -3.207367 -2.77563 -1.93379  ## gamma[7]  -5.87435 -5.02716 -4.594350 -4.16119 -3.34211  ## gamma[8]  -2.43738 -1.57860 -1.149767 -0.71914  0.10173  ## gamma[9]   1.10795  1.97121  2.394399  2.82109  3.66081  ## gamma[10] -0.78684  0.05873  0.484838  0.91732  1.75985  ## gamma[11] -0.81422  0.02778  0.465699  0.89415  1.72498  ## gamma[12] -0.45600  0.40278  0.841823  1.27229  2.09552  ## gamma[13] -2.90014 -2.00870 -1.575470 -1.14767 -0.32264  ## gamma[14] -2.87864 -2.01064 -1.581978 -1.14763 -0.35096  ## gamma[15] -2.86282 -2.01560 -1.583218 -1.15679 -0.32290  ## gamma[16] -4.02545 -3.17798 -2.743399 -2.31751 -1.49586  ## gamma[17] -6.31465 -5.46146 -5.026931 -4.59211 -3.79179  ## gamma[18] -5.46025 -4.60004 -4.176324 -3.74965 -2.91543  ## gamma[19] -2.60870 -1.74448 -1.305350 -0.88302 -0.06778  ## gamma[20] -0.26230  0.59741  1.024962  1.45275  2.28854  ## gamma[21]  1.03505  1.88831  2.319906  2.75294  3.60079  ## gamma[22]  2.98850  3.82871  4.256085  4.67533  5.52185  ## gamma[23]  0.38791  1.24198  1.677333  2.10926  2.93725  ## gamma[24]  1.95181  2.79313  3.226292  3.65460  4.51323  ## gamma[25]  2.53324  3.36055  3.793573  4.23512  5.06812  ## gamma[26]  4.57296  5.41174  5.848862  6.27689  7.15103  ## gamma[27] -1.03397 -0.18368  0.235404  0.67501  1.51956  ## gamma[28] -2.06357 -1.22295 -0.794349 -0.35386  0.46984  ## gamma[29]  0.02345  0.88405  1.316177  1.74737  2.57636  ## gamma[30]  1.04671  1.88275  2.317915  2.74095  3.57092

由此看来，空间位置和误差似乎是变异的最大来源，而且每日随机效应只起很小的作用。

绘制随机效果

 sum <- summary(samp)     names(sum)  ## [1] "statistics" "quantiles"  "start"      "end"        "thin"        ## [6] "nchain"     q <- sum$quantiles       R  <- Y-mean(Y,na.rm=TRUE)     boxplot(R,xlab="Data",ylab="Ozone (centered)",outline=FALSE,             main="Data versus posterior of the random effects")            legend("topright",c("Median","95% interval"),lty=1:2,col=2,bg=gray(1),inset=0.05)