R语言stan泊松回归Poisson regression

原文链接：http://tecdat.cn/?p=6560

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

## Model matrix  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) {  ##              ^  ## 2 warnings generated.  ##   ## 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)

## Show traceplot  traceplot(resStan, pars = c("beta"), inc_warmup = TRUE)

比较

## Frequentist  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

## Bayesian  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).