我正在研究使用组级预测变量拟合多级逻辑回归模型。我通过 R 使用 JAGS。当我用 runjags 和 R2Jags 包拟合模型时，我得到了不同的行为。
我已尝试编写一个可重现的示例来说明该问题。下面，我模拟二项式模型的数据，将数据索引为 8 个图和 2 个 block ，然后拟合多级逻辑回归以恢复成功概率(b1 和 b2) 在下面的代码中。滚动到底部以查看两次拟合的摘要。
我的问题是:
- 为什么这两个拟合的后验概率不同？我使用相同的数据、单一模型规范，并在每个之前设置随机数生成器。为什么后验概率的平均值不同，为什么 Rhat 值如此不同？
# -------------------------------------------------------------------
# Loading required packages
# -------------------------------------------------------------------
library(rjags)
library(R2jags)
library(MCMCvis)
包版本信息:
jags.version()
[1] ‘4.3.0’
R2jags_0.5-7 MCMCvis_0.13.5 rjags_4-10
# -------------------------------------------------------------------
# Simulate data
# -------------------------------------------------------------------
set.seed(10)
N.plots = 8
N.blocks = 2
trials=400
n = rep(100,trials)
N=length(n)
plotReps=N/N.plots
blockReps=N/N.blocks
# Block 1
b1<-rep(c(.25,.75,.9,.1),each=plotReps)-.05
# Block 2
b2<-rep(c(.25,.75,.9,.1),each=plotReps)+.05
y = rbinom(trials, 100, p = c(b1,b2))
# vectors indexing plots and blocks
plot = rep(1:8,each=plotReps)
block = rep(1:2,each=blockReps)
# pass data to list for JAGS
data = list(
y = y,
n = n,
N = length(n),
plot = plot,
block= block,
N.plots = N.plots,
N.blocks = N.blocks
)
# -------------------------------------------------------------------
# Code for JAGS model
# -------------------------------------------------------------------
modelString <- "model {
## Priors
# hyperpriors
mu.alpha ~ dnorm(0, 0.0001)
sigma.plot ~ dunif(0,100)
tau.plot <- 1 / sigma.plot^2
sigma.block ~ dunif(0,100)
tau.block <- 1 / sigma.block^2
# priors
for(i in 1:N.plots){
eps.plot[i]~dnorm(0,tau.plot)
}
for(i in 1:N.blocks){
eps.block[i]~dnorm(0,tau.block)
}
# Likelihood
for(i in 1:N){
logit(p[i]) <- mu.alpha + eps.plot[plot[i]] + eps.block[block[i]]
y[i] ~ dbin(p[i], n[i])
}
}"
# -------------------------------------------------------------------
# Initial values
# -------------------------------------------------------------------
# set inits for rjags
inits = list(list(mu.alpha = 0,sigma.plot=2,sigma.block=2),
list(mu.alpha = 0,sigma.plot=2,sigma.block=2),
list(mu.alpha = 0,sigma.plot=2,sigma.block=2))
# set inits function for R2jags
initsFun<-function(){list(
mu.alpha=0,
sigma.plot=2,
sigma.block=2
)}
# -------------------------------------------------------------------
# Set JAGS parameters and random seed
# -------------------------------------------------------------------
# scalars that specify the
# number of iterations in the chain for adaptation
# number of iterations for burn-in
# number of samples in the final chain
n.adapt = 500
n.update = 5000
n.iterations = 1000
n.thin = 1
parsToMonitor = c("mu.alpha","sigma.plot","sigma.block","eps.plot","eps.block")
# -------------------------------------------------------------------
# Call to JAGS via rjags
# -------------------------------------------------------------------
set.seed(2)
# tuning (n.adapt)
jm = jags.model(textConnection(modelString), data = data, inits = inits,
n.chains = length(inits), n.adapt = n.adapt)
# burn-in (n.update)
update(jm, n.iterations = n.update)
# chain (n.iter)
samples.rjags = coda.samples(jm, variable.names = c(parsToMonitor), n.iter = n.iterations, thin = n.thin)
# -------------------------------------------------------------------
# Call to JAGS via R2jags
# -------------------------------------------------------------------
set.seed(2)
samples.R2jags <-jags(data=data,inits=initsFun,parameters.to.save=parsToMonitor,model.file=textConnection(modelString),
n.thin=n.thin,n.chains=length(inits),n.burnin=n.adapt,n.iter=n.iterations,DIC=T)
# -------------------------------------------------------------------
# Summarize posteriors using MCMCvis
# -------------------------------------------------------------------
sum.rjags <- MCMCvis::MCMCsummary(samples.rjags,params=c("mu.alpha","eps.plot","sigma.plot","sigma.block","eps.block"))
