Processing data report for MHAMID station
Introduction
Data about pollution measured by this station has been provided by Prof Ouarzazi in 2013. It accounts for Co, NO2, Wind Speed, Temperature, PM10, SO2, Solar Radiation and Ozone hourly based.
This will try to forecast 24h ahead.
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## densityPlotLet’s load the data from the csv files
#
# if (file.exists("MHAMID.RData")) {
# load("MHAMID.RData")
# } else {
MHM<-read.csv(file="Mhamid_data.csv",sep=";",dec=",",
header=TRUE)
DMHM<-MHM[! is.na(as.Date(as.character(MHM[,1]))),
1:ncol(MHM)]
DMHM=DMHM[-as.numeric(which(apply(DMHM,1,function(x){return(sum(is.na(x)))}) > 0 )),]
newc<-paste(as.character(DMHM[,1]),
paste(DMHM[,2],":00:00",sep=""),sep= " ")
newd<-strptime(newc,"%d/%m/%y %H:%M:%S")
antes<-newd - 3600
NMHM<-DMHM[,-2]
NMHM[,1]<-as.data.frame(newd)
colnames(NMHM)=gsub('.Mhamid','',colnames(NMHM))
colnames(NMHM)[9]="WS"
colnames(NMHM)[10]="SR"
pNMHM=NMHM
pNMHM[,11]=as.numeric(format(NMHM$Date,"%H"))
colnames(pNMHM)[11]="Hour"
colnames(pNMHM)[5]="C_O3"
hourf=24
pNMHM[,12]=apply(NMHM,1,o3f,delta=hourf,ref=NMHM)
colnames(pNMHM)[12]="O3"
pNMHM=pNMHM[! is.na(pNMHM$O3),]
save(MHM,DMHM,NMHM,pNMHM,hourf,file="MHAMID.RData")
#}
rm(MHM)
NMHM=pNMHM
#
plt_pairs(NMHM[,-1],fich="./plots/MHM_pairs.pdf",pfile=TRUE)
## png
## 2# plt_pairs(pNMHM[,-1],fich="./plots/pMHM_pairs.pdf",pfile=TRUE) [,1] [,2]
Date "Min. :2009-06-01 01:00:00 " "1st Qu.:2009-12-26 13:00:00 "
CO "Min. :0.0000 " "1st Qu.:0.0300 "
HR "Min. : 8.00 " "1st Qu.:39.00 "
NO2 "Min. : 4.00 " "1st Qu.:12.00 "
C_O3 "Min. : 0.0 " "1st Qu.: 25.0 "
PM10 "Min. : 0.00 " "1st Qu.: 30.00 "
SO2 "Min. : 0.000 " "1st Qu.: 6.000 "
TC "Min. : 4.20 " "1st Qu.:15.20 "
WS "Min. :0.100 " "1st Qu.:0.700 "
SR "Min. : 0.00 " "1st Qu.: 0.00 "
Hour "Min. : 0.00 " "1st Qu.: 5.00 "
O3 "Min. : 0.00 " "1st Qu.: 25.00 "
[,3] [,4]
Date "Median :2010-04-05 20:00:00 " "Mean :2010-04-04 04:25:23 "
CO "Median :0.0500 " "Mean :0.1012 "
HR "Median :57.00 " "Mean :57.11 "
NO2 "Median :19.00 " "Mean :23.69 "
C_O3 "Median : 36.0 " "Mean : 43.5 "
PM10 "Median : 49.00 " "Mean : 60.96 "
SO2 "Median : 9.000 " "Mean : 9.503 "
TC "Median :19.40 " "Mean :20.53 "
WS "Median :1.100 " "Mean :1.229 "
SR "Median : 1.14 " "Mean : 197.05 "
Hour "Median :11.00 " "Mean :11.43 "
O3 "Median : 36.00 " "Mean : 43.49 "
[,5] [,6]
Date "3rd Qu.:2010-08-06 09:00:00 " "Max. :2010-11-27 23:00:00 "
CO "3rd Qu.:0.1000 " "Max. :4.0100 "
HR "3rd Qu.:75.00 " "Max. :99.00 "
NO2 "3rd Qu.:31.00 " "Max. :98.00 "
C_O3 "3rd Qu.: 54.0 " "Max. :236.0 "
PM10 "3rd Qu.: 74.00 " "Max. :4187.00 "
SO2 "3rd Qu.:11.000 " "Max. :46.000 "
TC "3rd Qu.:25.10 " "Max. :42.80 "
WS "3rd Qu.:1.600 " "Max. :7.600 "
SR "3rd Qu.: 371.40 " "Max. :1092.00 "
Hour "3rd Qu.:17.00 " "Max. :23.00 "
O3 "3rd Qu.: 54.00 " "Max. :270.00 " Numerical treatment will be performed by using the well known open source statistical environment R (http://www.r-project.org).
Processing
In order to compare with Prof Ouarzazi’s results (corr = 0.84) for a local based model O3 ~ remaining variables at the same period, we will use several technologies.
Basic methodology will be: * To apply cross correlation learning validation as it becomes more robust that the fixed approach 70%,15%,15% * To apply full validation to all dataset, after selecting the best model, as Prof Ouarzazi did. * The hourly based moted was selected as for learning what it is possible to do, even when \(O_3\) should be accounted by its maximum per day and/or the dosage by 8h periods, depending on the specific regulation. * Uncertainty about future predictors was removed as we were no predicting Ozone with any lag.
