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 48h ahead.

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Let’s load the data from the csv files

#
  hourf=48
if (file.exists(paste("MHAMID_",hourf,".RData",sep=""))) {
   load(paste("MHAMID_",hourf,".RData",sep=""))
} 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$Date,"%H"))
  colnames(pNMHM)[11]="Hour"
  colnames(pNMHM)[5]="C_O3"
  pNMHM[,12]=apply(NMHM,1,o3f,delta=hourf,ref=NMHM)
  colnames(pNMHM)[12]="O3"
  pNMHM=pNMHM[! is.na(pNMHM$O3),]
  save(MHM,DMHM,NMHM,pNMHM,hourf,file=paste("MHAMID_",hourf,".RData",sep=""))
}
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 00:00:00  "
  CO  "Min.   :0.000  "               "1st Qu.:0.030  "              
  HR  "Min.   : 8.00  "               "1st Qu.:40.00  "              
 NO2  "Min.   : 4.00  "               "1st Qu.:12.00  "              
 C_O3 "Min.   :  0.00  "              "1st Qu.: 25.00  "             
 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 :2010-03-24 23:00:00  " "Mean   :2010-04-03 05:38:13  "
  CO  "Median :0.050  "               "Mean   :0.102  "              
  HR  "Median :58.00  "               "Mean   :57.41  "              
 NO2  "Median :19.00  "               "Mean   :23.52  "              
 C_O3 "Median : 36.00  "              "Mean   : 43.32  "             
 PM10 "Median :  49.00  "             "Mean   :  60.59  "            
 SO2  "Median : 9.000  "              "Mean   : 9.565  "             
  TC  "Median :19.30  "               "Mean   :20.42  "              
  WS  "Median :1.100  "               "Mean   :1.231  "              
  SR  "Median :   0.65  "             "Mean   : 195.67  "            
 Hour "Median :11.00  "               "Mean   :11.42  "              
  O3  "Median : 36.00  "              "Mean   : 43.29  "             
      [,5]                            [,6]                           
 Date "3rd Qu.:2010-08-07 01:00:00  " "Max.   :2010-11-26 23:00:00  "
  CO  "3rd Qu.:0.100  "               "Max.   :4.010  "              
  HR  "3rd Qu.:75.00  "               "Max.   :99.00  "              
 NO2  "3rd Qu.:30.00  "               "Max.   :98.00  "              
 C_O3 "3rd Qu.: 53.00  "              "Max.   :236.00  "             
 PM10 "3rd Qu.:  73.00  "             "Max.   :1599.00  "            
 SO2  "3rd Qu.:11.000  "              "Max.   :46.000  "             
  TC  "3rd Qu.:24.90  "               "Max.   :43.90  "              
  WS  "3rd Qu.:1.600  "               "Max.   :7.600  "              
  SR  "3rd Qu.: 369.10  "             "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	1.88
HR	3.31
NO2	1.51
C_O3	1.44
PM10	1.63
SO2	1.15
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=""))
}

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	-7.6075	1.6330	-4.66	0.0000
CO	3.2618	1.2288	2.65	0.0080
HR	0.0965	0.0134	7.19	0.0000
NO2	0.0771	0.0131	5.87	0.0000
C_O3	0.8508	0.0070	121.42	0.0000
PM10	0.0201	0.0036	5.61	0.0000
TC	0.2957	0.0418	7.08	0.0000
WS	-1.8830	0.2606	-7.23	0.0000
SR	0.0058	0.0007	7.92	0.0000
Hour	0.0250	0.0273	0.92	0.3596

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	-8.4280	1.7721	-4.76	0.0000
CO	5.1560	1.3675	3.77	0.0002
HR	0.0973	0.0145	6.69	0.0000
NO2	0.0687	0.0143	4.82	0.0000
C_O3	0.8663	0.0075	114.89	0.0000
PM10	0.0196	0.0038	5.09	0.0000
TC	0.3127	0.0452	6.92	0.0000
WS	-1.8873	0.2809	-6.72	0.0000
SR	0.0058	0.0008	7.30	0.0000
Hour	0.0107	0.0296	0.36	0.7165

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	-19.7894	3.1894	-6.20	0.0000
CO	3.0262	2.9799	1.02	0.3099
HR	0.1871	0.0241	7.78	0.0000
NO2	0.0223	0.0205	1.09	0.2779
C_O3	0.9192	0.0097	94.68	0.0000
PM10	0.0179	0.0047	3.80	0.0001
TC	0.2375	0.0664	3.58	0.0004
WS	-1.4867	0.3914	-3.80	0.0001
SR	0.0059	0.0011	5.11	0.0000
Hour	0.5376	0.0935	5.75	0.0000

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	-6.5155	2.2363	-2.91	0.0036
CO	1.7822	1.6339	1.09	0.2755
HR	0.0866	0.0187	4.63	0.0000
NO2	0.1550	0.0202	7.67	0.0000
C_O3	0.7745	0.0123	62.93	0.0000
PM10	0.0274	0.0069	3.94	0.0001
TC	0.4258	0.0617	6.90	0.0000
WS	-3.0934	0.4273	-7.24	0.0000
Hour	-0.0757	0.0302	-2.50	0.0123

	r2	r2adj
M.lm	0.73	0.73
M.lmp	0.74	0.74
M.lmp_d	0.79	0.79
M.lmp_n	0.58	0.58

	Model	Tst
M.lm	0.86	0.00
M.lmp	0.86	0.82
M.lmp_d	0.89	0.86
M.lmp_n	0.76	0.71

tb1=M.lm[["model"]]$performances
table01=xtable(tb1)
print(table01,type="html")

	dummyparameter	error	dispersion
1	0.00	219.25	16.38

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	217.93	20.47

  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] 0.8242181

#
tb3=M.lmp_d[["model"]]$performances
table03=xtable(tb3)
print(table03,type="html")

	dummyparameter	error	dispersion
1	0.00	231.61	31.26

  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] 0.8625648

#
tb4=M.lmp_n[["model"]]$performances
table04=xtable(tb4)
print(table04,type="html")

	dummyparameter	error	dispersion
1	0.00	191.84	42.00

  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] 0.7119393

#
print(xtable(cc.lm),type="html")

	Model	Tst
M.lm	0.86	0.00
M.lmp	0.86	0.82
M.lmp_d	0.89	0.86
M.lmp_n	0.76	0.71

#

The results found account for a correlation of 0.8572399. It will considered as a reference.

