Final Project
Hector Santana, Harris Dupre, Christopher Ayre
5/9/2022
Our initial step is to import the relevant libraries containing the requisite models of this analysis.
library(mlbench)
library(randomForest)
library(caret)
library(party)
library(Cubist)
library(dplyr)
library(rpart.plot)
library(kernlab)
library(earth)
library(nnet)
library(DataExplorer)
library(RANN)
library(corrplot)
pacman::p_load(tidyverse,janitor,DataExplorer,knitr,arsenal,kableExtra,car,geoR,caret,
psych,gridExtra,DMwR2,lmtest,pscl,MKmisc,ROCR,survey,stats,rstatix,Rcpp,
corrplot,forecast,cowplot)
library(mice)
library(RColorBrewer)
library(VIM)
library(openxlsx)To create ease around the data importation process we converted the excel files into CSV and stored them in a GitHub repository.
studenttrainingdata = read.csv('https://raw.githubusercontent.com/manonfire86/Data624FinalProject/main/StudentData.csv')
studenttestdata = read.csv('https://raw.githubusercontent.com/manonfire86/Data624FinalProject/main/StudentEvaluation.csv')The below exploratory analysis indicates that missing values are fairly low. For our model to be robust and dynamic we will impute missing data, filter out correlations, near zero variables, scale the data, and center the data in our preprocess methodology.This will remove collinearity, remove skew, normalize distributions, scale the data, and remove non significant variables.
str(studenttrainingdata)## 'data.frame': 2571 obs. of 33 variables:
## $ ï..Brand.Code : chr "B" "A" "B" "A" ...
## $ Carb.Volume : num 5.34 5.43 5.29 5.44 5.49 ...
## $ Fill.Ounces : num 24 24 24.1 24 24.3 ...
## $ PC.Volume : num 0.263 0.239 0.263 0.293 0.111 ...
## $ Carb.Pressure : num 68.2 68.4 70.8 63 67.2 66.6 64.2 67.6 64.2 72 ...
## $ Carb.Temp : num 141 140 145 133 137 ...
## $ PSC : num 0.104 0.124 0.09 NA 0.026 0.09 0.128 0.154 0.132 0.014 ...
## $ PSC.Fill : num 0.26 0.22 0.34 0.42 0.16 0.24 0.4 0.34 0.12 0.24 ...
## $ PSC.CO2 : num 0.04 0.04 0.16 0.04 0.12 0.04 0.04 0.04 0.14 0.06 ...
## $ Mnf.Flow : num -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 ...
## $ Carb.Pressure1 : num 119 122 120 115 118 ...
## $ Fill.Pressure : num 46 46 46 46.4 45.8 45.6 51.8 46.8 46 45.2 ...
## $ Hyd.Pressure1 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Hyd.Pressure2 : num NA NA NA 0 0 0 0 0 0 0 ...
## $ Hyd.Pressure3 : num NA NA NA 0 0 0 0 0 0 0 ...
## $ Hyd.Pressure4 : int 118 106 82 92 92 116 124 132 90 108 ...
## $ Filler.Level : num 121 119 120 118 119 ...
## $ Filler.Speed : int 4002 3986 4020 4012 4010 4014 NA 1004 4014 4028 ...
## $ Temperature : num 66 67.6 67 65.6 65.6 66.2 65.8 65.2 65.4 66.6 ...
## $ Usage.cont : num 16.2 19.9 17.8 17.4 17.7 ...
## $ Carb.Flow : int 2932 3144 2914 3062 3054 2948 30 684 2902 3038 ...
## $ Density : num 0.88 0.92 1.58 1.54 1.54 1.52 0.84 0.84 0.9 0.9 ...
## $ MFR : num 725 727 735 731 723 ...
## $ Balling : num 1.4 1.5 3.14 3.04 3.04 ...
## $ Pressure.Vacuum : num -4 -4 -3.8 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 ...
## $ PH : num 8.36 8.26 8.94 8.24 8.26 8.32 8.4 8.38 8.38 8.5 ...
## $ Oxygen.Filler : num 0.022 0.026 0.024 0.03 0.03 0.024 0.066 0.046 0.064 0.022 ...
## $ Bowl.Setpoint : int 120 120 120 120 120 120 120 120 120 120 ...
## $ Pressure.Setpoint: num 46.4 46.8 46.6 46 46 46 46 46 46 46 ...
## $ Air.Pressurer : num 143 143 142 146 146 ...
## $ Alch.Rel : num 6.58 6.56 7.66 7.14 7.14 7.16 6.54 6.52 6.52 6.54 ...
## $ Carb.Rel : num 5.32 5.3 5.84 5.42 5.44 5.44 5.38 5.34 5.34 5.34 ...
## $ Balling.Lvl : num 1.48 1.56 3.28 3.04 3.04 3.02 1.44 1.44 1.44 1.38 ...summary(studenttrainingdata)## ï..Brand.Code Carb.Volume Fill.Ounces PC.Volume
## Length:2571 Min. :5.040 Min. :23.63 Min. :0.07933
## Class :character 1st Qu.:5.293 1st Qu.:23.92 1st Qu.:0.23917
## Mode :character Median :5.347 Median :23.97 Median :0.27133
## Mean :5.370 Mean :23.97 Mean :0.27712
## 3rd Qu.:5.453 3rd Qu.:24.03 3rd Qu.:0.31200
## Max. :5.700 Max. :24.32 Max. :0.47800
## NA's :10 NA's :38 NA's :39
## Carb.Pressure Carb.Temp PSC PSC.Fill
## Min. :57.00 Min. :128.6 Min. :0.00200 Min. :0.0000
## 1st Qu.:65.60 1st Qu.:138.4 1st Qu.:0.04800 1st Qu.:0.1000
## Median :68.20 Median :140.8 Median :0.07600 Median :0.1800
## Mean :68.19 Mean :141.1 Mean :0.08457 Mean :0.1954
## 3rd Qu.:70.60 3rd Qu.:143.8 3rd Qu.:0.11200 3rd Qu.:0.2600
## Max. :79.40 Max. :154.0 Max. :0.27000 Max. :0.6200
## NA's :27 NA's :26 NA's :33 NA's :23
## PSC.CO2 Mnf.Flow Carb.Pressure1 Fill.Pressure
## Min. :0.00000 Min. :-100.20 Min. :105.6 Min. :34.60
## 1st Qu.:0.02000 1st Qu.:-100.00 1st Qu.:119.0 1st Qu.:46.00
## Median :0.04000 Median : 65.20 Median :123.2 Median :46.40
## Mean :0.05641 Mean : 24.57 Mean :122.6 Mean :47.92
## 3rd Qu.:0.08000 3rd Qu.: 140.80 3rd Qu.:125.4 3rd Qu.:50.00
## Max. :0.24000 Max. : 229.40 Max. :140.2 Max. :60.40
## NA's :39 NA's :2 NA's :32 NA's :22
## Hyd.Pressure1 Hyd.Pressure2 Hyd.Pressure3 Hyd.Pressure4
## Min. :-0.80 Min. : 0.00 Min. :-1.20 Min. : 52.00
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 86.00
