<!DOCTYPE html>
ST 558 Project 2
Yan Liu & Mandy Liesch
library(rmarkdown)
library(usethis)
use_git_config(user.name="Mandy Liesch", user.email="amliesch@ncsu.edu")Introduction
Online News Popularity Data Set summarizes a heterogeneous set of features about articles published by Mashable in a period of two years. The goal is to predict the number of shares in social networks (popularity). Here we first showed some summary statistics and plots about the data grouped by weekdays. Then we create several models to predict the response, shares in different channels. The performance of these models will be evaluated by RMSE. The model having the lowest RMSE will be selected as a winner. The methods of modeling include:
- Regression Tree
- Log Transformed Full Linear Regression Model
- Linear Regression Model Without Day of the Week
- Subset Linear Regression Model #1
- Subset Linear Regression Model #2
- Backward Selection Linear Regression
- Bagged Regression Tree
- Random Forest Model
- Boosted Tree Model
Data preparation
Subset Data by Channel
library(tidyverse)
data_whole<-read_csv("OnlineNewsPopularity/OnlineNewsPopularity.csv")
#create a new variable, channel, to help with the subsetting.
data_whole$channel <- names(data_whole[14:19])[apply(data_whole[14:19],1, match, x = 1)]
data_whole$channel <-sub("data_channel_is_", "", data_whole$channel)
#Subset the data to work on the data channel of interest
#channel_interest = params[[1]]$team
#Get the important data
data_interest<-data_whole%>%
filter(channel==x[[2]]$team)%>%
select(-c(1,14:19,62))Establish Training Data
Split the data into a training (70% of the data) and test set (30% of the data)
library(caret)
library(rsample)
set.seed(14)
index <- initial_split(data_interest,
prop = 0.7)
train <- training(index)
test <- testing(index)Data Summaries
Correlation Plots
This graphical function looks at the correlation of all of the different variables against each other.
library(corrplot)
#drop values that are not important (the days of the week)
newTrain<-train[ -c(25:31) ]
lmNewTest<-test[ -c(25:31) ]
#drop the predictor variables
predictTrain<-newTrain[ -c(47) ]
#Calculate the correlation Matrix and round it
res <- cor(predictTrain)
#Plot the correlation matrix values by cluster
corrplot(res, type = "upper", order = "hclust",
tl.col = "black", tl.cex = 0.5)
From the results of this spot, it appears that we likely have some clusters of colinearity.
Table Summary
We summarize the train data of interest in tables grouped by weekdays, showing the pattern of shares in a week.
#create a new variable, weekday, to help with the creating plots.
train$weekday <- names(train[25:31])[apply(train[25:31],1, match, x = 1)]
train$weekday <-sub("weekday_is_", "", train$weekday)
#summarize the train data by weekday.knitr::kable(
summary<-train%>%group_by(weekday)%>%
summarise(Avg=round(mean(shares),0),Sd=round(sd(shares),0),Median=median(shares),IQR=round(IQR(shares),0))
knitr::kable(summary)| weekday | Avg | Sd | Median | IQR |
|---|---|---|---|---|
| friday | 3197 | 4735 | 1600 | 2100 |
| monday | 4624 | 16315 | 1700 | 2400 |
| saturday | 4082 | 5502 | 2000 | 2750 |
| sunday | 3669 | 4714 | 2000 | 2600 |
| thursday | 3954 | 6662 | 1700 | 2600 |
| tuesday | 4115 | 14886 | 1500 | 2050 |
| wednesday | 2983 | 4374 | 1500 | 1800 |
We summarize the train data of interest in the plots below. The histogram of shares shows that it is not a normal distribution. After log transformation, the distribution of log(share) is more close to a normal distribution.
#histogram of shares and log(shares).
hist(train$shares)
hist(log(train$shares))
Data Plots
Box Plots
We use box plots to show the difference in shares and num_images between weekdays and weekends.If the boxes of weekends are higher than the ones of weekdays, then articles be shared more often during weekends.