SVM approach

A wrapper for SVM based regressors is applied looking for best parameters of learning.

## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 07:34:39 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> kernel </th> <th> cost </th> <th> eps </th> <th> gamma </th> <th> nu </th> <th> rhp </th> <th> nsv </th> <th> degree </th> <th> type </th>  </tr>
##   <tr> <td align="right"> 1 </td> <td align="right"> 2.00 </td> <td align="right"> 8.00 </td> <td align="right"> 0.10 </td> <td align="right"> 0.25 </td> <td align="right"> 0.50 </td> <td align="right"> -0.54 </td> <td align="right"> 5882 </td> <td align="right"> 3.00 </td> <td align="right"> 3.00 </td> </tr>
##    </table>
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 07:34:39 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> kernel </th> <th> cost </th> <th> eps </th> <th> gamma </th> <th> nu </th> <th> rhp </th> <th> nsv </th> <th> degree </th> <th> type </th>  </tr>
##   <tr> <td align="right"> 1 </td> <td align="right"> 2.00 </td> <td align="right"> 4.00 </td> <td align="right"> 0.10 </td> <td align="right"> 0.25 </td> <td align="right"> 0.50 </td> <td align="right"> -0.50 </td> <td align="right"> 5038 </td> <td align="right"> 3.00 </td> <td align="right"> 3.00 </td> </tr>
##    </table>
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 07:34:39 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> kernel </th> <th> cost </th> <th> eps </th> <th> gamma </th> <th> nu </th> <th> rhp </th> <th> nsv </th> <th> degree </th> <th> type </th>  </tr>
##   <tr> <td align="right"> 1 </td> <td align="right"> 2.00 </td> <td align="right"> 4.00 </td> <td align="right"> 0.10 </td> <td align="right"> 0.25 </td> <td align="right"> 0.50 </td> <td align="right"> -0.34 </td> <td align="right"> 2413 </td> <td align="right"> 3.00 </td> <td align="right"> 3.00 </td> </tr>
##    </table>
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 07:34:39 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> kernel </th> <th> cost </th> <th> eps </th> <th> gamma </th> <th> nu </th> <th> rhp </th> <th> nsv </th> <th> degree </th> <th> type </th>  </tr>
##   <tr> <td align="right"> 1 </td> <td align="right"> 2.00 </td> <td align="right"> 8.00 </td> <td align="right"> 0.10 </td> <td align="right"> 0.50 </td> <td align="right"> 0.50 </td> <td align="right"> -0.44 </td> <td align="right"> 2689 </td> <td align="right"> 3.00 </td> <td align="right"> 3.00 </td> </tr>
##    </table>
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 07:34:39 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> r2 </th> <th> r2adj </th>  </tr>
##   <tr> <td align="right"> M.svm </td> <td align="right"> 0.89 </td> <td align="right"> 0.89 </td> </tr>
##   <tr> <td align="right"> M.svmp </td> <td align="right"> 0.88 </td> <td align="right"> 0.88 </td> </tr>
##   <tr> <td align="right"> M.svmp_d </td> <td align="right"> 0.92 </td> <td align="right"> 0.92 </td> </tr>
##   <tr> <td align="right"> M.svmp_n </td> <td align="right"> 0.91 </td> <td align="right"> 0.91 </td> </tr>
##    </table>
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 07:34:39 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> Model </th> <th> Tst </th>  </tr>
##   <tr> <td align="right"> M.svm </td> <td align="right"> 0.94 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> M.svmp </td> <td align="right"> 0.94 </td> <td align="right"> 0.87 </td> </tr>
##   <tr> <td align="right"> M.svmp_d </td> <td align="right"> 0.96 </td> <td align="right"> 0.90 </td> </tr>
##   <tr> <td align="right"> M.svmp_n </td> <td align="right"> 0.96 </td> <td align="right"> 0.81 </td> </tr>
##    </table>

tb1=t(summary(M.svm[["model"]]$performances))
table01=xtable(tb1)
print(table01,type="html")

	V1	V2	V3	V4	V5	V6
gamma </td> <td> Min. :0.1250 </td> <td> 1st Qu.:0.1250 </td> <td> Median :0.2500 </td> <td> Mean :0.2917 </td> <td> 3rd Qu.:0.5000 </td> <td> Max. :0.5000 </td> </tr>
cost </td> <td> Min. :2.000 </td> <td> 1st Qu.:2.000 </td> <td> Median :4.000 </td> <td> Mean :4.667 </td> <td> 3rd Qu.:8.000 </td> <td> Max. :8.000 </td> </tr>
error </td> <td> Min. :159.8 </td> <td> 1st Qu.:163.0 </td> <td> Median :165.3 </td> <td> Mean :165.4 </td> <td> 3rd Qu.:166.3 </td> <td> Max. :173.5 </td> </tr>
dispersion	Min. :13.16	1st Qu.:13.57	Median :14.91	Mean :14.93	3rd Qu.:15.50	Max. :17.47

  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
gamma </td> <td> Min. :0.1250 </td> <td> 1st Qu.:0.1250 </td> <td> Median :0.2500 </td> <td> Mean :0.2917 </td> <td> 3rd Qu.:0.5000 </td> <td> Max. :0.5000 </td> </tr>
cost </td> <td> Min. :2.000 </td> <td> 1st Qu.:2.000 </td> <td> Median :4.000 </td> <td> Mean :4.667 </td> <td> 3rd Qu.:8.000 </td> <td> Max. :8.000 </td> </tr>
error </td> <td> Min. :162.7 </td> <td> 1st Qu.:166.3 </td> <td> Median :169.5 </td> <td> Mean :169.4 </td> <td> 3rd Qu.:173.1 </td> <td> Max. :175.9 </td> </tr>
dispersion	Min. :11.64	1st Qu.:13.56	Median :15.13	Mean :15.49	3rd Qu.:16.43	Max. :20.38

