R2WinBUGS - 使用模拟数据进行逻辑回归

Question

我只是想知道是否有人有一些使用 R2WinBUGS 包来运行逻辑回归的 R 代码 - 理想情况下使用模拟数据来生成“真相”和两个连续协变量。

谢谢。

Christian

PS：

生成人工数据（一维情况）并通过 r2winbugs 运行 winbugs 的潜在代码（尚未工作）。

library(MASS)
library(R2WinBUGS)

setwd("d:/BayesianLogisticRegression")

n.site <- 150

X1<- sort(runif(n = n.site, min = -1, max =1))

xb <- 0.0 + 3.0*X1 

occ.prob <- 1/(1+exp(-xb))

plot(X1, occ.prob,xlab="X1",ylab="occ.prob")

true.presence <- rbinom(n = n.site, size = 1, prob = occ.prob)

plot(X1, true.presence,xlab="X1",ylab="true.presence")

# combine data as data frame and save
data <- data.frame(X1, true.presence)
write.matrix(data, file = "data.txt", sep = "\t")

sink("model.txt")
cat("
model {

# Priors
 alpha ~ dnorm(0,0.01)
 beta ~ dnorm(0,0.01)

# Likelihood
 for (i in 1:n) {
    C[i] ~ dbin(p[i], N)        # Note p before N
    logit(p[i]) <- alpha + beta *X1[i]
 }
}
",fill=TRUE)
sink()

# Bundle data
win.data <- list(mass = X1, n = length(X1))

# Inits function
inits <- function(){ list(alpha=rlnorm(1), beta=rlnorm(1))}

# Parameters to estimate
params <- c("alpha", "beta")

# MCMC settings
nc <- 3 #Number of Chains
ni <- 1200 #Number of draws from posterior
nb <- 200 #Number of draws to discard as burn-in
nt <- 2 Thinning rate

# Start Gibbs sampling
out <- bugs(data=win.data, inits=inits, parameters.to.save=params, 
model.file="model.txt", n.thin=nt, n.chains=nc, n.burnin=nb, 
n.iter=ni, debug = TRUE)

Answer 1

您的脚本正是这样做的方法。它几乎可以工作了，只需要进行一项简单的更改即可使其工作：

win.data <- list(X1 = X1, n = length(X1), C = true.presence, N = 1)

定义哪些数据进入 WinBugs。变量C必须填写true.presence，根据你生成的数据，N必须为1 - 注意，这是N = 1的二项式分布的特殊情况，称为伯努利 - 一个简单的“硬币翻转”。

这是输出：

> print(out, dig = 3)
Inference for Bugs model at "model.txt", fit using WinBUGS,
 3 chains, each with 1200 iterations (first 200 discarded), n.thin = 2
 n.sims = 1500 iterations saved
            mean    sd    2.5%     25%     50%     75%   97.5%  Rhat n.eff
alpha     -0.040 0.221  -0.465  -0.187  -0.037   0.114   0.390 1.001  1500
beta       3.177 0.478   2.302   2.845   3.159   3.481   4.165 1.000  1500
deviance 136.438 2.059 134.500 135.000 135.800 137.200 141.852 1.001  1500

如您所见，参数对应于用于生成数据的参数。另外，如果您与频率论解决方案进行比较，您会发现它是对应的。

编辑：但是典型的逻辑（~二项式）回归会用一些上限值 N[i] 来测量一些计数，并且它允许每个观察有不同的 N[i]。例如，青少年占总人口的比例（N）。这只需要在模型中向 N 添加索引：

C[i] ~ dbin(p[i], N[i])

数据生成将类似于：

N = rpois(n = n.site, lambda = 50) 
juveniles <- rbinom(n = n.site, size = N, prob = occ.prob)
win.data <- list(X1 = X1, n = length(X1), C = juveniles, N = N)

（编辑结束）

有关种群生态学的更多示例，请参阅 Marc Kéry 的书籍（生态学家的 WinBUGS 简介，特别是使用贝叶斯人口分析WinBUGS：分层视角，这是一本很棒的书）。

我使用的完整脚本 - 此处列出了您的更正脚本（与最后的频率论解决方案进行比较）：

#library(MASS)
library(R2WinBUGS)

#setwd("d:/BayesianLogisticRegression")

n.site <- 150

X1<- sort(runif(n = n.site, min = -1, max =1))

xb <- 0.0 + 3.0*X1 

occ.prob <- 1/(1+exp(-xb)) # inverse logit

plot(X1, occ.prob,xlab="X1",ylab="occ.prob")

true.presence <- rbinom(n = n.site, size = 1, prob = occ.prob)

plot(X1, true.presence,xlab="X1",ylab="true.presence")

# combine data as data frame and save
data <- data.frame(X1, true.presence)
write.matrix(data, file = "data.txt", sep = "\t")

sink("tmp_bugs/model.txt")
cat("
model {

# Priors
 alpha ~ dnorm(0,0.01)
 beta ~ dnorm(0,0.01)

# Likelihood
 for (i in 1:n) {
    C[i] ~ dbin(p[i], N)        # Note p before N
    logit(p[i]) <- alpha + beta *X1[i]
 }
}
",fill=TRUE)
sink()

# Bundle data
win.data <- list(X1 = X1, n = length(X1), C = true.presence, N = 1)

# Inits function
inits <- function(){ list(alpha=rlnorm(1), beta=rlnorm(1))}

# Parameters to estimate
params <- c("alpha", "beta")

# MCMC settings
nc <- 3 #Number of Chains
ni <- 1200 #Number of draws from posterior
nb <- 200 #Number of draws to discard as burn-in
nt <- 2 #Thinning rate

# Start Gibbs sampling
out <- bugs(data=win.data, inits=inits, parameters.to.save=params, 
model.file="model.txt", n.thin=nt, n.chains=nc, n.burnin=nb, 
n.iter=ni, 
working.directory = paste(getwd(), "/tmp_bugs/", sep = ""),
debug = TRUE)

print(out, dig = 3)

# Frequentist approach for comparison
m1 = glm(true.presence ~ X1, family = binomial)
summary(m1)

# normally, you should do it this way, but the above also works:
#m2 = glm(cbind(true.presence, 1 - true.presence) ~ X1, family = binomial)