读取数据
summary(eba1977) ## city age pop cases ## Fredericia:6 40-54:4 Min. : 509.0 Min. : 2.000 ## Horsens :6 55-59:4 1st Qu.: 628.0 1st Qu.: 7.000 ## Kolding :6 60-64:4 Median : 791.0 Median :10.000 ## Vejle :6 65-69:4 Mean :1100.3 Mean : 9.333 ## 70-74:4 3rd Qu.: 954.8 3rd Qu.:11.000 ## 75+ :4 Max. :3142.0 Max. :15.000
普通 Poisson model
glm1 <- glm(formula = cases ~ age + city + offset(log(pop)), family = poisson(link = "log"), data = eba1977) summary(glm1) ## ## Call: ## glm(formula = cases ~ age + city + offset(log(pop)), family = poisson(link = "log"), ## data = eba1977) ## ## Deviance Residuals: ## Min 1Q Median 3Q Max ## -2.63573 -0.67296 -0.03436 0.37258 1.85267 ## ## Coefficients: ## Estimate Std. Error z value Pr(>|z|) ## (Intercept) -5.6321 0.2003 -28.125 < 2e-16 *** ## age55-59 1.1010 0.2483 4.434 9.23e-06 *** ## age60-64 1.5186 0.2316 6.556 5.53e-11 *** ## age65-69 1.7677 0.2294 7.704 1.31e-14 *** ## age70-74 1.8569 0.2353 7.891 3.00e-15 *** ## age75+ 1.4197 0.2503 5.672 1.41e-08 *** ## cityHorsens -0.3301 0.1815 -1.818 0.0690 . ## cityKolding -0.3715 0.1878 -1.978 0.0479 * ## cityVejle -0.2723 0.1879 -1.450 0.1472 ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## (Dispersion parameter for poisson family taken to be 1) ## ## Null deviance: 129.908 on 23 degrees of freedom ## Residual deviance: 23.447 on 15 degrees of freedom ## AIC: 137.84 ## ## Number of Fisher Scoring iterations: 5
Stan
数据
# 模型矩阵 modMat <- as.data.frame(model.matrix(glm1)) modMat$offset <- log(eba1977$pop) names(modMat) <- c("intercept", "age55_59", "age60_64", "age65_69", "age70_74", "age75plus", "cityHorsens", "cityKolding", "cityVejle", "offset") dat <- as.list(modMat) dat$y <- eba1977$cases dat$N <- nrow(modMat) dat$p <- ncol(modMat) - 1 ## Load Stan file fileName <- "./poisson.stan" stan_code <- readChar(fileName, file.info(fileName)$size) cat(stan_code) ## Run Stan resStan <- stan(model_code = stan_code, data = dat, chains = 3, iter = 3000, warmup = 500, thin = 10) ## ## TRANSLATING MODEL 'stan_code' FROM Stan CODE TO C++ CODE NOW. ## COMPILING THE C++ CODE FOR MODEL 'stan_code' NOW. ## In file included from file60814bc1cb78.cpp:8: ## In file included from /Library/Frameworks/R.framework/Versions/3.1/Resources/library/rstan/include//stansrc/stan/model/model_header.hpp:17: ## In file included from /Library/Frameworks/R.framework/Versions/3.1/Resources/library/rstan/include//stansrc/stan/agrad/rev.hpp:5: ## /Library/Frameworks/R.framework/Versions/3.1/Resources/library/rstan/include//stansrc/stan/agrad/rev/chainable.hpp:87:17: warning: 'static' function 'set_zero_all_adjoints' declared in header file should be declared 'static inline' [-Wunneeded-internal-declaration] ## static void set_zero_all_adjoints() { ## ^ ## In file included from file60814bc1cb78.cpp:8: ## In file included from /Library/Frameworks/R.framework/Versions/3.1/Resources/library/rstan/include//stansrc/stan/model/model_header.hpp:21: ## /Library/Frameworks/R.framework/Versions/3.1/Resources/library/rstan/include//stansrc/stan/io/dump.hpp:26:14: warning: function 'product' is not needed and will not be emitted [-Wunneeded-internal-declaration] ## size_t product(std::vector<size_t> dims) { ## ^ ## ## ## SAMPLING FOR MODEL 'stan_code' NOW (CHAIN 1). ## ## Iteration: 1 / 3000 [ 0%] (Warmup) ## Iteration: 300 / 3000 [ 10%] (Warmup) ## Iteration: 501 / 3000 [ 16%] (Sampling) ## Iteration: 