  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] 0.8719688

#
tb3=t(summary(M.svmp_d[["model"]]$performances))
table03=xtable(tb3)
print(table03,type="html")

	V1	V2	V3	V4	V5	V6
gamma </td> <td> Min. :0.1250 </td> <td> 1st Qu.:0.1250 </td> <td> Median :0.2500 </td> <td> Mean :0.2917 </td> <td> 3rd Qu.:0.5000 </td> <td> Max. :0.5000 </td> </tr>
cost </td> <td> Min. :2.000 </td> <td> 1st Qu.:2.000 </td> <td> Median :4.000 </td> <td> Mean :4.667 </td> <td> 3rd Qu.:8.000 </td> <td> Max. :8.000 </td> </tr>
error </td> <td> Min. :175.9 </td> <td> 1st Qu.:179.3 </td> <td> Median :179.7 </td> <td> Mean :185.8 </td> <td> 3rd Qu.:195.5 </td> <td> Max. :205.5 </td> </tr>
dispersion	Min. :17.69	1st Qu.:19.33	Median :19.97	Mean :21.93	3rd Qu.:26.05	Max. :27.91

  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] 0.9028872

#
tb4=t(summary(M.svmp_n[["model"]]$performances))
table04=xtable(tb4)
print(table04,type="html")

	V1	V2	V3	V4	V5	V6
gamma </td> <td> Min. :0.1250 </td> <td> 1st Qu.:0.1250 </td> <td> Median :0.2500 </td> <td> Mean :0.2917 </td> <td> 3rd Qu.:0.5000 </td> <td> Max. :0.5000 </td> </tr>
cost </td> <td> Min. :2.000 </td> <td> 1st Qu.:2.000 </td> <td> Median :4.000 </td> <td> Mean :4.667 </td> <td> 3rd Qu.:8.000 </td> <td> Max. :8.000 </td> </tr>
error </td> <td> Min. :144.2 </td> <td> 1st Qu.:147.6 </td> <td> Median :151.0 </td> <td> Mean :152.6 </td> <td> 3rd Qu.:158.9 </td> <td> Max. :162.8 </td> </tr>
dispersion	Min. :29.42	1st Qu.:29.86	Median :30.64	Mean :30.82	3rd Qu.:32.01	Max. :32.62

  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] 0.8099317

#
print(xtable(cc.svm),type="html")

	Model	Tst
M.svm	0.94	0.00
M.svmp	0.94	0.87
M.svmp_d	0.96	0.90
M.svmp_n	0.96	0.81

The results found account for a correlation of 0.9449091 which outperforms the initial proposal carried out by Prof. Ouarzazi.

RandomForest

Let’s test the randomForest technology.

## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 12:59:25 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> %IncMSE </th> <th> IncNodePurity </th>  </tr>
##   <tr> <td align="right"> CO </td> <td align="right"> 57.03 </td> <td align="right"> 229172.28 </td> </tr>
##   <tr> <td align="right"> HR </td> <td align="right"> 133.74 </td> <td align="right"> 271488.63 </td> </tr>
##   <tr> <td align="right"> NO2 </td> <td align="right"> 94.59 </td> <td align="right"> 367136.01 </td> </tr>
##   <tr> <td align="right"> C_O3 </td> <td align="right"> 1021.33 </td> <td align="right"> 4090432.62 </td> </tr>
##   <tr> <td align="right"> PM10 </td> <td align="right"> 37.58 </td> <td align="right"> 224834.50 </td> </tr>
##   <tr> <td align="right"> TC </td> <td align="right"> 131.32 </td> <td align="right"> 378995.90 </td> </tr>
##   <tr> <td align="right"> WS </td> <td align="right"> 20.67 </td> <td align="right"> 157950.16 </td> </tr>
##   <tr> <td align="right"> SR </td> <td align="right"> 103.38 </td> <td align="right"> 523152.17 </td> </tr>
##   <tr> <td align="right"> Hour </td> <td align="right"> 117.01 </td> <td align="right"> 334947.28 </td> </tr>
##    </table>
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 12:59:25 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> %IncMSE </th> <th> IncNodePurity </th>  </tr>
##   <tr> <td align="right"> CO </td> <td align="right"> 56.62 </td> <td align="right"> 193342.88 </td> </tr>
##   <tr> <td align="right"> HR </td> <td align="right"> 125.76 </td> <td align="right"> 243566.46 </td> </tr>
##   <tr> <td align="right"> NO2 </td> <td align="right"> 95.58 </td> <td align="right"> 334385.66 </td> </tr>
##   <tr> <td align="right"> C_O3 </td> <td align="right"> 1045.73 </td> <td align="right"> 3536722.84 </td> </tr>
##   <tr> <td align="right"> PM10 </td> <td align="right"> 35.86 </td> <td align="right"> 185906.68 </td> </tr>
##   <tr> <td align="right"> TC </td> <td align="right"> 128.10 </td> <td align="right"> 335533.71 </td> </tr>
##   <tr> <td align="right"> WS </td> <td align="right"> 18.67 </td> <td align="right"> 133251.26 </td> </tr>
##   <tr> <td align="right"> SR </td> <td align="right"> 100.75 </td> <td align="right"> 479583.70 </td> </tr>
##   <tr> <td align="right"> Hour </td> <td align="right"> 116.83 </td> <td align="right"> 304133.73 </td> </tr>
##    </table>
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 12:59:25 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> %IncMSE </th> <th> IncNodePurity </th>  </tr>
##   <tr> <td align="right"> CO </td> <td align="right"> 43.97 </td> <td align="right"> 111895.95 </td> </tr>
##   <tr> <td align="right"> HR </td> <td align="right"> 139.01 </td> <td align="right"> 151654.95 </td> </tr>
##   <tr> <td align="right"> NO2 </td> <td align="right"> 121.97 </td> <td align="right"> 241964.20 </td> </tr>
##   <tr> <td align="right"> C_O3 </td> <td align="right"> 1476.92 </td> <td align="right"> 2367957.40 </td> </tr>
##   <tr> <td align="right"> PM10 </td> <td align="right"> 33.74 </td> <td align="right"> 97727.43 </td> </tr>
##   <tr> <td align="right"> TC </td> <td align="right"> 109.62 </td> <td align="right"> 179191.81 </td> </tr>
##   <tr> <td align="right"> WS </td> <td align="right"> 21.40 </td> <td align="right"> 72493.98 </td> </tr>
##   <tr> <td align="right"> SR </td> <td align="right"> 96.46 </td> <td align="right"> 223458.28 </td> </tr>
##   <tr> <td align="right"> Hour </td> <td align="right"> 117.91 </td> <td align="right"> 241243.18 </td> </tr>
##    </table>
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 12:59:25 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> %IncMSE </th> <th> IncNodePurity </th>  </tr>
##   <tr> <td align="right"> CO </td> <td align="right"> 50.39 </td> <td align="right"> 81616.85 </td> </tr>
##   <tr> <td align="right"> HR </td> <td align="right"> 60.20 </td> <td align="right"> 88190.99 </td> </tr>
##   <tr> <td align="right"> NO2 </td> <td align="right"> 90.87 </td> <td align="right"> 140871.96 </td> </tr>
##   <tr> <td align="right"> C_O3 </td> <td align="right"> 527.45 </td> <td align="right"> 876222.74 </td> </tr>
##   <tr> <td align="right"> PM10 </td> <td align="right"> 40.11 </td> <td align="right"> 91241.72 </td> </tr>
##   <tr> <td align="right"> TC </td> <td align="right"> 91.88 </td> <td align="right"> 116270.38 </td> </tr>
##   <tr> <td align="right"> WS </td> <td align="right"> 19.25 </td> <td align="right"> 62142.00 </td> </tr>
##   <tr> <td align="right"> Hour </td> <td align="right"> 46.72 </td> <td align="right"> 65045.42 </td> </tr>
##    </table>
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 12:59:25 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> r2 </th> <th> r2adj </th>  </tr>
##   <tr> <td align="right"> M.rf </td> <td align="right"> 0.97 </td> <td align="right"> 0.97 </td> </tr>
##   <tr> <td align="right"> M.rfp </td> <td align="right"> 0.97 </td> <td align="right"> 0.97 </td> </tr>
##   <tr> <td align="right"> M.rfp_d </td> <td align="right"> 0.97 </td> <td align="right"> 0.97 </td> </tr>
##   <tr> <td align="right"> M.rfp_n </td> <td align="right"> 0.95 </td> <td align="right"> 0.95 </td> </tr>
##    </table>
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 12:59:25 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> Model </th> <th> Tst </th>  </tr>
##   <tr> <td align="right"> M.rf </td> <td align="right"> 0.98 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> M.rfp </td> <td align="right"> 0.98 </td> <td align="right"> 0.89 </td> </tr>
##   <tr> <td align="right"> M.rfp_d </td> <td align="right"> 0.99 </td> <td align="right"> 0.91 </td> </tr>
##   <tr> <td align="right"> M.rfp_n </td> <td align="right"> 0.98 </td> <td align="right"> 0.82 </td> </tr>
##    </table>