Linear approach as reference
A linear model is considered as reference, for comparison of results in order to evaluate the degree of linearity
#
print(xtable(as.data.frame(car::vif(lm(O3~.,data=NMHM[,-1])))),type="html")| car::vif(lm(O3 ~ ., data = NMHM[, -1])) | |
|---|---|
| CO | 1.72 |
| HR | 3.31 |
| NO2 | 1.49 |
| C_O3 | 1.43 |
| PM10 | 1.37 |
| SO2 | 1.14 |
| TC | 3.20 |
| WS | 1.21 |
| SR | 1.51 |
| Hour | 1.33 |
if (file.exists(paste("MHM_lm_",hourf,".RData",sep=""))) {
load(paste("MHM_lm_",hourf,".RData",sep=""))
} else {
rej=which(colnames(NMHM) %in% c("Date","SO2"))
M.lm=m_lin(NMHM[,-rej],vprd="O3",vexp=".",cv=10)
#
idx = sample(1:nrow(NMHM),floor(0.15*nrow(NMHM)),replace=FALSE)
NMHM.trn = NMHM[-idx,]
NMHM.tst = NMHM[idx,]
M.lmp=m_lin(NMHM.trn[,-rej],vprd="O3",vexp=".",cv=10)
c.lmp=plt_prd(NMHM.tst[,-1],11,ylb=expression(O[3] ~ LM ~ predicted),
fich="./plots/O3_LM_pt.pdf",M.lmp,pfile=FALSE)
# For the day
NMHM.trn_d = NMHM.trn[NMHM.trn$SR>0,]
NMHM.tst_d = NMHM.tst[NMHM.tst$SR>0,]
M.lmp_d=m_lin(NMHM.trn_d[,-rej],vprd="O3",vexp=".",cv=10)
c.lmp_d=plt_prd(NMHM.tst_d[,-1],11,ylb=expression(O[3] ~ LM ~ predicted),
fich="./plots/O3_LM_pt_d.pdf",M.lmp_d,pfile=FALSE)
# For the night
NMHM.trn_n = NMHM.trn[NMHM.trn$SR==0,]
NMHM.tst_n = NMHM.tst[NMHM.tst$SR==0,]
rej2=which(colnames(NMHM) %in% c("Date","SO2","SR"))
M.lmp_n=m_lin(NMHM.trn_n[,-rej2],vprd="O3",vexp=".",cv=10)
c.lmp_n=plt_prd(NMHM.tst_n[,-1],11,ylb=expression(O[3] ~ LM ~ predicted),
fich="./plots/O3_LM_pt_n.pdf",M.lmp_n,pfile=FALSE)
#
print(xtable(summary(M.lm[["model"]]$best.model)),type="html")
print(xtable(summary(M.lmp[["model"]]$best.model)),type="html")
print(xtable(summary(M.lmp_d[["model"]]$best.model)),type="html")
print(xtable(summary(M.lmp_n[["model"]]$best.model)),type="html")
#
r2=data.frame(r2=(summary(M.lm[["model"]]$best.model))$r.squared,
r2adj=(summary(M.lm[["model"]]$best.model))$adj.r.squared)
r2=rbind(r2,c((summary(M.lmp[["model"]]$best.model))$r.squared,
r2adj=(summary(M.lmp[["model"]]$best.model))$adj.r.squared))
r2=rbind(r2,c((summary(M.lmp_d[["model"]]$best.model))$r.squared,
r2adj=(summary(M.lmp_d[["model"]]$best.model))$adj.r.squared))
r2=rbind(r2,c((summary(M.lmp_n[["model"]]$best.model))$r.squared,
r2adj=(summary(M.lmp_n[["model"]]$best.model))$adj.r.squared))
rownames(r2)=c("M.lm","M.lmp","M.lmp_d","M.lmp_n")
print(xtable(r2),type="html")
#
cc=data.frame(Model=M.lm[["cc"]],Tst=0)
cc=rbind(cc,c(M.lmp[["cc"]],c.lmp))
cc=rbind(cc,c(M.lmp_d[["cc"]],c.lmp_d))
cc=rbind(cc,c(M.lmp_n[["cc"]],c.lmp_n))
rownames(cc)=c("M.lm","M.lmp","M.lmp_d","M.lmp_n")
print(xtable(cc),type="html")
#
cc.lm=cc
r2.lm=r2
rm(list=c("cc","r2"))
save(M.lm,M.lmp,M.lmp_d,M.lmp_n,NMHM,NMHM.trn,rej,rej2,
NMHM.tst,NMHM.trn_d,NMHM.trn_n,cc.lm,r2.lm,
NMHM.tst_d,NMHM.tst_n,file=paste("MHM_lm_",hourf,".RData",sep=""))
}tb1=M.lm[["model"]]$performances
table01=xtable(tb1)
print(table01,type="html")| dummyparameter | error | dispersion | |
|---|---|---|---|
| 1 | 0.00 | 180.27 | 19.35 |
plt(NMHM.trn,11,ylb=expression(O[3] ~ LM ~ predicted),
fich="./plots/O3_LM.pdf",model=M.lm,pfile=TRUE)
png 2
#
tb2=M.lmp[["model"]]$performances
table02=xtable(tb2)
print(table02,type="html")| dummyparameter | error | dispersion | |
|---|---|---|---|
| 1 | 0.00 | 176.53 | 16.05 |
plt(NMHM.trn,11,ylb=expression(O[3] ~ LM ~ predicted),
fich="./plots/O3_LM_p.pdf",model=M.lmp,pfile=TRUE)
png 2
plt_prd(NMHM.tst[,-1],11,ylb=expression(O[3] ~ LM ~ predicted),
fich="./plots/O3_LM_pt.pdf",M.lmp,pfile=TRUE)
[1] 0.8721071
#
tb3=M.lmp_d[["model"]]$performances
table03=xtable(tb3)
print(table03,type="html")| dummyparameter | error | dispersion | |
|---|---|---|---|
| 1 | 0.00 | 180.21 | 22.37 |
plt(NMHM.trn_d,11,ylb=expression(O[3] ~ LM ~ predicted),
fich="./plots/O3_LM_p_d.pdf",model=M.lmp_d,pfile=TRUE)
png 2
plt_prd(NMHM.tst_d[,-1],11,ylb=expression(O[3] ~ LM ~ predicted),
fich="./plots/O3_LM_pt_d.pdf",M.lmp_d,pfile=TRUE)
[1] 0.8864268
#
tb4=M.lmp_n[["model"]]$performances
table04=xtable(tb4)
print(table04,type="html")| dummyparameter | error | dispersion | |
|---|---|---|---|
| 1 | 0.00 | 164.48 | 23.92 |
plt(NMHM.trn_n,11,ylb=expression(O[3] ~ LM ~ predicted),
fich="./plots/O3_LM_p_n.pdf",model=M.lmp_n,pfile=TRUE)
png 2
plt_prd(NMHM.tst_n[,-1],11,ylb=expression(O[3] ~ LM ~ predicted),
fich="./plots/O3_LM_pt_n.pdf",M.lmp_n,pfile=TRUE)
[1] 0.8141526
#
print(xtable(cc.lm),type="html")| Model | Tst | |
|---|---|---|
| M.lm | 0.88 | 0.00 |
| M.lmp | 0.89 | 0.87 |
| M.lmp_d | 0.91 | 0.89 |
| M.lmp_n | 0.79 | 0.81 |
#The results found account for a correlation of 0.8843296. It will considered as a reference.
