質問編集履歴
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test
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```R
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#### R2Winbugs Code for a Bayesian hierarchical test of the Geurts data.
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#### Do children with ADHD perform worse on the Wisconsin Card Sorting Task
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#### than children who develop typically (i.e., normal controls)?
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bugsdir <- "C:/Program Files/WinBUGS14"
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### Geurts data:
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# Normal Controls:
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num.errors <- c(15,10, 61,11, 60, 44, 63, 70, 57,11, 67, 21, 89,12, 63, 11, 96,10, 37,19, 44,18, 78, 27, 60,14)
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nc <- c(89,74,128,87,128,121,128,128,128,78,128,106,128,83,128,100,128,73,128,86,128,86,128,100,128,79)
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kc <- nc - num.errors
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nsc <- length(kc)
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# ADHD:
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num.errors <- c(88, 50, 58,17, 40, 18,21, 50, 21, 69,19, 29,11, 76, 46, 36, 37, 72,27, 92,13, 39, 53, 31, 49,
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57,17,10,12,21, 39, 43, 49,17, 39,13, 68, 24, 21,27, 48, 54, 41, 75, 38, 76,21, 41, 61,24, 28,21)
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na <- c(128,128,128,86,128,117,89,128,110,128,93,107,87,128,128,113,128,128,98,128,93,116,128,116,128,
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128,93,86,86,96,128,128,128,86,128,78,128,111,100,95,128,128,128,128,128,128,98,127,128,93,110,96)
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ka <- na - num.errors
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nsa <- length(ka)
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# two-sided p-value = .72
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t.test(kc/nc, ka/na, alternative = c("two.sided"), paired=F)
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data <- list("nc","kc","nsc","na","ka","nsa") # to be passed on to WinBUGS
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myinits <- list(
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list(mu = 0, sigma = 1, delta = 0),
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list(mu = -.8, sigma = 2, delta = -.5),
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list(mu = .8, sigma = 1.5, delta = .5))
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parameters <- c("delta")
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# The following command calls WinBUGS with specific options.
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# For a detailed description see Sturtz, Ligges, & Gelman (2005).
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samples <- bugs(data, inits=myinits, parameters,
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model.file ="Geurts.txt",
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n.chains=3, n.iter=100000, n.burnin=1000, n.thin=1,
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DIC=T, bugs.directory=bugsdir, #DIC=T or else error message
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codaPkg=F, debug=T)
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# Now the values for delta are in the "samples" object, ready for inspection.
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# Collect posterior samples across all chains:
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delta.posterior <- samples$sims.list$delta
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#============ Unrestricted analysis ===========================
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#============ BFs based on logspline fit ===========================
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library(polspline) # this package can be installed from within R
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fit.posterior <- logspline(delta.posterior)
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# 95% confidence interval:
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x0 <- qlogspline(0.025,fit.posterior)
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x1 <- qlogspline(0.975,fit.posterior)
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posterior <- dlogspline(0, fit.posterior) # this gives the pdf at point delta = 0
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prior <- dnorm(0) # height of order-restricted prior at delta = 0
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BF01 <- posterior/prior
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# BF01 = 3.96, BF10 = 0.25
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#####################################################################
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### Plot Prior and Posterior
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#####################################################################
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par(cex.main = 1.5, mar = c(5, 6, 4, 5) + 0.1, mgp = c(3.5, 1, 0), cex.lab = 1.5,
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font.lab = 2, cex.axis = 1.3, bty = "n", las=1)
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Nbreaks <- 80
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y <- hist(delta.posterior, Nbreaks, plot=F)
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plot(c(y$breaks, max(y$breaks)), c(0,y$density,0), type="S", lwd=2, lty=2,
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xlim=c(-3,3), ylim=c(0,2), xlab=" ", ylab="Density", axes=F)
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axis(1, at = c(-3,-2,-1,0,1,2,3), lab=c("-3","-2", "-1", "0", "1", "2", "3"))
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axis(2)
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mtext(expression(delta), side=1, line = 2.8, cex=2)
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#now bring in log spline density estimation:
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par(new=T)
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plot(fit.posterior, ylim=c(0,2), xlim=c(-3,3), lty=1, lwd=1, axes=F)
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points(0, dlogspline(0, fit.posterior),pch=19, cex=2)
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# plot the prior:
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par(new=T)
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plot ( function( x ) dnorm( x, 0, 1 ), -3, 3, xlim=c(-3,3), ylim=c(0,2), lwd=2, lty=1, ylab=" ", xlab = " ")
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points(0, dnorm(0), pch=19, cex=2)
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text(0.3, 1.5, labels = "Posterior", cex = 1.5, pos=4)
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text(1, 0.3, labels = "Prior", cex=1.5, pos=4)
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Geurts.txtは以下の内容です(これは自分で書きました).
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# Geurts
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model{
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for (i in 1:nsc){
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kc[i] ~ dbin(thetac[i], nc[i])
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thetac[i] <- phi(phic[i])
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phic[i] ~ dnorm(muc, lambda)
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}
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for (j in 1:nsa){
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ka[j] ~ dbin(thetaa[j], na[j])
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thetaa[j] <- phi(phia[j])
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phia[j] ~ dnorm(mua, lambda)
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}
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muc <- mu+alpha/2
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mua <- mu-alpha/2
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# Priors
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mu ~ dnorm(0,1)
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sigma ~ dunif(0,10)
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alpha <- delta*sigma
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lambda <- pow(sigma,-2)
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delta ~dnorm(0,1)
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# sampling from Prior Distribution for Delta
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deltaprior ~ dnorm(0,1)
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}
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