	mtry	ntree	error	dispersion
1	2	300.00	150.36	10.03
2	3	300.00	145.17	9.31
3	4	300.00	144.58	9.20
4	5	300.00	146.13	10.18
5	6	300.00	146.80	10.57
6	2	500.00	149.60	9.57
7	3	500.00	145.07	9.59
8	4	500.00	144.70	9.30
9	5	500.00	145.35	10.29
10	6	500.00	146.95	10.58
11	2	700.00	149.93	9.67
12	3	700.00	144.77	9.29
13	4	700.00	144.53	9.56
14	5	700.00	145.30	9.73
15	6	700.00	146.79	10.32
16	2	900.00	149.57	9.40
17	3	900.00	145.01	9.42
18	4	900.00	144.62	9.72
19	5	900.00	145.42	9.96
20	6	900.00	146.66	10.31

png 2

	mtry	ntree	error	dispersion
1	2	300.00	155.14	14.79
2	3	300.00	149.70	15.88
3	4	300.00	149.19	15.96
4	5	300.00	151.06	16.77
5	6	300.00	152.57	17.99
6	2	500.00	154.63	15.14
7	3	500.00	149.52	15.63
8	4	500.00	149.41	15.80
9	5	500.00	150.29	16.56
10	6	500.00	152.39	17.29
11	2	700.00	154.79	15.78
12	3	700.00	148.99	14.94
13	4	700.00	149.31	15.89
14	5	700.00	150.32	16.73
15	6	700.00	151.85	17.26
16	2	900.00	154.61	15.35
17	3	900.00	149.05	15.41
18	4	900.00	148.81	15.46
19	5	900.00	150.47	16.90
20	6	900.00	152.30	17.57

png 2 [1] 0.8881983

	mtry	ntree	error	dispersion
1	2	300.00	175.33	28.35
2	3	300.00	166.25	27.49
3	4	300.00	164.33	29.89
4	5	300.00	165.82	29.35
5	6	300.00	167.31	31.04
6	2	500.00	175.50	29.69
7	3	500.00	165.84	28.74
8	4	500.00	164.58	28.82
9	5	500.00	165.74	28.81
10	6	500.00	167.81	31.08
11	2	700.00	174.97	28.63
12	3	700.00	165.66	26.88
13	4	700.00	164.74	28.95
14	5	700.00	165.36	29.74
15	6	700.00	167.20	30.03
16	2	900.00	174.95	28.71
17	3	900.00	166.53	28.30
18	4	900.00	164.09	27.86
19	5	900.00	165.39	30.27
20	6	900.00	166.80	30.51

png 2 [1] 0.9115427

	mtry	ntree	error	dispersion
1	2	300.00	140.02	13.53
2	3	300.00	138.08	13.68
3	4	300.00	136.01	13.45
4	5	300.00	137.97	14.32
5	6	300.00	137.97	13.23
6	2	500.00	139.92	12.92
7	3	500.00	136.49	13.20
8	4	500.00	137.30	14.10
9	5	500.00	137.87	13.57
10	6	500.00	138.23	13.63
11	2	700.00	139.26	13.60
12	3	700.00	136.68	12.93
13	4	700.00	136.69	13.54
14	5	700.00	137.43	13.65
15	6	700.00	137.41	13.72
16	2	900.00	139.27	12.76
17	3	900.00	136.69	13.21
18	4	900.00	137.21	13.52
19	5	900.00	137.11	13.62
20	6	900.00	138.10	13.87

png 2 [1] 0.8158353

	Model	Tst
M.rf	0.98	0.00
M.rfp	0.98	0.89
M.rfp_d	0.99	0.91
M.rfp_n	0.98	0.82

The results found account for a correlation of 0.9849308.