## Median :11.40 Median :28.60 Median :27.60 Median : 96.00
## Mean :12.44 Mean :20.96 Mean :20.46 Mean : 96.29
## 3rd Qu.:20.20 3rd Qu.:34.60 3rd Qu.:33.40 3rd Qu.:102.00
## Max. :58.00 Max. :59.40 Max. :50.00 Max. :142.00
## NA's :11 NA's :15 NA's :15 NA's :30
## Filler.Level Filler.Speed Temperature Usage.cont Carb.Flow
## Min. : 55.8 Min. : 998 Min. :63.60 Min. :12.08 Min. : 26
## 1st Qu.: 98.3 1st Qu.:3888 1st Qu.:65.20 1st Qu.:18.36 1st Qu.:1144
## Median :118.4 Median :3982 Median :65.60 Median :21.79 Median :3028
## Mean :109.3 Mean :3687 Mean :65.97 Mean :20.99 Mean :2468
## 3rd Qu.:120.0 3rd Qu.:3998 3rd Qu.:66.40 3rd Qu.:23.75 3rd Qu.:3186
## Max. :161.2 Max. :4030 Max. :76.20 Max. :25.90 Max. :5104
## NA's :20 NA's :57 NA's :14 NA's :5 NA's :2
## Density MFR Balling Pressure.Vacuum
## Min. :0.240 Min. : 31.4 Min. :-0.170 Min. :-6.600
## 1st Qu.:0.900 1st Qu.:706.3 1st Qu.: 1.496 1st Qu.:-5.600
## Median :0.980 Median :724.0 Median : 1.648 Median :-5.400
## Mean :1.174 Mean :704.0 Mean : 2.198 Mean :-5.216
## 3rd Qu.:1.620 3rd Qu.:731.0 3rd Qu.: 3.292 3rd Qu.:-5.000
## Max. :1.920 Max. :868.6 Max. : 4.012 Max. :-3.600
## NA's :1 NA's :212 NA's :1
## PH Oxygen.Filler Bowl.Setpoint Pressure.Setpoint
## Min. :7.880 Min. :0.00240 Min. : 70.0 Min. :44.00
## 1st Qu.:8.440 1st Qu.:0.02200 1st Qu.:100.0 1st Qu.:46.00
## Median :8.540 Median :0.03340 Median :120.0 Median :46.00
## Mean :8.546 Mean :0.04684 Mean :109.3 Mean :47.62
## 3rd Qu.:8.680 3rd Qu.:0.06000 3rd Qu.:120.0 3rd Qu.:50.00
## Max. :9.360 Max. :0.40000 Max. :140.0 Max. :52.00
## NA's :4 NA's :12 NA's :2 NA's :12
## Air.Pressurer Alch.Rel Carb.Rel Balling.Lvl
## Min. :140.8 Min. :5.280 Min. :4.960 Min. :0.00
## 1st Qu.:142.2 1st Qu.:6.540 1st Qu.:5.340 1st Qu.:1.38
## Median :142.6 Median :6.560 Median :5.400 Median :1.48
## Mean :142.8 Mean :6.897 Mean :5.437 Mean :2.05
## 3rd Qu.:143.0 3rd Qu.:7.240 3rd Qu.:5.540 3rd Qu.:3.14
## Max. :148.2 Max. :8.620 Max. :6.060 Max. :3.66
## NA's :9 NA's :10 NA's :1dim(studenttrainingdata)## [1] 2571 33df_features <- studenttrainingdata %>%
dplyr::select(-c(`ï..Brand.Code`))
correlation = cor(df_features, use = 'pairwise.complete.obs')
corrplot(correlation, 'ellipse', type = 'lower', order = 'hclust',
col=brewer.pal(n=8, name="RdYlBu"), tl.cex=0.5)
mice_plot <- aggr(studenttrainingdata, col=c('navyblue','yellow'),
numbers=TRUE, sortVars=TRUE,
labels=names(studenttrainingdata), cex.axis=.7,
gap=3, ylab=c("Missing data","Pattern"))## Warning in plot.aggr(res, ...): not enough vertical space to display frequencies
## (too many combinations)
##
## Variables sorted by number of missings:
## Variable Count
## MFR 0.0824581875
## Filler.Speed 0.0221703617
## PC.Volume 0.0151691949
## PSC.CO2 0.0151691949
## Fill.Ounces 0.0147802412
## PSC 0.0128354726
## Carb.Pressure1 0.0124465189
## Hyd.Pressure4 0.0116686114
## Carb.Pressure 0.0105017503
## Carb.Temp 0.0101127966
## PSC.Fill 0.0089459354
## Fill.Pressure 0.0085569817
## Filler.Level 0.0077790743
## Hyd.Pressure2 0.0058343057
## Hyd.Pressure3 0.0058343057
## Temperature 0.0054453520
## Oxygen.Filler 0.0046674446
## Pressure.Setpoint 0.0046674446
## Hyd.Pressure1 0.0042784909
## Carb.Volume 0.0038895371
## Carb.Rel 0.0038895371
## Alch.Rel 0.0035005834
## Usage.cont 0.0019447686
## PH 0.0015558149
## Mnf.Flow 0.0007779074
## Carb.Flow 0.0007779074
## Bowl.Setpoint 0.0007779074
## Density 0.0003889537
## Balling 0.0003889537
## Balling.Lvl 0.0003889537
## ï..Brand.Code 0.0000000000
## Pressure.Vacuum 0.0000000000
## Air.Pressurer 0.0000000000plot_missing(studenttrainingdata)
plot_histogram(studenttrainingdata)
plot_density(studenttrainingdata)
plot_boxplot(
data = studenttrainingdata,
by = "PH")## Warning: Removed 302 rows containing non-finite values (stat_boxplot).
## Warning: Removed 372 rows containing non-finite values (stat_boxplot).
## Warning: Removed 46 rows containing non-finite values (stat_boxplot).
set.seed(100)
studentrainingdata <- studenttrainingdata[complete.cases(studenttrainingdata$PH),]
preprocess_data_model = preProcess(studenttrainingdata, c("center", "scale", "knnImpute", "corr", "nzv"))
new_dataset = predict(preprocess_data_model,studenttrainingdata)We will now split our data into a training set and validation set to analyze model outputs. Given the evaluation set we will need to verify our model analytics using RMSE, R^2, and MAE prior to running our predictions. Obtaining a model with a combination of the lowest RMSE, highest R^2, and lowest MAE will be optimal.
training_partition = createDataPartition(new_dataset$PH,p=.8,list=FALSE)
training_df = new_dataset[training_partition,]
validation_df = new_dataset[-training_partition,]We will now build models using various linear, nonlinear, and tree based approaches.