SVM approach
A wrapper for SVM based regressors is applied looking for best parameters of learning.
tb1=t(summary(M.svm[["model"]]$performances))
table01=xtable(tb1)
print(table01,type="html")| V1 | V2 | V3 | V4 | V5 | V6 | |
|---|---|---|---|---|---|---|
| ||||||
| ||||||
| ||||||
| dispersion | Min. :16.51 | 1st Qu.:17.71 | Median :18.12 | Mean :18.91 | 3rd Qu.:20.08 | Max. :22.89 |
plt(NMHM,11,ylb=expression(O[3] ~ SVM ~ predicted),
fich="./plots/O3_SVM.pdf",model=M.svm,pfile=TRUE)
png 2
#
tb2=t(summary(M.svmp[["model"]]$performances))
table02=xtable(tb2)
print(table02,type="html")| V1 | V2 | V3 | V4 | V5 | V6 | |
|---|---|---|---|---|---|---|
| ||||||
| ||||||
| ||||||
| dispersion | Min. :14.57 | 1st Qu.:14.99 | Median :16.13 | Mean :16.64 | 3rd Qu.:17.96 | Max. :19.92 |
plt(NMHM.trn,11,ylb=expression(O[3] ~ SVM ~ predicted),
fich="./plots/O3_SVM_p.pdf",model=M.svmp,pfile=TRUE)
png 2
plt_prd(NMHM.tst[,-1],11,ylb=expression(O[3] ~ SVM ~ predicted),
fich="./plots/O3_SVM_pt.pdf",M.svmp,pfile=TRUE)
[1] 0.8989905
#
tb3=t(summary(M.svmp_d[["model"]]$performances))
table03=xtable(tb3)
print(table03,type="html")| V1 | V2 | V3 | V4 | V5 | V6 | |
|---|---|---|---|---|---|---|
| ||||||
| ||||||
| ||||||
| dispersion | Min. :13.70 | 1st Qu.:14.21 | Median :14.55 | Mean :15.37 | 3rd Qu.:16.17 | Max. :18.96 |
plt(NMHM.trn_d,11,ylb=expression(O[3] ~ SVM ~ predicted),
fich="./plots/O3_SVM_p_d.pdf",model=M.svmp_d,pfile=TRUE)
png 2
plt_prd(NMHM.tst_d[,-1],11,ylb=expression(O[3] ~ SVM ~ predicted),
fich="./plots/O3_SVM_pt_d.pdf",M.svmp_d,pfile=TRUE)
[1] 0.9140482
#
tb4=t(summary(M.svmp_n[["model"]]$performances))
table04=xtable(tb4)
print(table04,type="html")| V1 | V2 | V3 | V4 | V5 | V6 | |
|---|---|---|---|---|---|---|
| ||||||
| ||||||
| ||||||
| dispersion | Min. :16.25 | 1st Qu.:18.08 | Median :19.95 | Mean :19.82 | 3rd Qu.:22.01 | Max. :23.42 |
plt(NMHM.trn_n,11,ylb=expression(O[3] ~ SVM ~ predicted),
fich="./plots/O3_SVM_p_n.pdf",model=M.svmp_n,pfile=TRUE)
png 2
plt_prd(NMHM.tst_n[,-1],11,ylb=expression(O[3] ~ SVM ~ predicted),
fich="./plots/O3_SVM_pt_n.pdf",M.svmp_n,pfile=TRUE)
[1] 0.8461495
#
print(xtable(cc.svm),type="html")| Model | Tst | |
|---|---|---|
| M.svm | 0.95 | 0.00 |
| M.svmp | 0.95 | 0.90 |
| M.svmp_d | 0.96 | 0.91 |
| M.svmp_n | 0.94 | 0.85 |
The results found account for a correlation of 0.9490801 which outperforms the initial proposal carried out by Prof. Ouarzazi.
RandomForest
Let’s test the randomForest technology.
| mtry | ntree | error | dispersion | |
|---|---|---|---|---|
| 1 | 2 | 300.00 | 137.73 | 12.31 |
| 2 | 3 | 300.00 | 133.33 | 10.73 |
| 3 | 4 | 300.00 | 133.55 | 9.78 |
| 4 | 5 | 300.00 | 134.57 | 9.18 |
| 5 | 6 | 300.00 | 136.09 | 8.78 |
| 6 | 2 | 500.00 | 136.70 | 12.35 |
| 7 | 3 | 500.00 | 133.37 | 10.98 |
| 8 | 4 | 500.00 | 133.68 | 9.78 |
| 9 | 5 | 500.00 | 134.91 | 9.79 |
| 10 | 6 | 500.00 | 136.27 | 9.07 |
| 11 | 2 | 700.00 | 136.80 | 12.51 |
| 12 | 3 | 700.00 | 133.31 | 11.04 |
| 13 | 4 | 700.00 | 133.50 | 9.95 |
| 14 | 5 | 700.00 | 134.28 | 9.51 |
| 15 | 6 | 700.00 | 136.11 | 9.15 |
| 16 | 2 | 900.00 | 136.91 | 12.67 |
| 17 | 3 | 900.00 | 133.19 | 10.59 |
| 18 | 4 | 900.00 | 133.37 | 9.95 |
| 19 | 5 | 900.00 | 134.19 | 9.53 |
| 20 | 6 | 900.00 | 135.70 | 8.79 |
png 2
| mtry | ntree | error | dispersion | |
|---|---|---|---|---|
| 1 | 2 | 300.00 | 138.82 | 12.38 |
| 2 | 3 | 300.00 | 134.82 | 11.41 |
| 3 | 4 | 300.00 | 135.27 | 11.03 |
| 4 | 5 | 300.00 | 136.52 | 11.53 |
| 5 | 6 | 300.00 | 137.37 | 10.76 |
| 6 | 2 | 500.00 | 138.98 | 12.23 |
| 7 | 3 | 500.00 | 134.39 | 11.79 |
| 8 | 4 | 500.00 | 134.72 | 11.64 |
| 9 | 5 | 500.00 | 136.04 | 10.99 |
| 10 | 6 | 500.00 | 137.83 | 11.23 |
| 11 | 2 | 700.00 | 138.76 | 12.79 |
| 12 | 3 | 700.00 | 135.36 | 11.77 |
| 13 | 4 | 700.00 | 135.09 | 10.94 |
| 14 | 5 | 700.00 | 135.87 | 11.15 |
| 15 | 6 | 700.00 | 137.46 | 11.24 |
| 16 | 2 | 900.00 | 138.90 | 12.75 |
| 17 | 3 | 900.00 | 134.62 | 11.42 |
| 18 | 4 | 900.00 | 134.84 | 10.91 |
| 19 | 5 | 900.00 | 135.62 | 11.07 |
| 20 | 6 | 900.00 | 136.94 | 11.20 |
png 2 
[1] 0.9116535
| mtry | ntree | error | dispersion | |
|---|---|---|---|---|
| 1 | 2 | 300.00 | 154.00 | 25.90 |
| 2 | 3 | 300.00 | 147.06 | 23.68 |
| 3 | 4 | 300.00 | 145.65 | 22.00 |
| 4 | 5 | 300.00 | 147.36 | 21.90 |
| 5 | 6 | 300.00 | 148.80 | 21.64 |
| 6 | 2 | 500.00 | 152.77 | 23.74 |
| 7 | 3 | 500.00 | 145.45 | 22.31 |
| 8 | 4 | 500.00 | 145.67 | 22.18 |
| 9 | 5 | 500.00 | 146.92 | 21.97 |
| 10 | 6 | 500.00 | 149.29 | 22.42 |
| 11 | 2 | 700.00 | 152.57 | 24.14 |
| 12 | 3 | 700.00 | 145.57 | 23.34 |
| 13 | 4 | 700.00 | 145.55 | 22.51 |
| 14 | 5 | 700.00 | 146.50 | 21.90 |
| 15 | 6 | 700.00 | 148.65 | 21.29 |
| 16 | 2 | 900.00 | 152.67 | 24.69 |