FFNN: MLP

Let’s test backpropagation trained multilayer perceptron type neural network do their work.

## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 13:55:39 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> M.mlp[["model"]]$best.model$n </th>  </tr>
##   <tr> <td align="right"> 1 </td> <td align="right">   9 </td> </tr>
##   <tr> <td align="right"> 2 </td> <td align="right">  20 </td> </tr>
##   <tr> <td align="right"> 3 </td> <td align="right">   1 </td> </tr>
##    </table>
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 13:55:39 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> M.mlpp[["model"]]$best.model$n </th>  </tr>
##   <tr> <td align="right"> 1 </td> <td align="right">   9 </td> </tr>
##   <tr> <td align="right"> 2 </td> <td align="right">  20 </td> </tr>
##   <tr> <td align="right"> 3 </td> <td align="right">   1 </td> </tr>
##    </table>
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 13:55:39 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> M.mlpp_d[["model"]]$best.model$n </th>  </tr>
##   <tr> <td align="right"> 1 </td> <td align="right">   9 </td> </tr>
##   <tr> <td align="right"> 2 </td> <td align="right">   7 </td> </tr>
##   <tr> <td align="right"> 3 </td> <td align="right">   1 </td> </tr>
##    </table>
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 13:55:39 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> M.mlpp_n[["model"]]$best.model$n </th>  </tr>
##   <tr> <td align="right"> 1 </td> <td align="right">   8 </td> </tr>
##   <tr> <td align="right"> 2 </td> <td align="right">   6 </td> </tr>
##   <tr> <td align="right"> 3 </td> <td align="right">   1 </td> </tr>
##    </table>
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 13:55:39 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> r2 </th> <th> r2adj </th>  </tr>
##   <tr> <td align="right"> M.mlp </td> <td align="right"> 0.76 </td> <td align="right"> 0.76 </td> </tr>
##   <tr> <td align="right"> M.mlpp </td> <td align="right"> 0.76 </td> <td align="right"> 0.76 </td> </tr>
##   <tr> <td align="right"> M.mlpp_d </td> <td align="right"> 0.81 </td> <td align="right"> 0.81 </td> </tr>
##   <tr> <td align="right"> M.mlpp_n </td> <td align="right"> 0.61 </td> <td align="right"> 0.61 </td> </tr>
##    </table>
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 13:55:39 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> Model </th> <th> Tst </th>  </tr>
##   <tr> <td align="right"> M.mlp </td> <td align="right"> 0.87 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> M.mlpp </td> <td align="right"> 0.87 </td> <td align="right"> 0.83 </td> </tr>
##   <tr> <td align="right"> M.mlpp_d </td> <td align="right"> 0.90 </td> <td align="right"> 0.87 </td> </tr>
##   <tr> <td align="right"> M.mlpp_n </td> <td align="right"> 0.78 </td> <td align="right"> 0.71 </td> </tr>
##    </table>

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	216.57	11.33
2	TRUE	5	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	218.00	13.91
3	TRUE	6	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	217.75	14.70
4	TRUE	7	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	217.20	11.62
5	TRUE	8	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	214.80	13.95
6	TRUE	9	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	216.86	14.99
7	TRUE	10	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	214.67	11.83
8	TRUE	11	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	214.12	13.02
9	TRUE	12	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	212.56	11.02
10	TRUE	13	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	216.38	16.40
11	TRUE	14	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	214.21	16.30
12	TRUE	15	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	211.84	14.72
13	TRUE	16	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	214.56	13.80
14	TRUE	17	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	212.16	13.63
15	TRUE	18	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	214.29	12.25
16	TRUE	19	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	213.80	12.58
17	TRUE	20	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	209.43	15.63

  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	214.30	20.31
2	TRUE	5	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	213.79	19.43
3	TRUE	6	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	217.09	18.04
4	TRUE	7	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	216.47	21.43
5	TRUE	8	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	214.68	17.53
6	TRUE	9	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	215.47	22.63
7	TRUE	10	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	214.56	20.16
8	TRUE	11	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	213.87	17.59
9	TRUE	12	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	216.00	19.40
10	TRUE	13	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	213.23	18.96
11	TRUE	14	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	212.64	18.24
12	TRUE	15	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	214.81	19.55
13	TRUE	16	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	213.85	19.96
14	TRUE	17	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	215.60	21.36
15	TRUE	18	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	212.57	16.52
16	TRUE	19	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	214.74	19.82
17	TRUE	20	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	210.40	22.89

  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,] 0.8315941

#
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	226.34	28.45
2	TRUE	5	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	231.26	29.15
3	TRUE	6	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	231.00	33.93
4	TRUE	7	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	224.57	24.86
5	TRUE	8	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	225.00	30.45
6	TRUE	9	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	230.51	29.18
7	TRUE	10	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	228.48	30.54
8	TRUE	11	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	229.91	27.61
9	TRUE	12	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	224.84	27.82
10	TRUE	13	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	229.69	26.32
11	TRUE	14	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	229.44	22.64
12	TRUE	15	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	235.05	33.53
13	TRUE	16	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	229.95	31.85
14	TRUE	17	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	229.49	31.32
15	TRUE	18	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	226.67	31.52
16	TRUE	19	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	225.61	28.68
17	TRUE	20	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	228.80	29.88