800 / 3000 [ 26%] (Sampling) ## Iteration: 1100 / 3000 [ 36%] (Sampling) ## Iteration: 1400 / 3000 [ 46%] (Sampling) ## Iteration: 1700 / 3000 [ 56%] (Sampling) ## Iteration: 2000 / 3000 [ 66%] (Sampling) ## Iteration: 2300 / 3000 [ 76%] (Sampling) ## Iteration: 2600 / 3000 [ 86%] (Sampling) ## Iteration: 2900 / 3000 [ 96%] (Sampling) ## Iteration: 3000 / 3000 [100%] (Sampling) ## # Elapsed Time: 0.142295 seconds (Warm-up) ## # 0.543612 seconds (Sampling) ## # 0.685907 seconds (Total) ## ## ## SAMPLING FOR MODEL 'stan_code' NOW (CHAIN 2). ## ## Iteration: 1 / 3000 [ 0%] (Warmup) ## Iteration: 300 / 3000 [ 10%] (Warmup) ## Iteration: 501 / 3000 [ 16%] (Sampling) ## Iteration: 800 / 3000 [ 26%] (Sampling) ## Iteration: 1100 / 3000 [ 36%] (Sampling) ## Iteration: 1400 / 3000 [ 46%] (Sampling) ## Iteration: 1700 / 3000 [ 56%] (Sampling) ## Iteration: 2000 / 3000 [ 66%] (Sampling) ## Iteration: 2300 / 3000 [ 76%] (Sampling) ## Iteration: 2600 / 3000 [ 86%] (Sampling) ## Iteration: 2900 / 3000 [ 96%] (Sampling) ## Iteration: 3000 / 3000 [100%] (Sampling) ## # Elapsed Time: 0.13526 seconds (Warm-up) ## # 0.517139 seconds (Sampling) ## # 0.652399 seconds (Total) ## ## ## SAMPLING FOR MODEL 'stan_code' NOW (CHAIN 3). ## ## Iteration: 1 / 3000 [ 0%] (Warmup) ## Iteration: 300 / 3000 [ 10%] (Warmup) ## Iteration: 501 / 3000 [ 16%] (Sampling) ## Iteration: 800 / 3000 [ 26%] (Sampling) ## Iteration: 1100 / 3000 [ 36%] (Sampling) ## Iteration: 1400 / 3000 [ 46%] (Sampling) ## Iteration: 1700 / 3000 [ 56%] (Sampling) ## Iteration: 2000 / 3000 [ 66%] (Sampling) ## Iteration: 2300 / 3000 [ 76%] (Sampling) ## Iteration: 2600 / 3000 [ 86%] (Sampling) ## Iteration: 2900 / 3000 [ 96%] (Sampling) ## Iteration: 3000 / 3000 [100%] (Sampling) ## # Elapsed Time: 0.120931 seconds (Warm-up) ## # 0.509901 seconds (Sampling) ## # 0.630832 seconds (Total) ## 绘制路径图 traceplot(resStan, pars = c("beta"), inc_warmup = TRUE)
比较
## 频率 tableone::ShowRegTable(glm1, exp = FALSE) ## beta [confint] p ## (Intercept) -5.63 [-6.04, -5.26] <0.001 ## age55-59 1.10 [0.61, 1.59] <0.001 ## age60-64 1.52 [1.07, 1.98] <0.001 ## age65-69 1.77 [1.32, 2.22] <0.001 ## age70-74 1.86 [1.40, 2.32] <0.001 ## age75+ 1.42 [0.93, 1.91] <0.001 ## cityHorsens -0.33 [-0.69, 0.03] 0.069 ## cityKolding -0.37 [-0.74, -0.00] 0.048 ## cityVejle -0.27 [-0.64, 0.09] 0.147
## 贝叶斯 print(resStan, pars = c("beta")) ## Inference for Stan model: stan_code. ## 3 chains, each with iter=3000; warmup=500; thin=10; ## post-warmup draws per chain=250, total post-warmup draws=750. ## ## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat ## beta[1] -5.66 0.01 0.21 -6.13 -5.80 -5.64 -5.51 -5.29 655 1 ## beta[2] 1.11 0.01 0.25 0.60 0.95 1.11 1.28 1.60 750 1 ## beta[3] 1.53 0.01 0.23 1.10 1.38 1.51 1.68 2.00 750 1 ## beta[4] 1.77 0.01 0.25 1.30 1.60 1.76 1.94 2.24 750 1 ## beta[5] 1.87 0.01 0.24 1.40 1.71 1.86 2.02 2.37 750 1 ## beta[6] 1.42 0.01 0.25 0.94 1.25 1.42 1.58 1.95 631 1 ## beta[7] -0.33 0.01 0.18 -0.69 -0.45 -0.32 -0.21 0.03 703 1 ## beta[8] -0.37 0.01 0.19 -0.74 -0.50 -0.38 -0.24 -0.01 664 1 ## beta[9] -0.28 0.01 0.19 -0.66 -0.40 -0.27 -0.15 0.09 698 1 ## ## Samples were drawn using NUTS(diag_e) at Mon Apr 13 21:43:02 2015. ## For each parameter, n_eff is a crude measure of effective sample size, ## and Rhat is the potential scale reduction factor on split chains (at ## convergence, Rhat=1).