g1<-ggplot(train, aes(x=factor(is_weekend,labels=c("No", "Yes")),y=shares))
g1+geom_boxplot(fill="white", width=0.5,lwd=1.5,color='black',outlier.shape = NA)+
scale_y_continuous(limits = quantile(train$shares, c(0.1, 0.9)))+
labs(subtitle = "Shares on weekend",x="On weekend or not")
g2<-ggplot(train, aes(x=factor(is_weekend,labels=c("No", "Yes")),y=num_imgs))
g2+geom_boxplot(fill="white", width=0.5,lwd=1.5,color='black',outlier.shape = NA)+
scale_y_continuous(limits = quantile(train$num_imgs, c(0, 0.95)))+
labs(subtitle = "number of images on weekend",x="On weekend or not")
Linear Model
We can inspect the trend of shares as a function of num_images. If the points show an upward trend, then articles with more images tend to be shared more often. If we see a negative trend then articles with more images tend to be shared less often. We can also observe the difference after the log transformation.
g3<-ggplot(train,aes(x=num_imgs,y=shares))
g3+geom_point()+
labs(subtitle = "num_imgs vs shares")+
scale_y_continuous(limits = quantile(train$shares, c(0, 0.9)))+
scale_x_continuous(limits = quantile(train$num_imgs, c(0, 0.9)))+
geom_smooth(method="lm")
g4<-ggplot(train,aes(x=num_imgs,y=log(shares)))
g4+geom_point()+
labs(subtitle = "num_imgs vs log(shares)")+
scale_y_continuous(limits = quantile(log(train$shares), c(0, 0.9)))+
scale_x_continuous(limits = quantile(train$num_imgs, c(0, 0.9)))+
geom_smooth(method="lm")
#remove weekday from data set
train<-train%>%select(-weekday)Models
Regression Tree
Classification trees are machine learning algorithms that have several benefits, including the ease of operation, and less pre-processing. Data does not require normalization, scaling, and removal of missing values. The results are usually easy to explain, and stakeholders usually can understand them. A regression tree is a tree that uses numerical values to predict the nodes and tree branches. Despite all of the benefits, the Decision Tree algorithm can’t be used for regression and predicting continuous values, it also does not transfer well to other datasets.
library(tree)
tree.news<-tree(shares~., data=train)
summary(tree.news)##
## Regression tree:
## tree(formula = shares ~ ., data = train)
## Variables actually used in tree construction:
## [1] "num_videos" "LDA_00" "kw_avg_avg"
## [4] "n_unique_tokens"
## Number of terminal nodes: 5
## Residual mean deviance: 79550000 = 1.165e+11 / 1464
## Distribution of residuals:
## Min. 1st Qu. Median Mean 3rd Qu.
## -43560.00 -2278.00 -1678.00 0.00 -78.36
## Max.
## 163200.00plot(tree.news)
text(tree.news, pretty=0)
yhat.regTree<- predict(tree.news, newdata = test)
yhat.test<-test["shares"]
yhat.regTree<-as.data.frame(yhat.regTree)
meanRegTree<-mean((yhat.regTree$yhat.regTree-yhat.test$shares)^2)
RMSE_regTree<-sqrt(meanRegTree)These results can vary widely depending on the datasets.
Linear Models
Linear models are very valuable and powerful tools, and are very versatile, and can be applied to many situations. Multiple regression examines the relationship between several independent variables and one dependent variable (in this case, total Shares). Regression models give users the ability to determine the relative influence of one or more predictor variables to the predictor, and it also allows users to identify outliers, or anomalies. The main disadvantages have to do with the input quality of data. Input that is incomplete may lead to wrong conclusions. It also assumes that data is independent, which is not always the case.
There are several different types of linear models. In this project, we use multiple different multiple regression values that were log transformed, representing the full dataset, and several partial subsets with multiple variables removed at different points for multicolinearity reasons.
There are also several different types of variable selection, including forward, backward, and stepwise, which user predefined criteria set the entry and/or exit criteria of the models. Backwards selection starts with a full model, and then removes variables that are least significant one at a time, until the model criteria defined by the user are hit. Forward regression does the opposite, and is not represented here.
Linear Regression After Log Transformation
Transform the response with log, then fit a linear regression model with all the variables. Then calculate the RMSE of the model.