  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,] 0.8666309

#
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	191.46	18.48
2	TRUE	5	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	190.72	20.75
3	TRUE	6	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	188.26	19.42
4	TRUE	7	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	192.25	20.39
5	TRUE	8	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	188.82	19.06
6	TRUE	9	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	193.21	21.39
7	TRUE	10	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	193.35	21.90
8	TRUE	11	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	193.26	25.22
9	TRUE	12	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	190.42	26.21
10	TRUE	13	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	195.78	16.96
11	TRUE	14	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	192.55	24.31
12	TRUE	15	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	191.25	27.31
13	TRUE	16	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	188.98	24.64
14	TRUE	17	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	192.78	24.03
15	TRUE	18	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	195.06	23.77
16	TRUE	19	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	190.44	21.26
17	TRUE	20	50000.00	0.02	0.00	0.00	FALSE	0.00	7.00	TRUE	193.56	26.52

  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,] 0.7132626

#
print(xtable(cc.mlp),type="html")

	Model	Tst
M.mlp	0.87	0.00
M.mlpp	0.87	0.83
M.mlpp_d	0.90	0.87
M.mlpp_n	0.78	0.71

#

The results found account for a correlation of 0.8703202.

CART solution

Now we will use classification and regression trees to have a look at their capabilities for this particular problem.

## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 13:57:10 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> CP </th> <th> nsplit </th> <th> rel error </th> <th> xerror </th> <th> xstd </th>  </tr>
##   <tr> <td align="right"> 1 </td> <td align="right"> 0.49 </td> <td align="right"> 0.00 </td> <td align="right"> 1.00 </td> <td align="right"> 1.00 </td> <td align="right"> 0.03 </td> </tr>
##   <tr> <td align="right"> 2 </td> <td align="right"> 0.12 </td> <td align="right"> 1.00 </td> <td align="right"> 0.51 </td> <td align="right"> 0.52 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 3 </td> <td align="right"> 0.06 </td> <td align="right"> 2.00 </td> <td align="right"> 0.40 </td> <td align="right"> 0.41 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 4 </td> <td align="right"> 0.04 </td> <td align="right"> 3.00 </td> <td align="right"> 0.34 </td> <td align="right"> 0.35 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 5 </td> <td align="right"> 0.02 </td> <td align="right"> 4.00 </td> <td align="right"> 0.30 </td> <td align="right"> 0.31 </td> <td align="right"> 0.01 </td> </tr>
##    </table>
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 13:57:10 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> CP </th> <th> nsplit </th> <th> rel error </th> <th> xerror </th> <th> xstd </th>  </tr>
##   <tr> <td align="right"> 1 </td> <td align="right"> 0.49 </td> <td align="right"> 0.00 </td> <td align="right"> 1.00 </td> <td align="right"> 1.00 </td> <td align="right"> 0.03 </td> </tr>
##   <tr> <td align="right"> 2 </td> <td align="right"> 0.12 </td> <td align="right"> 1.00 </td> <td align="right"> 0.51 </td> <td align="right"> 0.52 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 3 </td> <td align="right"> 0.06 </td> <td align="right"> 2.00 </td> <td align="right"> 0.39 </td> <td align="right"> 0.41 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 3.00 </td> <td align="right"> 0.33 </td> <td align="right"> 0.34 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 5 </td> <td align="right"> 0.02 </td> <td align="right"> 4.00 </td> <td align="right"> 0.31 </td> <td align="right"> 0.31 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 6 </td> <td align="right"> 0.01 </td> <td align="right"> 5.00 </td> <td align="right"> 0.29 </td> <td align="right"> 0.29 </td> <td align="right"> 0.01 </td> </tr>
##    </table>
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 13:57:10 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> CP </th> <th> nsplit </th> <th> rel error </th> <th> xerror </th> <th> xstd </th>  </tr>
##   <tr> <td align="right"> 1 </td> <td align="right"> 0.53 </td> <td align="right"> 0.00 </td> <td align="right"> 1.00 </td> <td align="right"> 1.00 </td> <td align="right"> 0.04 </td> </tr>
##   <tr> <td align="right"> 2 </td> <td align="right"> 0.11 </td> <td align="right"> 1.00 </td> <td align="right"> 0.47 </td> <td align="right"> 0.47 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 3 </td> <td align="right"> 0.08 </td> <td align="right"> 2.00 </td> <td align="right"> 0.36 </td> <td align="right"> 0.37 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 3.00 </td> <td align="right"> 0.28 </td> <td align="right"> 0.29 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 5 </td> <td align="right"> 0.01 </td> <td align="right"> 4.00 </td> <td align="right"> 0.26 </td> <td align="right"> 0.27 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 6 </td> <td align="right"> 0.01 </td> <td align="right"> 5.00 </td> <td align="right"> 0.25 </td> <td align="right"> 0.26 </td> <td align="right"> 0.01 </td> </tr>
##   <tr> <td align="right"> 7 </td> <td align="right"> 0.01 </td> <td align="right"> 6.00 </td> <td align="right"> 0.23 </td> <td align="right"> 0.24 </td> <td align="right"> 0.01 </td> </tr>
##    </table>
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 13:57:10 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> CP </th> <th> nsplit </th> <th> rel error </th> <th> xerror </th> <th> xstd </th>  </tr>
##   <tr> <td align="right"> 1 </td> <td align="right"> 0.44 </td> <td align="right"> 0.00 </td> <td align="right"> 1.00 </td> <td align="right"> 1.00 </td> <td align="right"> 0.04 </td> </tr>
##   <tr> <td align="right"> 2 </td> <td align="right"> 0.05 </td> <td align="right"> 1.00 </td> <td align="right"> 0.56 </td> <td align="right"> 0.56 </td> <td align="right"> 0.03 </td> </tr>
##   <tr> <td align="right"> 3 </td> <td align="right"> 0.05 </td> <td align="right"> 2.00 </td> <td align="right"> 0.50 </td> <td align="right"> 0.52 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 3.00 </td> <td align="right"> 0.45 </td> <td align="right"> 0.46 </td> <td align="right"> 0.02 </td> </tr>
##   <tr> <td align="right"> 5 </td> <td align="right"> 0.01 </td> <td align="right"> 4.00 </td> <td align="right"> 0.44 </td> <td align="right"> 0.46 </td> <td align="right"> 0.02 </td> </tr>
##    </table>
## <!-- html table generated in R 3.2.2 by xtable 1.8-0 package -->
## <!-- Mon Dec 28 13:57:10 2015 -->
## <table border=1>
## <tr> <th>  </th> <th> Model </th> <th> Tst </th>  </tr>
##   <tr> <td align="right"> M.rpt </td> <td align="right"> 0.84 </td> <td align="right"> 0.00 </td> </tr>
##   <tr> <td align="right"> M.rptp </td> <td align="right"> 0.84 </td> <td align="right"> 0.81 </td> </tr>
##   <tr> <td align="right"> M.rptp_d </td> <td align="right"> 0.88 </td> <td align="right"> 0.86 </td> </tr>
##   <tr> <td align="right"> M.rptp_n </td> <td align="right"> 0.75 </td> <td align="right"> 0.72 </td> </tr>
##    </table>

