R語言stan泊松迴歸Poisson regression

原文連接：http://tecdat.cn/?p=6560

讀取數據

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

數據

## 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).
## 
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## #  Elapsed Time: 0.142295 seconds (Warm-up)
## #                0.543612 seconds (Sampling)
## #                0.685907 seconds (Total)
## 
## 
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## #  Elapsed Time: 0.13526 seconds (Warm-up)
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## 
## 
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## #  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)

​​

比較

## 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).

 

 

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