lm<- lm(log(shares)~.,train)
summary(lm)##
## Call:
## lm(formula = log(shares) ~ ., data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9490 -0.5683 -0.1498 0.4752 4.1539
##
## Coefficients: (4 not defined because of singularities)
## Estimate Std. Error
## (Intercept) 6.903e+00 4.121e-01
## timedelta 8.946e-04 1.947e-04
## n_tokens_title 1.280e-02 1.335e-02
## n_tokens_content -7.124e-06 7.247e-05
## n_unique_tokens -1.128e+00 8.469e-01
## n_non_stop_words -1.808e+00 7.583e-01
## n_non_stop_unique_tokens 1.099e+00 7.246e-01
## num_hrefs 5.406e-03 2.731e-03
## num_self_hrefs -8.279e-03 9.033e-03
## num_imgs 1.403e-02 4.652e-03
## num_videos 4.451e-02 1.601e-02
## average_token_length 1.726e-01 1.045e-01
## num_keywords 3.096e-02 1.725e-02
## kw_min_min 2.820e-04 5.527e-04
## kw_max_min 1.573e-05 2.131e-05
## kw_avg_min -1.184e-04 1.495e-04
## kw_min_max 4.595e-07 1.920e-06
## kw_max_max 6.914e-08 2.097e-07
## kw_avg_max 3.758e-07 5.836e-07
## kw_min_avg -3.432e-05 3.022e-05
## kw_max_avg -3.370e-05 8.627e-06
## kw_avg_avg 2.432e-04 5.410e-05
## self_reference_min_shares 1.531e-05 7.497e-06
## self_reference_max_shares 3.339e-06 4.731e-06
## self_reference_avg_sharess -1.055e-05 1.125e-05
## weekday_is_monday -9.674e-02 9.918e-02
## weekday_is_tuesday -2.289e-01 1.000e-01
## weekday_is_wednesday -2.564e-01 9.563e-02
## weekday_is_thursday -1.049e-01 9.762e-02
## weekday_is_friday -1.750e-01 9.989e-02
## weekday_is_saturday 1.218e-01 1.104e-01
## weekday_is_sunday NA NA
## is_weekend NA NA
## LDA_00 1.054e-01 9.933e-02
## LDA_01 1.407e-01 2.711e-01
## LDA_02 -1.306e-01 2.347e-01
## LDA_03 -2.486e-01 1.637e-01
## LDA_04 NA NA
## global_subjectivity -1.049e-01 3.952e-01
## global_sentiment_polarity -9.504e-01 7.686e-01
## global_rate_positive_words 5.815e+00 3.257e+00
## global_rate_negative_words -5.904e-01 7.377e+00
## rate_positive_words -1.391e-01 5.881e-01
## rate_negative_words NA NA
## avg_positive_polarity -2.487e-01 6.187e-01
## min_positive_polarity 1.038e+00 4.863e-01
## max_positive_polarity 5.477e-03 1.887e-01
## avg_negative_polarity -1.333e-02 5.457e-01
## min_negative_polarity -1.552e-01 1.854e-01
## max_negative_polarity -2.218e-01 4.560e-01
## title_subjectivity 6.015e-03 1.110e-01
## title_sentiment_polarity -1.837e-01 1.059e-01
## abs_title_subjectivity 1.299e-01 1.553e-01
## abs_title_sentiment_polarity 9.282e-02 1.527e-01
## t value Pr(>|t|)
## (Intercept) 16.750 < 2e-16 ***
## timedelta 4.594 4.72e-06 ***
## n_tokens_title 0.959 0.33789
## n_tokens_content -0.098 0.92170
## n_unique_tokens -1.332 0.18315
## n_non_stop_words -2.385 0.01721 *
## n_non_stop_unique_tokens 1.517 0.12955
## num_hrefs 1.980 0.04793 *
## num_self_hrefs -0.917 0.35954
## num_imgs 3.016 0.00261 **
## num_videos 2.780 0.00551 **
## average_token_length 1.651 0.09889 .
## num_keywords 1.794 0.07298 .
## kw_min_min 0.510 0.60993
## kw_max_min 0.738 0.46063
## kw_avg_min -0.792 0.42865
## kw_min_max 0.239 0.81090
## kw_max_max 0.330 0.74162
## kw_avg_max 0.644 0.51976
## kw_min_avg -1.136 0.25618
## kw_max_avg -3.906 9.81e-05 ***
## kw_avg_avg 4.495 7.53e-06 ***
## self_reference_min_shares 2.043 0.04124 *
## self_reference_max_shares 0.706 0.48052
## self_reference_avg_sharess -0.938 0.34845
## weekday_is_monday -0.975 0.32953
## weekday_is_tuesday -2.289 0.02223 *
## weekday_is_wednesday -2.681 0.00743 **
## weekday_is_thursday -1.074 0.28286
## weekday_is_friday -1.752 0.07993 .