tb1=M.rpt[["model"]]$performances
table01=xtable(tb1)
print(table01,type="html")

	method	cp	minsplit	error	dispersion
1	anova	0.01	3	259.20	19.90
2	anova	0.02	3	258.75	18.79
3	anova	0.03	3	261.82	19.86
4	anova	0.04	3	285.48	22.94
5	anova	0.05	3	288.85	19.16
6	anova	0.06	3	295.95	22.55
7	anova	0.07	3	338.75	23.29
8	anova	0.08	3	338.75	23.29
9	anova	0.09	3	338.75	23.29
10	anova	0.10	3	338.75	23.29
11	anova	0.01	4	259.20	19.90
12	anova	0.02	4	258.75	18.79
13	anova	0.03	4	261.82	19.86
14	anova	0.04	4	285.48	22.94
15	anova	0.05	4	288.85	19.16
16	anova	0.06	4	295.95	22.55
17	anova	0.07	4	338.75	23.29
18	anova	0.08	4	338.75	23.29
19	anova	0.09	4	338.75	23.29
20	anova	0.10	4	338.75	23.29
21	anova	0.01	5	259.20	19.90
22	anova	0.02	5	258.75	18.79
23	anova	0.03	5	261.82	19.86
24	anova	0.04	5	285.48	22.94
25	anova	0.05	5	288.85	19.16
26	anova	0.06	5	295.95	22.55
27	anova	0.07	5	338.75	23.29
28	anova	0.08	5	338.75	23.29
29	anova	0.09	5	338.75	23.29
30	anova	0.10	5	338.75	23.29
31	anova	0.01	6	259.20	19.90
32	anova	0.02	6	258.75	18.79
33	anova	0.03	6	261.82	19.86
34	anova	0.04	6	285.48	22.94
35	anova	0.05	6	288.85	19.16
36	anova	0.06	6	295.95	22.55
37	anova	0.07	6	338.75	23.29
38	anova	0.08	6	338.75	23.29
39	anova	0.09	6	338.75	23.29
40	anova	0.10	6	338.75	23.29
41	anova	0.01	7	259.20	19.90
42	anova	0.02	7	258.75	18.79
43	anova	0.03	7	261.82	19.86
44	anova	0.04	7	285.48	22.94
45	anova	0.05	7	288.85	19.16
46	anova	0.06	7	295.95	22.55
47	anova	0.07	7	338.75	23.29
48	anova	0.08	7	338.75	23.29
49	anova	0.09	7	338.75	23.29
50	anova	0.10	7	338.75	23.29

  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	252.10	25.90
2	anova	0.02	3	265.57	28.53
3	anova	0.03	3	281.56	33.19
4	anova	0.04	3	290.55	28.73
5	anova	0.05	3	290.55	28.73
6	anova	0.06	3	309.88	29.80
7	anova	0.07	3	319.93	38.48
8	anova	0.08	3	344.57	28.70
9	anova	0.09	3	344.57	28.70
10	anova	0.10	3	360.58	58.11
11	anova	0.01	4	252.10	25.90
12	anova	0.02	4	265.57	28.53
13	anova	0.03	4	281.56	33.19
14	anova	0.04	4	290.55	28.73
15	anova	0.05	4	290.55	28.73
16	anova	0.06	4	309.88	29.80
17	anova	0.07	4	319.93	38.48
18	anova	0.08	4	344.57	28.70
19	anova	0.09	4	344.57	28.70
20	anova	0.10	4	360.58	58.11
21	anova	0.01	5	252.10	25.90
22	anova	0.02	5	265.57	28.53
23	anova	0.03	5	281.56	33.19
24	anova	0.04	5	290.55	28.73
25	anova	0.05	5	290.55	28.73
26	anova	0.06	5	309.88	29.80
27	anova	0.07	5	319.93	38.48
28	anova	0.08	5	344.57	28.70
29	anova	0.09	5	344.57	28.70
30	anova	0.10	5	360.58	58.11
31	anova	0.01	6	252.10	25.90
32	anova	0.02	6	265.57	28.53
33	anova	0.03	6	281.56	33.19
34	anova	0.04	6	290.55	28.73
35	anova	0.05	6	290.55	28.73
36	anova	0.06	6	309.88	29.80
37	anova	0.07	6	319.93	38.48
38	anova	0.08	6	344.57	28.70
39	anova	0.09	6	344.57	28.70
40	anova	0.10	6	360.58	58.11
41	anova	0.01	7	252.10	25.90
42	anova	0.02	7	265.57	28.53
43	anova	0.03	7	281.56	33.19
44	anova	0.04	7	290.55	28.73
45	anova	0.05	7	290.55	28.73
46	anova	0.06	7	309.88	29.80
47	anova	0.07	7	319.93	38.48
48	anova	0.08	7	344.57	28.70
49	anova	0.09	7	344.57	28.70
50	anova	0.10	7	360.58	58.11