Linear Models
Ordinary Least Regression
olrmod = train(PH~.,data = training_df,method='lm',trControl=trainControl('cv',number=10))
olrpred = predict(olrmod,validation_df)
olrpred_results = postResample(pred = olrpred, obs = validation_df$PH)Partial Least Squares
pls_mod = train(PH~.,data = training_df,method='pls',trControl=trainControl('cv',number=10),center=T,tunelength=20)
plot(pls_mod)
plspred = predict(pls_mod,validation_df)
plspred_results = postResample(pred = plspred, obs = validation_df$PH)Ridge Regression
set.seed(100)
rrfit = train(PH~.,data=training_df,method='ridge',tuneGrid=data.frame(.lambda=seq(0,.1,length=15)),trControl=trainControl('cv',number=10))
plot(rrfit)
rrpred = predict(rrfit,validation_df)
rrpred_results = postResample(pred = rrpred, obs = validation_df$PH)Non Linear Models
Neural Networks
set.seed(100)
nnetmod = train(PH~.,data=training_df,
method = "avNNet",
preProc = c("center", "scale"),
tuneGrid = expand.grid( .decay = c(0, 0.01, .1), .size = c(1:10), .bag= F ),
trControl = trainControl(method = "cv",number = 10),
linout = T,
trace= F,
MaxNWts = 5 * (ncol(training_df) + 1) + 5 + 1,
maxit = 500)
nnetpred = predict(nnetmod,validation_df)
nnetpred_results = postResample(pred = nnetpred, obs = validation_df$PH)MARS
set.seed(100)
marsmod = train(PH~.,data=training_df,method='earth',trControl=trainControl(method='cv'))
marspred = predict(marsmod,validation_df)
marspred_results = postResample(pred = marspred, obs = validation_df$PH)SVM
set.seed(100)
svmmod = train(PH~., data = training_df,
method= "svmLinear",
trControl = trainControl(method = "repeatedcv",number = 10, repeats=3),
tuneLength = 10)
svmpred = predict(svmmod,validation_df)
svmpred_results = postResample(pred = svmpred, obs = validation_df$PH)KNN
set.seed(100)
knnmod = train(PH~., data = training_df,
method= "knn",
trControl = trainControl(method = "repeatedcv",number = 10, repeats=3),
tuneLength = 10)
knnpred = predict(knnmod,validation_df)
knnpred_results = postResample(pred = knnpred, obs = validation_df$PH)Trees
Random Forest
randomforest_model = train(PH~.,data=training_df,method='rf',
preProcess = c('center', 'scale'),trControl=trainControl('cv'))
randomforest_pred = predict(randomforest_model, validation_df)
randomforest_results = postResample(pred = randomforest_pred, obs = validation_df$PH)Boosted Trees
gbm_model = train(PH~.,data=training_df,method='gbm',tuneGrid=expand.grid(.interaction.depth = seq(1, 7, by = 2),
.n.trees = seq(100, 1000, by = 100),
.shrinkage = c(0.01, 0.1),
.n.minobsinnode = 8),
trControl=trainControl('cv'))
gbm_pred = predict(gbm_model, validation_df)
gbm_results = postResample(pred = gbm_pred, obs = validation_df$PH)Cubist
cub_model = train(PH~.,data=training_df,method='cubist',
preProcess = c('center', 'scale'),trControl=trainControl('cv'))
cub_pred = predict(cub_model, validation_df)
cub_results = postResample(pred = cub_pred, obs = validation_df$PH)Single Tree
rp_model = train(PH~.,data=training_df,method='rpart2',
preProcess = c('center', 'scale'),trControl=trainControl('cv'))
rp_pred = predict(rp_model, validation_df)
rp_results = postResample(pred = rp_pred, obs = validation_df$PH)
plot(rp_model)
GLMNET
glm_model = train(PH~.,data=training_df,method='glmnet',
preProcess = c('center', 'scale'),trControl=trainControl('cv'))
glm_pred = predict(glm_model, validation_df)
glm_results = postResample(pred = glm_pred, obs = validation_df$PH)
plot(glm_model)
PCR
pcr_model = train(PH~.,data=training_df,method='pcr',
preProcess = c('center', 'scale'),trControl=trainControl('cv'))
pcr_pred = predict(pcr_model, validation_df)
pcr_results = postResample(pred = pcr_pred, obs = validation_df$PH)
plot(pcr_model)
Evaluation
Aggregating the model results we see our cubist model performs the best among the 13 selected model types. The multi node linear model tree based methodology accounts best for the various intricacies of the data set. There is of course the risk of over fitting, however the cubist model we discerned to be best fit in this scenario.
