Predicting
The JAGS/RJAGS system has no predict() function that I know of. What I therefore did is adapt the model so during estimation of the parameters the predictions were made. Using this adapted model, two prediction steps were made.In step one predictions from the whole design space were combined. To keep the number of predictions at least somewhat limited, only a few levels were used for the continuous variables. This step was used to select the best region within the whole space. Step two focuses on the best region and provides more detailed predictions.
Step 1
After predicting from the whole experimental space, the mean and lower 5% limits of predicted times were plotted.It was decided to focus on the region top right. At least 2.7 for the lower 5% limit, and at least 3.7 for the mean time. The associated settings are summarized below.
PaperType WingLength BodyWidth BodyLength TapedBody
bond :72 Min. : 7.408 Min. :2.540 Min. : 3.810 No :114
regular1 :72 1st Qu.:12.065 1st Qu.:3.387 1st Qu.: 6.562 Yes: 54
construction:24 Median :12.065 Median :4.233 Median : 6.562
Mean :11.871 Mean :4.163 Mean : 6.955
3rd Qu.:12.065 3rd Qu.:5.080 3rd Qu.: 9.313
Max. :12.065 Max. :5.080 Max. :12.065
TapedWing PaperClip PaperClip2 Fold test Time
No : 68 No :84 No: 20 No:168 WH:168 Mode:logical
Yes:100 Yes:84 WH:148 NA's:168
RH: 0
Mean u95 l05
Min. :3.203 Min. :3.574 Min. :2.701
1st Qu.:3.327 1st Qu.:3.808 1st Qu.:2.776
Median :3.465 Median :3.975 Median :2.847
Mean :3.486 Mean :4.108 Mean :2.873
3rd Qu.:3.636 3rd Qu.:4.388 3rd Qu.:2.952
Max. :3.877 Max. :5.044 Max. :3.165
Phase 2
The second prediction only varied PaperType, BodyWidth, BodyLength and TapedWing. All others were set at their most occurring setting. As can be seen, there is a bit of a trade-off. It is possible to select the longest time, but that incurs some chance of a much lower time, because of model uncertainty. On the other hand, for a slightly lesser mean time, we can have the certainty.It is my choice to avoid the more uncertain region. Hence I will base my choice on the lower limit. Here we can see that there is a tradeoff. The bond paper needs a slightly longer BodyLength, while Regular paper can have a short BodyLength. BodyWidth should be maximized, but that is not a sensitive parameter.
For completeness, the mean prediction. This shows hardly any interaction. Hence the need for higher BodyLength in bond type paper is due to lack of experiments in this region. A few confirming final experiments seem to be in order. Within those, we could also include a low BodyWidth, since the models are unclear if this should be maximized or minimized.
Code used
Code for actual data are in previous post. This code starts after reading in those data.helis <- rbind(h1,h2)
helis$test <- factor(helis$test)
helis$PaperClip2 <- factor(ifelse(helis$PaperClip=='No','No',as.character(helis$test)),
levels=c('No','WH','RH'))
library(R2jags)
library(ggplot2)
helispred <- expand.grid(
PaperType=c('bond','regular1','construction'),
WingLength=seq(min(helis$WingLength),max(helis$WingLength),length.out=4),
BodyWidth=seq(min(helis$BodyWidth),max(helis$BodyWidth),length.out=4),
BodyLength=seq(min(helis$BodyLength),max(helis$BodyLength),length.out=4),
TapedBody=c('No','Yes'),
TapedWing=c('No','Yes'),
PaperClip=c('No','Yes'),
PaperClip2=c('No','WH','RH'),
Fold='No',
test='WH',
Time=NA)
helisboth <- rbind(helis,helispred)
#################################
datain <- list(
PaperType=c(2,1,3,1)[helisboth$PaperType],
WingLength=helisboth$WingLength,
BodyLength=helisboth$BodyLength,
BodyWidth=helisboth$BodyWidth,
PaperClip=c(1,2,3)[helisboth$PaperClip2],
TapedBody=c(0,1)[helisboth$TapedBody],
TapedWing=c(0,1)[helisboth$TapedWing],
test=c(1,2)[helisboth$test],
Time=helisboth$Time,
n=nrow(helis),