  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] 0.8055746

#
tb3=M.rptp_d[["model"]]$performances
table03=xtable(tb3)
print(table03,type="html")

	method	cp	minsplit	error	dispersion
1	anova	0.01	3	264.15	22.73
2	anova	0.02	3	308.57	21.44
3	anova	0.03	3	309.47	23.79
4	anova	0.04	3	309.47	23.79
5	anova	0.05	3	309.47	23.79
6	anova	0.06	3	309.47	23.79
7	anova	0.07	3	309.47	23.79
8	anova	0.08	3	354.42	44.00
9	anova	0.09	3	395.93	26.39
10	anova	0.10	3	395.93	26.39
11	anova	0.01	4	264.15	22.73
12	anova	0.02	4	308.57	21.44
13	anova	0.03	4	309.47	23.79
14	anova	0.04	4	309.47	23.79
15	anova	0.05	4	309.47	23.79
16	anova	0.06	4	309.47	23.79
17	anova	0.07	4	309.47	23.79
18	anova	0.08	4	354.42	44.00
19	anova	0.09	4	395.93	26.39
20	anova	0.10	4	395.93	26.39
21	anova	0.01	5	264.15	22.73
22	anova	0.02	5	308.57	21.44
23	anova	0.03	5	309.47	23.79
24	anova	0.04	5	309.47	23.79
25	anova	0.05	5	309.47	23.79
26	anova	0.06	5	309.47	23.79
27	anova	0.07	5	309.47	23.79
28	anova	0.08	5	354.42	44.00
29	anova	0.09	5	395.93	26.39
30	anova	0.10	5	395.93	26.39
31	anova	0.01	6	264.15	22.73
32	anova	0.02	6	308.57	21.44
33	anova	0.03	6	309.47	23.79
34	anova	0.04	6	309.47	23.79
35	anova	0.05	6	309.47	23.79
36	anova	0.06	6	309.47	23.79
37	anova	0.07	6	309.47	23.79
38	anova	0.08	6	354.42	44.00
39	anova	0.09	6	395.93	26.39
40	anova	0.10	6	395.93	26.39
41	anova	0.01	7	264.15	22.73
42	anova	0.02	7	308.57	21.44
43	anova	0.03	7	309.47	23.79
44	anova	0.04	7	309.47	23.79
45	anova	0.05	7	309.47	23.79
46	anova	0.06	7	309.47	23.79
47	anova	0.07	7	309.47	23.79
48	anova	0.08	7	354.42	44.00
49	anova	0.09	7	395.93	26.39
50	anova	0.10	7	395.93	26.39

  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] 0.8573526

#
tb4=M.rptp_n[["model"]]$performances
table04=xtable(tb4)
print(table04,type="html")

	method	cp	minsplit	error	dispersion
1	anova	0.01	3	209.52	26.88
2	anova	0.02	3	213.64	30.28
3	anova	0.03	3	213.64	30.28
4	anova	0.04	3	213.64	30.28
5	anova	0.05	3	241.65	52.19
6	anova	0.06	3	257.95	47.13
7	anova	0.07	3	257.95	47.13
8	anova	0.08	3	257.95	47.13
9	anova	0.09	3	257.95	47.13
10	anova	0.10	3	257.95	47.13
11	anova	0.01	4	209.52	26.88
12	anova	0.02	4	213.64	30.28
13	anova	0.03	4	213.64	30.28
14	anova	0.04	4	213.64	30.28
15	anova	0.05	4	241.65	52.19
16	anova	0.06	4	257.95	47.13
17	anova	0.07	4	257.95	47.13
18	anova	0.08	4	257.95	47.13
19	anova	0.09	4	257.95	47.13
20	anova	0.10	4	257.95	47.13
21	anova	0.01	5	209.52	26.88
22	anova	0.02	5	213.64	30.28
23	anova	0.03	5	213.64	30.28
24	anova	0.04	5	213.64	30.28
25	anova	0.05	5	241.65	52.19
26	anova	0.06	5	257.95	47.13
27	anova	0.07	5	257.95	47.13
28	anova	0.08	5	257.95	47.13
29	anova	0.09	5	257.95	47.13
30	anova	0.10	5	257.95	47.13
31	anova	0.01	6	209.52	26.88
32	anova	0.02	6	213.64	30.28
33	anova	0.03	6	213.64	30.28
34	anova	0.04	6	213.64	30.28
35	anova	0.05	6	241.65	52.19
36	anova	0.06	6	257.95	47.13
37	anova	0.07	6	257.95	47.13
38	anova	0.08	6	257.95	47.13
39	anova	0.09	6	257.95	47.13
40	anova	0.10	6	257.95	47.13
41	anova	0.01	7	209.52	26.88
42	anova	0.02	7	213.64	30.28
43	anova	0.03	7	213.64	30.28
44	anova	0.04	7	213.64	30.28
45	anova	0.05	7	241.65	52.19
46	anova	0.06	7	257.95	47.13
47	anova	0.07	7	257.95	47.13
48	anova	0.08	7	257.95	47.13
49	anova	0.09	7	257.95	47.13
50	anova	0.10	7	257.95	47.13

  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] 0.7151531

#
print(xtable(cc.rpt),type="html")

	Model	Tst
M.rpt	0.84	0.00
M.rptp	0.84	0.81
M.rptp_d	0.88	0.86
M.rptp_n	0.75	0.72

#

The results found account for a correlation of 0.8373584.

Conclusions

After this short analysis we can conclude that:

	LM	SVM	RF	MLP	CART
Full_Model	0.86	0.94	0.98	0.87	0.84
Partial_Model	0.86	0.94	0.98	0.87	0.84
Daily_P_Model	0.89	0.96	0.99	0.90	0.88
Nightly_P_Model	0.76	0.96	0.98	0.78	0.75

	LM	SVM	RF	MLP	CART
Partial_Model	0.82	0.87	0.89	0.83	0.81
Daily_P_Model	0.86	0.90	0.91	0.87	0.86
Nightly_P_Model	0.71	0.81	0.82	0.71	0.72

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 0.887013 method with a corrlation factor of 0.961723

Ensembles

Let’s see how it becomes the emsemble method