titles <- list("OLR","PLS","RR","NNet","MARS","SVM","KNN","Random Forest","Boosted Model","Cubist","RPart","GLMNET","PCR")
results <- list(olrpred_results,plspred_results,rrpred_results,nnetpred_results,marspred_results,svmpred_results,knnpred_results,randomforest_results,gbm_results,cub_results,rp_results,glm_results,pcr_results)
df = NULL
for (x in 1:length(results)) {
Model = titles[[x]]
RMSE = unname(results[[x]]["RMSE"])
Rsquared = unname(results[[x]]["Rsquared"])
MAE = unname(results[[x]]["MAE"])
df = rbind(df,data.frame(Model,RMSE,Rsquared,MAE))
}
knitr::kable(df[order(df$Rsquared,decreasing=TRUE),], digits=4, row.names=F)| Model | RMSE | Rsquared | MAE |
|---|---|---|---|
| Cubist | 0.5796 | 0.6668 | 0.4223 |
| Random Forest | 0.5940 | 0.6508 | 0.4213 |
| Boosted Model | 0.6504 | 0.5822 | 0.4872 |
| NNet | 0.6872 | 0.5294 | 0.5075 |
| KNN | 0.7294 | 0.4790 | 0.5414 |
| MARS | 0.7886 | 0.3931 | 0.6009 |
| RR | 0.7845 | 0.3885 | 0.6027 |
| GLMNET | 0.7848 | 0.3878 | 0.6025 |
| OLR | 0.7852 | 0.3876 | 0.6025 |
| SVM | 0.7904 | 0.3862 | 0.5906 |
| PLS | 0.8074 | 0.3518 | 0.6176 |
| RPart | 0.8081 | 0.3507 | 0.6358 |
| PCR | 0.8969 | 0.1983 | 0.6952 |
ggplot(data=df,aes(x=Model,y=RMSE)) +geom_bar(stat='identity',aes(fill=Model))+ coord_flip()
ggplot(data=df,aes(x=Model,y=Rsquared)) +geom_bar(stat='identity',aes(fill=Model))+ coord_flip()
ggplot(data=df,aes(x=Model,y=MAE)) +geom_bar(stat='identity',aes(fill=Model))+ coord_flip()
Variable Importance
Using the cubist model we can discern how variables are weighted for predictor ‘PH’. Mnf.Flow is the most significant variable in the model.
cub_var_imp = varImp(cub_model)
ggplot(data=cub_var_imp$importance,aes(x=reorder(rownames(cub_var_imp$importance), Overall),y=Overall)) +geom_bar(stat='identity',aes(fill=rownames(cub_var_imp$importance)))+ coord_flip() +theme(legend.position = "none") + labs(x='Variables')
Predictions
#studenteval_scaled = preProcess(studenttestdata, c("center", "scale","corr", "nzv"))
#studenteval_scaled_dataset = predict(studenteval_scaled,studenttestdata)
eval_cub_pred = predict(cub_model, studenttestdata)
scaled_ph = scale(studenttrainingdata$PH, center= TRUE, scale=TRUE)
scaledeval_predictions = eval_cub_pred * attr(scaled_ph, 'scaled:scale') + attr(scaled_ph, 'scaled:center')
eval_df = data.frame(scaledeval_predictions)
#write.xlsx(eval_df, 'FinalProject_Predictions.xlsx')
eval_df## scaledeval_predictions
## 1 8.635917
## 2 8.735001
## 3 8.737451
## 4 8.637508
## 5 8.645494
## 6 8.735781
## 7 8.723944
## 8 8.723379
## 9 8.348160
## 10 8.738002
## 11 8.727838
## 12 8.568844
## 13 8.727591
## 14 8.727823
## 15 8.750464
## 16 8.730200
## 17 8.341952
## 18 8.392659
## 19 8.576176
## 20 8.577821
## 21 8.573695
## 22 8.638799
## 23 8.647669
## 24 8.647156
## 25 8.567853
## 26 8.611181
## 27 8.437625
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## 30 8.564879
## 31 8.563874
## 32 8.719247
## 33 8.621498
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