| 17 | 3 | 900.00 | 145.95 | 23.57 |
| 18 | 4 | 900.00 | 145.30 | 22.63 |
| 19 | 5 | 900.00 | 146.82 | 21.65 |
| 20 | 6 | 900.00 | 149.06 | 22.00 |
png 2 
[1] 0.9233124
| mtry | ntree | error | dispersion | |
|---|---|---|---|---|
| 1 | 2 | 300.00 | 130.69 | 19.73 |
| 2 | 3 | 300.00 | 128.96 | 18.70 |
| 3 | 4 | 300.00 | 128.80 | 18.33 |
| 4 | 5 | 300.00 | 130.05 | 18.03 |
| 5 | 6 | 300.00 | 129.96 | 18.18 |
| 6 | 2 | 500.00 | 129.76 | 19.21 |
| 7 | 3 | 500.00 | 127.92 | 18.71 |
| 8 | 4 | 500.00 | 128.19 | 18.04 |
| 9 | 5 | 500.00 | 129.75 | 17.93 |
| 10 | 6 | 500.00 | 130.71 | 17.87 |
| 11 | 2 | 700.00 | 130.01 | 19.62 |
| 12 | 3 | 700.00 | 128.07 | 18.24 |
| 13 | 4 | 700.00 | 128.01 | 18.20 |
| 14 | 5 | 700.00 | 129.28 | 17.81 |
| 15 | 6 | 700.00 | 130.89 | 18.16 |
| 16 | 2 | 900.00 | 129.83 | 19.72 |
| 17 | 3 | 900.00 | 127.96 | 18.45 |
| 18 | 4 | 900.00 | 128.15 | 18.14 |
| 19 | 5 | 900.00 | 129.69 | 18.34 |
| 20 | 6 | 900.00 | 130.60 | 18.03 |
png 2 
[1] 0.8656699
| Model | Tst | |
|---|---|---|
| M.rf | 0.99 | 0.00 |
| M.rfp | 0.98 | 0.91 |
| M.rfp_d | 0.99 | 0.92 |
| M.rfp_n | 0.97 | 0.87 |
The results found account for a correlation of 0.9851756.
FFNN: MLP
Let’s test backpropagation trained multilayer perceptron type neural network do their work.
tb1=M.mlp[["model"]]$performances
table01=xtable(tb1)
print(table01,type="html")| linout | size | maxit | decay | abstol | reltol | trace | rang | Var9 | skip | error | dispersion | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | TRUE | 4 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 178.60 | 15.85 |
| 2 | TRUE | 5 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 178.27 | 16.04 |
| 3 | TRUE | 6 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 179.90 | 14.54 |
| 4 | TRUE | 7 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 177.49 | 16.32 |
| 5 | TRUE | 8 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 178.47 | 15.71 |
| 6 | TRUE | 9 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 178.82 | 17.90 |
| 7 | TRUE | 10 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 177.28 | 16.25 |
| 8 | TRUE | 11 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 177.02 | 15.10 |
| 9 | TRUE | 12 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 177.16 | 15.65 |
| 10 | TRUE | 13 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 177.33 | 16.68 |
| 11 | TRUE | 14 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 176.42 | 15.52 |
| 12 | TRUE | 15 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 177.08 | 16.89 |
| 13 | TRUE | 16 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 174.85 | 14.84 |
| 14 | TRUE | 17 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 177.50 | 14.82 |
| 15 | TRUE | 18 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 174.97 | 13.07 |
| 16 | TRUE | 19 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 177.39 | 15.40 |
| 17 | TRUE | 20 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 176.30 | 14.74 |
plt(NMHM,11,ylb=expression(O[3] ~ MLP ~ predicted),
fich="./plots/O3_MLP.pdf",model=M.mlp,pfile=TRUE)## Loading required package: scales
##
## Attaching package: 'scales'
##
## The following object is masked from 'package:plotrix':
##
## rescale
##
## The following object is masked from 'package:kernlab':
##
## alpha
png 2
#
tb2=M.mlpp[["model"]]$performances
table02=xtable(tb2)
print(table02,type="html")| linout | size | maxit | decay | abstol | reltol | trace | rang | Var9 | skip | error | dispersion | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | TRUE | 4 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 174.58 | 14.87 |
| 2 | TRUE | 5 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 175.84 | 15.17 |
| 3 | TRUE | 6 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 176.16 | 14.51 |
| 4 | TRUE | 7 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 174.30 | 14.42 |
| 5 | TRUE | 8 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 174.43 | 14.94 |
| 6 | TRUE | 9 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 173.59 | 14.56 |
| 7 | TRUE | 10 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 173.34 | 15.31 |
| 8 | TRUE | 11 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 174.77 | 15.62 |
| 9 | TRUE | 12 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 173.18 | 13.83 |
| 10 | TRUE | 13 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 174.71 | 14.88 |
| 11 | TRUE | 14 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 174.17 | 13.34 |
| 12 | TRUE | 15 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 172.58 | 14.18 |
| 13 | TRUE | 16 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 173.29 | 15.52 |
| 14 | TRUE | 17 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 173.51 | 12.74 |
