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)