m=nrow(helispred))
parameters <- c('Mul','WL','BL','PT','BW','PC','TB','TW','StDev',
'WLBW','WLPC', 'WLWL',
'BLPT' ,'BLPC', 'BLBL',
'BWPC', 'BWBW', 'other','pred')
jmodel <- function() {
for (i in 1:(n+m)) {
premul[i] <- (test[i]==1)+Mul*(test[i]==2)
mu[i] <- premul[i] * (
WL*WingLength[i]+
BL*BodyLength[i] +
PT[PaperType[i]] +
BW*BodyWidth[i] +
PC[PaperClip[i]] +
TB*TapedBody[i]+
TW*TapedWing[i]+
WLBW*WingLength[i]*BodyWidth[i]+
WLPC[1]*WingLength[i]*(PaperClip[i]==2)+
WLPC[2]*WingLength[i]*(PaperClip[i]==3)+
BLPT[1]*BodyLength[i]*(PaperType[i]==2)+
BLPT[2]*BodyLength[i]*(PaperType[i]==3)+
BLPC[1]*BodyLength[i]*(PaperClip[i]==2)+
BLPC[2]*BodyLength[i]*(PaperClip[i]==3)+
BWPC[1]*BodyWidth[i]*(PaperClip[i]==2)+
BWPC[2]*BodyWidth[i]*(PaperClip[i]==3) +
WLWL*WingLength[i]*WingLength[i]+
BLBL*BodyLength[i]*BodyLength[i]+
BWBW*BodyWidth[i]*BodyWidth[i]
)
}
for (i in 1:n) {
Time[i] ~ dnorm(mu[i],tau[test[i]])
}
# residual[i] <- Time[i]-mu[i]
for (i in 1:2) {
tau[i] <- pow(StDev[i],-2)
StDev[i] ~dunif(0,3)
WLPC[i] ~dnorm(0,1)
BLPT[i] ~dnorm(0,1)
BLPC[i] ~dnorm(0,1)
BWPC[i] ~dnorm(0,1)
}
for (i in 1:3) {
PT[i] ~ dnorm(PTM,tauPT)
}
tauPT <- pow(sdPT,-2)
sdPT ~dunif(0,3)
PTM ~dnorm(0,0.01)
WL ~dnorm(0,0.01)
BL ~dnorm(0,0.01)
BW ~dnorm(0,0.01)
PC[1] <- 0
PC[2]~dnorm(0,0.01)
PC[3]~dnorm(0,0.01)
TB ~dnorm(0,0.01)
TW ~dnorm(0,0.01)
WLBW~dnorm(0,1)
WLTW~dnorm(0,1)
WLWL~dnorm(0,1)
BLBL~dnorm(0,1)
BWBW~dnorm(0,1)
other~dnorm(0,1)
Mul ~ dnorm(1,1) %_% I(0,2)
for (i in 1:m) {
pred[i] <- mu[i+n]
}
}
jj <- jags(model.file=jmodel,
data=datain,
parameters=parameters,
progress.bar='gui',
n.chain=5,
n.iter=4000,
inits=function() list(Mul=1.3,WL=0.15,BL=-.08,PT=rep(1,3),
PC=c(NA,0,0),TB=0,TW=0))
#jj
predmat <- jj$BUGSoutput$sims.matrix[,grep('pred',dimnames(jj$BUGSoutput$sims.matrix)[[2]],value=TRUE)]
helispred$Mean <- colMeans(predmat)
helispred$u95 <- apply(predmat,2,function(x) quantile(x,.95))
helispred$l05 <- apply(predmat,2,function(x) quantile(x,.05))
png('select1.png')
qplot(y=Mean,x=l05,data=helispred)
dev.off()
select <- helispred[helispred$Mean>3.2 & helispred$l05>2.7,]
summary(select)
########
helispred <- expand.grid(
PaperType=c('bond','regular1'),
WingLength=12.065,
BodyWidth=seq(2.5,5,length.out=11),
BodyLength=seq(3.8,12,length.out=11),
TapedBody=c('No'),
TapedWing=c('No','Yes'),
PaperClip='No',
PaperClip2=c('WH'),
Fold='No',
test='WH',
Time=NA)
helisboth <- rbind(helis,helispred)
datain <- list(
PaperType=c(2,1,3,1)[helisboth$PaperType],
WingLength=helisboth$WingLength,
BodyLength=helisboth$BodyLength,
BodyWidth=helisboth$BodyWidth,
PaperClip=c(1,2,3)[helisboth$PaperClip2],
TapedBody=c(0,1)[helisboth$TapedBody],
TapedWing=c(0,1)[helisboth$TapedWing],
test=c(1,2)[helisboth$test],
Time=helisboth$Time,
n=nrow(helis),
m=nrow(helispred))
jj <- jags(model.file=jmodel,
data=datain,
parameters=parameters,
progress.bar='gui',
n.chain=5,
n.iter=4000,
inits=function() list(Mul=1.3,WL=0.15,BL=-.08,PT=rep(1,3),
PC=c(NA,0,0),TB=0,TW=0))
#jj
predmat <- jj$BUGSoutput$sims.matrix[,grep('pred',dimnames(jj$BUGSoutput$sims.matrix)[[2]],value=TRUE)]
helispred$Mean <- colMeans(predmat)
helispred$u95 <- apply(predmat,2,function(x) quantile(x,.95))
helispred$l05 <- apply(predmat,2,function(x) quantile(x,.05))
#
png('select2.png')
qplot(y=Mean,x=l05,data=helispred)
dev.off()
png('l05.png')
v <- ggplot(helispred, aes(BodyLength, BodyWidth, z = l05))
v + stat_contour(aes(colour= ..level.. )) +
scale_colour_gradient(name='Time' )+
facet_grid(PaperType ~ TapedWing )+
ggtitle('Lower 95% predicion')
dev.off()
png('mean.png')
v <- ggplot(helispred, aes(BodyLength, BodyWidth, z = Mean))
v + stat_contour(aes(colour= ..level.. )) +
scale_colour_gradient(name='Time' )+
facet_grid(PaperType ~ TapedWing ) +
ggtitle('Mean prediction')
dev.off()
No comments:
Post a Comment