| 15 | TRUE | 18 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 172.54 | 14.10 |
| 16 | TRUE | 19 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 175.30 | 15.24 |
| 17 | TRUE | 20 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 173.92 | 15.88 |
plt(NMHM.trn,11,ylb=expression(O[3] ~ MLP ~ predicted),
fich="./plots/O3_MLP_p.pdf",model=M.mlpp,pfile=TRUE)
png 2
plt_prd(NMHM.tst[,-1],11,ylb=expression(O[3] ~ MLP ~ predicted),
fich="./plots/O3_MLP_pt.pdf",M.mlpp,pfile=TRUE)
[,1][1,] 0.8750303
#
tb3=M.mlpp_d[["model"]]$performances
table03=xtable(tb3)
print(table03,type="html")| linout | size | maxit | decay | abstol | reltol | trace | rang | Var9 | skip | error | dispersion | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | TRUE | 4 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 177.35 | 21.03 |
| 2 | TRUE | 5 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 178.17 | 23.83 |
| 3 | TRUE | 6 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 177.31 | 20.31 |
| 4 | TRUE | 7 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 178.89 | 20.24 |
| 5 | TRUE | 8 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 179.37 | 19.76 |
| 6 | TRUE | 9 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 176.03 | 20.23 |
| 7 | TRUE | 10 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 180.69 | 21.82 |
| 8 | TRUE | 11 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 180.27 | 20.02 |
| 9 | TRUE | 12 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 180.59 | 19.87 |
| 10 | TRUE | 13 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 178.46 | 19.68 |
| 11 | TRUE | 14 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 179.87 | 16.80 |
| 12 | TRUE | 15 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 178.64 | 22.18 |
| 13 | TRUE | 16 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 176.26 | 21.60 |
| 14 | TRUE | 17 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 182.02 | 20.85 |
| 15 | TRUE | 18 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 180.15 | 24.89 |
| 16 | TRUE | 19 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 180.04 | 16.83 |
| 17 | TRUE | 20 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 181.40 | 21.49 |
plt(NMHM.trn_d,11,ylb=expression(O[3] ~ MLP ~ predicted),
fich="./plots/O3_MLP_p_d.pdf",model=M.mlpp_d,pfile=TRUE)
png 2
plt_prd(NMHM.tst_d[,-1],11,ylb=expression(O[3] ~ MLP ~ predicted),
fich="./plots/O3_MLP_pt_d.pdf",M.mlpp_d,pfile=TRUE)
[,1][1,] 0.8887564
#
tb4=M.mlpp_n[["model"]]$performances
table04=xtable(tb4)
print(table04,type="html")| linout | size | maxit | decay | abstol | reltol | trace | rang | Var9 | skip | error | dispersion | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | TRUE | 4 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 164.17 | 19.77 |
| 2 | TRUE | 5 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 163.73 | 19.57 |
| 3 | TRUE | 6 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 164.93 | 17.92 |
| 4 | TRUE | 7 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 163.95 | 18.40 |
| 5 | TRUE | 8 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 163.65 | 21.63 |
| 6 | TRUE | 9 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 164.82 | 16.77 |
| 7 | TRUE | 10 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 164.99 | 19.95 |
| 8 | TRUE | 11 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 164.25 | 20.74 |
| 9 | TRUE | 12 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 160.89 | 15.95 |
| 10 | TRUE | 13 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 161.98 | 17.00 |
| 11 | TRUE | 14 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 162.29 | 19.32 |
| 12 | TRUE | 15 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 164.34 | 24.00 |
| 13 | TRUE | 16 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 161.72 | 18.97 |
| 14 | TRUE | 17 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 169.01 | 25.53 |
| 15 | TRUE | 18 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 165.33 | 23.34 |
| 16 | TRUE | 19 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 167.62 | 20.64 |
| 17 | TRUE | 20 | 50000.00 | 0.02 | 0.00 | 0.00 | FALSE | 0.00 | 7.00 | TRUE | 167.11 | 24.30 |
plt(NMHM.trn_n,11,ylb=expression(O[3] ~ MLP ~ predicted),
fich="./plots/O3_MLP_p_n.pdf",model=M.mlpp_n,pfile=TRUE)
png 2
plt_prd(NMHM.tst_n[,-1],11,ylb=expression(O[3] ~ MLP ~ predicted),
fich="./plots/O3_MLP_pt_n.pdf",M.mlpp_n,pfile=TRUE)
[,1][1,] 0.8072019
#
print(xtable(cc.mlp),type="html")| Model | Tst | |
|---|---|---|
| M.mlp | 0.89 | 0.00 |
| M.mlpp | 0.90 | 0.88 |
| M.mlpp_d | 0.91 | 0.89 |
| M.mlpp_n | 0.80 | 0.81 |
#The results found account for a correlation of 0.8864128.