sum.rjags
sum.R2jags2 <- MCMCvis::MCMCsummary(samples.R2jags,params=c("mu.alpha","eps.plot","sigma.plot","sigma.block","eps.block"))
sum.R2jags2
这是 rjags 拟合的输出:
mean sd 2.5% 50% 97.5% Rhat n.eff
mu.alpha 0.07858079 21.2186737 -48.99286669 -0.04046538 45.16440893 1.11 4063
eps.plot[1] -1.77570813 0.8605892 -3.45736942 -1.77762035 -0.02258692 1.00 2857
eps.plot[2] -0.37359614 0.8614370 -2.07913650 -0.37581522 1.36611635 1.00 2846
eps.plot[3] 0.43387001 0.8612820 -1.24273657 0.42332033 2.20253810 1.00 2833
eps.plot[4] 1.31279883 0.8615840 -0.38750596 1.31179143 3.06307745 1.00 2673
eps.plot[5] -1.34317034 0.8749558 -3.06843578 -1.34747145 0.44451006 1.00 2664
eps.plot[6] -0.40064738 0.8749104 -2.13233876 -0.41530587 1.37910977 1.00 2677
eps.plot[7] 0.36515253 0.8738092 -1.35364716 0.35784379 2.15597251 1.00 2692
eps.plot[8] 1.71826293 0.8765952 -0.01057452 1.70627507 3.50314147 1.00 2650
sigma.plot 1.67540914 0.6244529 0.88895789 1.53080631 3.27418094 1.01 741
sigma.block 19.54287007 26.1348353 0.14556791 6.68959552 93.21927035 1.22 94
eps.block[1] -0.55924545 21.2126905 -46.34099332 -0.24261169 48.81435107 1.11 4009
eps.block[2] 0.35658731 21.2177540 -44.65998407 0.25801739 49.31921639 1.11 4457
这是 R2jags 拟合的输出:
mean sd 2.5% 50% 97.5% Rhat n.eff
mu.alpha -0.09358847 19.9972601 -45.81215297 -0.03905447 47.32288503 1.04 1785
eps.plot[1] -1.70448172 0.8954054 -3.41749845 -1.70817566 0.08187877 1.00 1141
eps.plot[2] -0.30070570 0.8940527 -2.01982416 -0.30458798 1.46954632 1.00 1125
eps.plot[3] 0.50295713 0.8932038 -1.20985348 0.50458106 2.29271214 1.01 1156
eps.plot[4] 1.37862742 0.8950657 -0.34965321 1.37627777 3.19545411 1.01 1142
eps.plot[5] -1.40421696 0.8496819 -3.10743244 -1.41880218 0.25843323 1.01 1400
eps.plot[6] -0.45810643 0.8504694 -2.16755579 -0.47087931 1.20827684 1.01 1406
eps.plot[7] 0.30319019 0.8492508 -1.39045509 0.28668886 1.96325582 1.01 1500
eps.plot[8] 1.65474420 0.8500635 -0.03632306 1.63399429 3.29585024 1.01 1395
sigma.plot 1.66375532 0.6681285 0.88231891 1.49564854 3.45544415 1.04 304
sigma.block 20.64694333 23.0418085 0.41071589 11.10308188 85.56459886 1.09 78
eps.block[1] -0.45810120 19.9981027 -46.85060339 -0.33090743 46.27709625 1.04 1795
eps.block[2] 0.58896195 19.9552211 -46.39310677 0.28183123 46.57874408 1.04 1769
这是 2 次拟合的 mu.alpha 轨迹图。首先，从 rjags 适合:
其次，从 R2jags 拟合:
最佳答案
虽然部分问题与 mu.alpha 缺乏收敛性有关，但另一个问题是两个包如何确定从后验分布中收集的样本数量。此外，jags.model 之后的 update 调用应该是:
更新(jm，n.iter = n.update)
代替
更新(jm，n.iterations = n.update)
对于 rjags，您可以很容易地指定适应步骤、更新步骤和迭代步骤的数量。查看 samples.rjags 很明显，每个链的后验长度为 n.iterations，总共(在此示例中)3000 个样本( n.iterations * n.chains).相反，R2jags::jags 将对后验样本进行采样，次数等于 n.iter 参数减去 n.burnin 参数。因此，正如您指定的那样，您 1) 没有将 n.update 步骤包含在 R2jags::jags 中，并且 2) 仅对后验样本进行了总共 1500 次采样(每个链仅保留 500 个样本)，而 rjags 则保留 3000 次。
如果您想进行类似的老化并采样相同次数，您可以改为运行:
samples.R2jags <-jags(
data=data,
inits=inits,
parameters.to.save=parsToMonitor,
model.file=textConnection(modelString),
n.thin=n.thin,
n.chains=length(inits),
n.burnin=n.adapt + n.update ,
n.iter=n.iterations +n.update + n.adapt,
DIC=T
)
最后，R2jags默认加载了glm模块，而rjags则没有。这可能会导致一些差异，因为使用的采样器可能不同(至少在这种情况下，因为您正在安装 glm)。您可以在调用 jags.model 之前使用 rjags::load.module('glm') 调用加载 glm 模块。
虽然这与问题本身无关，但我会避免在每个循环的模型内的 for 循环中使用 i(如果迭代次数因人而异，请使用不同的字母)循环):
modelString <- "model {
## Priors
# hyperpriors
mu.alpha ~ dnorm(0, 0.0001)
sigma.plot ~ dunif(0,100)
tau.plot <- 1 / sigma.plot^2
sigma.block ~ dunif(0,100)
tau.block <- 1 / sigma.block^2
# priors
for(i in 1:N.plots){
eps.plot[i]~dnorm(0,tau.plot)
}
for(j in 1:N.blocks){
eps.block[j]~dnorm(0,tau.block)
}
# Likelihood
for(k in 1:N){
logit(p[k]) <- mu.alpha + eps.plot[plot[k]] + eps.block[block[k]]
y[k] ~ dbin(p[k], n[k])
}
}"
关于r - 为什么拟合 rjags 和 R2Jags 的模型输出不同？，我们在Stack Overflow上找到一个类似的问题： https://stackoverflow.com/questions/60305150/