CART solution
Now we will use classification and regression trees to have a look at their capabilities for this particular problem.
tb1=M.rpt[["model"]]$performances
table01=xtable(tb1)
print(table01,type="html")| method | cp | minsplit | error | dispersion | |
|---|---|---|---|---|---|
| 1 | anova | 0.01 | 3 | 200.65 | 18.85 |
| 2 | anova | 0.02 | 3 | 221.98 | 18.63 |
| 3 | anova | 0.03 | 3 | 245.00 | 18.23 |
| 4 | anova | 0.04 | 3 | 245.00 | 18.23 |
| 5 | anova | 0.05 | 3 | 245.00 | 18.23 |
| 6 | anova | 0.06 | 3 | 245.00 | 18.23 |
| 7 | anova | 0.07 | 3 | 245.00 | 18.23 |
| 8 | anova | 0.08 | 3 | 245.00 | 18.23 |
| 9 | anova | 0.09 | 3 | 302.03 | 29.84 |
| 10 | anova | 0.10 | 3 | 314.51 | 14.55 |
| 11 | anova | 0.01 | 4 | 200.65 | 18.85 |
| 12 | anova | 0.02 | 4 | 221.98 | 18.63 |
| 13 | anova | 0.03 | 4 | 245.00 | 18.23 |
| 14 | anova | 0.04 | 4 | 245.00 | 18.23 |
| 15 | anova | 0.05 | 4 | 245.00 | 18.23 |
| 16 | anova | 0.06 | 4 | 245.00 | 18.23 |
| 17 | anova | 0.07 | 4 | 245.00 | 18.23 |
| 18 | anova | 0.08 | 4 | 245.00 | 18.23 |
| 19 | anova | 0.09 | 4 | 302.03 | 29.84 |
| 20 | anova | 0.10 | 4 | 314.51 | 14.55 |
| 21 | anova | 0.01 | 5 | 200.65 | 18.85 |
| 22 | anova | 0.02 | 5 | 221.98 | 18.63 |
| 23 | anova | 0.03 | 5 | 245.00 | 18.23 |
| 24 | anova | 0.04 | 5 | 245.00 | 18.23 |
| 25 | anova | 0.05 | 5 | 245.00 | 18.23 |
| 26 | anova | 0.06 | 5 | 245.00 | 18.23 |
| 27 | anova | 0.07 | 5 | 245.00 | 18.23 |
| 28 | anova | 0.08 | 5 | 245.00 | 18.23 |
| 29 | anova | 0.09 | 5 | 302.03 | 29.84 |
| 30 | anova | 0.10 | 5 | 314.51 | 14.55 |
| 31 | anova | 0.01 | 6 | 200.65 | 18.85 |
| 32 | anova | 0.02 | 6 | 221.98 | 18.63 |
| 33 | anova | 0.03 | 6 | 245.00 | 18.23 |
| 34 | anova | 0.04 | 6 | 245.00 | 18.23 |
| 35 | anova | 0.05 | 6 | 245.00 | 18.23 |
| 36 | anova | 0.06 | 6 | 245.00 | 18.23 |
| 37 | anova | 0.07 | 6 | 245.00 | 18.23 |
| 38 | anova | 0.08 | 6 | 245.00 | 18.23 |
| 39 | anova | 0.09 | 6 | 302.03 | 29.84 |
| 40 | anova | 0.10 | 6 | 314.51 | 14.55 |
| 41 | anova | 0.01 | 7 | 200.65 | 18.85 |
| 42 | anova | 0.02 | 7 | 221.98 | 18.63 |
| 43 | anova | 0.03 | 7 | 245.00 | 18.23 |
| 44 | anova | 0.04 | 7 | 245.00 | 18.23 |
| 45 | anova | 0.05 | 7 | 245.00 | 18.23 |
| 46 | anova | 0.06 | 7 | 245.00 | 18.23 |
| 47 | anova | 0.07 | 7 | 245.00 | 18.23 |
| 48 | anova | 0.08 | 7 | 245.00 | 18.23 |
| 49 | anova | 0.09 | 7 | 302.03 | 29.84 |
| 50 | anova | 0.10 | 7 | 314.51 | 14.55 |
plt(NMHM,11,ylb=expression(O[3] ~ CART ~ predicted),
fich="./plots/O3_CRT.pdf",model=M.rpt,pfile=TRUE)
png 2
#
tb2=M.rptp[["model"]]$performances
table02=xtable(tb2)
print(table02,type="html")| method | cp | minsplit | error | dispersion | |
|---|---|---|---|---|---|
| 1 | anova | 0.01 | 3 | 202.85 | 23.14 |
| 2 | anova | 0.02 | 3 | 222.31 | 23.32 |
| 3 | anova | 0.03 | 3 | 241.92 | 25.16 |
| 4 | anova | 0.04 | 3 | 241.92 | 25.16 |
| 5 | anova | 0.05 | 3 | 241.92 | 25.16 |
| 6 | anova | 0.06 | 3 | 241.92 | 25.16 |
| 7 | anova | 0.07 | 3 | 241.92 | 25.16 |
| 8 | anova | 0.08 | 3 | 241.92 | 25.16 |
| 9 | anova | 0.09 | 3 | 302.26 | 37.82 |
| 10 | anova | 0.10 | 3 | 314.30 | 28.57 |
| 11 | anova | 0.01 | 4 | 202.85 | 23.14 |
| 12 | anova | 0.02 | 4 | 222.31 | 23.32 |
| 13 | anova | 0.03 | 4 | 241.92 | 25.16 |
| 14 | anova | 0.04 | 4 | 241.92 | 25.16 |
| 15 | anova | 0.05 | 4 | 241.92 | 25.16 |
| 16 | anova | 0.06 | 4 | 241.92 | 25.16 |
| 17 | anova | 0.07 | 4 | 241.92 | 25.16 |
| 18 | anova | 0.08 | 4 | 241.92 | 25.16 |
| 19 | anova | 0.09 | 4 | 302.26 | 37.82 |
| 20 | anova | 0.10 | 4 | 314.30 | 28.57 |
| 21 | anova | 0.01 | 5 | 202.85 | 23.14 |
| 22 | anova | 0.02 | 5 | 222.31 | 23.32 |
| 23 | anova | 0.03 | 5 | 241.92 | 25.16 |
| 24 | anova | 0.04 | 5 | 241.92 | 25.16 |
| 25 | anova | 0.05 | 5 | 241.92 | 25.16 |
| 26 | anova | 0.06 | 5 | 241.92 | 25.16 |
| 27 | anova | 0.07 | 5 | 241.92 | 25.16 |
| 28 | anova | 0.08 | 5 | 241.92 | 25.16 |
| 29 | anova | 0.09 | 5 | 302.26 | 37.82 |
| 30 | anova | 0.10 | 5 | 314.30 | 28.57 |
| 31 | anova | 0.01 | 6 | 202.85 | 23.14 |
| 32 | anova | 0.02 | 6 | 222.31 | 23.32 |
| 33 | anova | 0.03 | 6 | 241.92 | 25.16 |
| 34 | anova | 0.04 | 6 | 241.92 | 25.16 |
| 35 | anova | 0.05 | 6 | 241.92 | 25.16 |
| 36 | anova | 0.06 | 6 | 241.92 | 25.16 |
| 37 | anova | 0.07 | 6 | 241.92 | 25.16 |
| 38 | anova | 0.08 | 6 | 241.92 | 25.16 |
| 39 | anova | 0.09 | 6 | 302.26 | 37.82 |
| 40 | anova | 0.10 | 6 | 314.30 | 28.57 |
| 41 | anova | 0.01 | 7 | 202.85 | 23.14 |
| 42 | anova | 0.02 | 7 | 222.31 | 23.32 |
| 43 | anova | 0.03 | 7 | 241.92 | 25.16 |
| 44 | anova | 0.04 | 7 | 241.92 | 25.16 |
| 45 | anova | 0.05 | 7 | 241.92 | 25.16 |
| 46 | anova | 0.06 | 7 | 241.92 | 25.16 |
| 47 | anova | 0.07 | 7 | 241.92 | 25.16 |
| 48 | anova | 0.08 | 7 | 241.92 | 25.16 |
| 49 | anova | 0.09 | 7 | 302.26 | 37.82 |
| 50 | anova | 0.10 | 7 | 314.30 | 28.57 |
plt(NMHM.trn,11,ylb=expression(O[3] ~ CART ~ predicted),
fich="./plots/O3_CRT_p.pdf",model=M.rptp,pfile=TRUE)
png 2
plt_prd(NMHM.tst[,-1],11,ylb=expression(O[3] ~ CRT ~ predicted),
fich="./plots/O3_CRT_pt.pdf",M.rptp,pfile=TRUE)
[1] 0.8591158
#
tb3=M.rptp_d[["model"]]$performances
table03=xtable(tb3)
print(table03,type="html")| method | cp | minsplit | error | dispersion | |
|---|---|---|---|---|---|
| 1 | anova | 0.01 | 3 | 205.78 | 32.30 |
| 2 | anova | 0.02 | 3 | 249.56 | 32.69 |
| 3 | anova | 0.03 | 3 | 261.96 | 25.69 |
| 4 | anova | 0.04 | 3 | 261.96 | 25.69 |
| 5 | anova | 0.05 | 3 | 261.96 | 25.69 |
| 6 | anova | 0.06 | 3 | 261.96 | 25.69 |
| 7 | anova | 0.07 | 3 | 261.96 | 25.69 |
| 8 | anova | 0.08 | 3 | 261.96 | 25.69 |
| 9 | anova | 0.09 | 3 | 347.53 | 32.54 |
| 10 | anova | 0.10 | 3 | 347.53 | 32.54 |
| 11 | anova | 0.01 | 4 | 205.78 | 32.30 |
| 12 | anova | 0.02 | 4 | 249.56 | 32.69 |
| 13 | anova | 0.03 | 4 | 261.96 | 25.69 |
| 14 | anova | 0.04 | 4 | 261.96 | 25.69 |
| 15 | anova | 0.05 | 4 | 261.96 | 25.69 |
| 16 | anova | 0.06 | 4 | 261.96 | 25.69 |
| 17 | anova | 0.07 | 4 | 261.96 | 25.69 |
| 18 | anova | 0.08 | 4 | 261.96 | 25.69 |
| 19 | anova | 0.09 | 4 | 347.53 | 32.54 |
| 20 | anova | 0.10 | 4 | 347.53 | 32.54 |
| 21 | anova | 0.01 | 5 | 205.78 | 32.30 |
| 22 | anova | 0.02 | 5 | 249.56 | 32.69 |
| 23 | anova | 0.03 | 5 | 261.96 | 25.69 |
| 24 | anova | 0.04 | 5 | 261.96 | 25.69 |
| 25 | anova | 0.05 | 5 | 261.96 | 25.69 |
| 26 | anova | 0.06 | 5 | 261.96 | 25.69 |
| 27 | anova | 0.07 | 5 | 261.96 | 25.69 |
| 28 | anova | 0.08 | 5 | 261.96 | 25.69 |
| 29 | anova | 0.09 | 5 | 347.53 | 32.54 |
| 30 | anova | 0.10 | 5 | 347.53 | 32.54 |
| 31 | anova | 0.01 | 6 | 205.78 | 32.30 |
| 32 | anova | 0.02 | 6 | 249.56 | 32.69 |
| 33 | anova | 0.03 | 6 | 261.96 | 25.69 |
| 34 | anova | 0.04 | 6 | 261.96 | 25.69 |
| 35 | anova | 0.05 | 6 | 261.96 | 25.69 |
| 36 | anova | 0.06 | 6 | 261.96 | 25.69 |
| 37 | anova | 0.07 | 6 | 261.96 | 25.69 |
| 38 | anova | 0.08 | 6 | 261.96 | 25.69 |
| 39 | anova | 0.09 | 6 | 347.53 | 32.54 |
| 40 | anova | 0.10 | 6 | 347.53 | 32.54 |
| 41 | anova | 0.01 | 7 | 205.78 | 32.30 |
| 42 | anova | 0.02 | 7 | 249.56 | 32.69 |
| 43 | anova | 0.03 | 7 | 261.96 | 25.69 |
| 44 | anova | 0.04 | 7 | 261.96 | 25.69 |
| 45 | anova | 0.05 | 7 | 261.96 | 25.69 |
| 46 | anova | 0.06 | 7 | 261.96 | 25.69 |
| 47 | anova | 0.07 | 7 | 261.96 | 25.69 |
| 48 | anova | 0.08 | 7 | 261.96 | 25.69 |
| 49 | anova | 0.09 | 7 | 347.53 | 32.54 |
| 50 | anova | 0.10 | 7 | 347.53 | 32.54 |
plt(NMHM.trn_d,11,ylb=expression(O[3] ~ CART ~ predicted),
fich="./plots/O3_CRT_p_d.pdf",model=M.rptp_d,pfile=TRUE)
png 2
plt_prd(NMHM.tst_d[,-1],11,ylb=expression(O[3] ~ CART ~ predicted),
fich="./plots/O3_CRT_pt_d.pdf",M.rptp_d,pfile=TRUE)
[1] 0.8814218
#
tb4=M.rptp_n[["model"]]$performances
table04=xtable(tb4)
print(table04,type="html")| method | cp | minsplit | error | dispersion | |
|---|---|---|---|---|---|
| 1 | anova | 0.01 | 3 | 178.53 | 19.90 |
| 2 | anova | 0.02 | 3 | 185.87 | 20.95 |
| 3 | anova | 0.03 | 3 | 185.87 | 20.95 |
| 4 | anova | 0.04 | 3 | 185.87 | 20.95 |
| 5 | anova | 0.05 | 3 | 197.76 | 38.15 |
| 6 | anova | 0.06 | 3 | 207.53 | 34.97 |
| 7 | anova | 0.07 | 3 | 233.92 | 33.70 |
| 8 | anova | 0.08 | 3 | 233.92 | 33.70 |
| 9 | anova | 0.09 | 3 | 233.92 | 33.70 |
| 10 | anova | 0.10 | 3 | 233.92 | 33.70 |
| 11 | anova | 0.01 | 4 | 178.53 | 19.90 |
| 12 | anova | 0.02 | 4 | 185.87 | 20.95 |
| 13 | anova | 0.03 | 4 | 185.87 | 20.95 |
| 14 | anova | 0.04 | 4 | 185.87 | 20.95 |
| 15 | anova | 0.05 | 4 | 197.76 | 38.15 |
| 16 | anova | 0.06 | 4 | 207.53 | 34.97 |
| 17 | anova | 0.07 | 4 | 233.92 | 33.70 |
| 18 | anova | 0.08 | 4 | 233.92 | 33.70 |
| 19 | anova | 0.09 | 4 | 233.92 | 33.70 |
| 20 | anova | 0.10 | 4 | 233.92 | 33.70 |
| 21 | anova | 0.01 | 5 | 178.53 | 19.90 |
| 22 | anova | 0.02 | 5 | 185.87 | 20.95 |
| 23 | anova | 0.03 | 5 | 185.87 | 20.95 |
| 24 | anova | 0.04 | 5 | 185.87 | 20.95 |
| 25 | anova | 0.05 | 5 | 197.76 | 38.15 |
| 26 | anova | 0.06 | 5 | 207.53 | 34.97 |
| 27 | anova | 0.07 | 5 | 233.92 | 33.70 |
| 28 | anova | 0.08 | 5 | 233.92 | 33.70 |
| 29 | anova | 0.09 | 5 | 233.92 | 33.70 |
| 30 | anova | 0.10 | 5 | 233.92 | 33.70 |
| 31 | anova | 0.01 | 6 | 178.53 | 19.90 |
| 32 | anova | 0.02 | 6 | 185.87 | 20.95 |
| 33 | anova | 0.03 | 6 | 185.87 | 20.95 |
| 34 | anova | 0.04 | 6 | 185.87 | 20.95 |
| 35 | anova | 0.05 | 6 | 197.76 | 38.15 |
| 36 | anova | 0.06 | 6 | 207.53 | 34.97 |
| 37 | anova | 0.07 | 6 | 233.92 | 33.70 |
| 38 | anova | 0.08 | 6 | 233.92 | 33.70 |
| 39 | anova | 0.09 | 6 | 233.92 | 33.70 |
| 40 | anova | 0.10 | 6 | 233.92 | 33.70 |
| 41 | anova | 0.01 | 7 | 178.53 | 19.90 |
| 42 | anova | 0.02 | 7 | 185.87 | 20.95 |
| 43 | anova | 0.03 | 7 | 185.87 | 20.95 |
| 44 | anova | 0.04 | 7 | 185.87 | 20.95 |
| 45 | anova | 0.05 | 7 | 197.76 | 38.15 |
| 46 | anova | 0.06 | 7 | 207.53 | 34.97 |
| 47 | anova | 0.07 | 7 | 233.92 | 33.70 |
| 48 | anova | 0.08 | 7 | 233.92 | 33.70 |
| 49 | anova | 0.09 | 7 | 233.92 | 33.70 |
| 50 | anova | 0.10 | 7 | 233.92 | 33.70 |
plt(NMHM.trn_n,11,ylb=expression(O[3] ~ CART ~ predicted),
fich="./plots/O3_CRT_p_n.pdf",model=M.rptp_n,pfile=TRUE)
png 2
plt_prd(NMHM.tst_n[,-1],11,ylb=expression(O[3] ~ CART ~ predicted),
fich="./plots/O3_CRT_pt_n.pdf",M.rptp_n,pfile=TRUE)
[1] 0.7870983
#
print(xtable(cc.rpt),type="html")| Model | Tst | |
|---|---|---|
| M.rpt | 0.87 | 0.00 |
| M.rptp | 0.87 | 0.86 |
| M.rptp_d | 0.90 | 0.88 |
| M.rptp_n | 0.77 | 0.79 |
#The results found account for a correlation of 0.8709754.
Conclusions
After this short analysis we can conclude that:
| LM | SVM | RF | MLP | CART | |
|---|---|---|---|---|---|
| Full_Model | 0.88 | 0.95 | 0.99 | 0.89 | 0.87 |
| Partial_Model | 0.89 | 0.95 | 0.98 | 0.90 | 0.87 |
| Daily_P_Model | 0.91 | 0.96 | 0.99 | 0.91 | 0.90 |
| Nightly_P_Model | 0.79 | 0.94 | 0.97 | 0.80 | 0.77 |
| LM | SVM | RF | MLP | CART | |
|---|---|---|---|---|---|
| Partial_Model | 0.87 | 0.90 | 0.91 | 0.88 | 0.86 |
| Daily_P_Model | 0.89 | 0.91 | 0.92 | 0.89 | 0.88 |
| Nightly_P_Model | 0.81 | 0.85 | 0.87 | 0.81 | 0.79 |
From the figures, it is clear that RF produces some kind of understimation of higher values, probably because the data set is density imbalanced. Regarding this particular factor it exhibits a pretty nice performance the SVM technology.
In a global view we can conclude that the best fit was scored for 0.9097719 method with a corrlation factor of 0.9556527
Ensembles
Let’s see how it becomes the emsemble method