## weekday_is_saturday 1.103 0.27002
## weekday_is_sunday NA NA
## is_weekend NA NA
## LDA_00 1.061 0.28881
## LDA_01 0.519 0.60395
## LDA_02 -0.556 0.57799
## LDA_03 -1.519 0.12903
## LDA_04 NA NA
## global_subjectivity -0.265 0.79082
## global_sentiment_polarity -1.236 0.21649
## global_rate_positive_words 1.786 0.07435 .
## global_rate_negative_words -0.080 0.93622
## rate_positive_words -0.237 0.81306
## rate_negative_words NA NA
## avg_positive_polarity -0.402 0.68776
## min_positive_polarity 2.134 0.03304 *
## max_positive_polarity 0.029 0.97685
## avg_negative_polarity -0.024 0.98051
## min_negative_polarity -0.837 0.40269
## max_negative_polarity -0.486 0.62679
## title_subjectivity 0.054 0.95679
## title_sentiment_polarity -1.734 0.08314 .
## abs_title_subjectivity 0.836 0.40303
## abs_title_sentiment_polarity 0.608 0.54341
## ---
## Signif. codes:
## 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9049 on 1419 degrees of freedom
## Multiple R-squared: 0.1083, Adjusted R-squared: 0.07755
## F-statistic: 3.519 on 49 and 1419 DF, p-value: 1.548e-14yhat_lm<-predict(lm,test)
RMSE_lm<-sqrt(mean((test$shares - exp(yhat_lm))^2))Plot the lm Residuals
par(mfrow=c(2,2))
plot(lm)
Looking at our residuals, there seems to be skewing in both direction, indicating that the data, even after transformation, has extreme outliers in both directions.
Model Removing the Day Variable
#look at the data for multicolinearity
lmNewTest<-test[ -c(25:31) ]
lm2<- lm(log(shares)~.,newTrain)
yhat_lm2<-predict(lm2,lmNewTest)
RMSE_lm2<-sqrt(mean((lmNewTest$shares - exp(yhat_lm2))^2))
library(mctest)
omcdiag(lm2)##
## Call:
## omcdiag(mod = lm2)
##
##
## Overall Multicollinearity Diagnostics
##
## MC Results detection
## Determinant |X'X|: 0.000000e+00 1
## Farrar Chi-Square: 1.456565e+05 1
## Red Indicator: 1.790000e-01 0
## Sum of Lambda Inverse: 8.953332e+15 1
## Theil's Method: 2.865380e+01 1
## Condition Number: NaN NA
##
## 1 --> COLLINEARITY is detected by the test
## 0 --> COLLINEARITY is not detected by the testimcdiag(lm2)##
## Call:
## imcdiag(mod = lm2)
##
##
## All Individual Multicollinearity Diagnostics Result
##
## VIF TOL
## timedelta 3.295300e+00 0.3035
## n_tokens_title 1.145400e+00 0.8731
## n_tokens_content 3.298000e+00 0.3032
## n_unique_tokens 1.508940e+01 0.0663
## n_non_stop_words 4.503600e+15 0.0000
## n_non_stop_unique_tokens 1.300410e+01 0.0769
## num_hrefs 1.697800e+00 0.5890
## num_self_hrefs 1.301400e+00 0.7684
## num_imgs 2.871400e+00 0.3483
## num_videos 1.122700e+00 0.8907
## average_token_length 5.957700e+00 0.1679
## num_keywords 1.488800e+00 0.6717
## kw_min_min 3.800900e+00 0.2631
## kw_max_min 2.079440e+01 0.0481
## kw_avg_min 2.138410e+01 0.0468
## kw_min_max 1.863900e+00 0.5365
## kw_max_max 5.344300e+00 0.1871
## kw_avg_max 5.703400e+00 0.1753
## kw_min_avg 2.639000e+00 0.3789
## kw_max_avg 7.156300e+00 0.1397
## kw_avg_avg 1.011760e+01 0.0988
## self_reference_min_shares 1.186230e+01 0.0843
## self_reference_max_shares 3.404480e+01 0.0294
## self_reference_avg_sharess 6.179350e+01 0.0162
## is_weekend 1.132000e+00 0.8834
## LDA_00 Inf 0.0000
## LDA_01 Inf 0.0000
## LDA_02 Inf 0.0000
## LDA_03 Inf 0.0000
## LDA_04 Inf 0.0000
## global_subjectivity 2.508200e+00 0.3987
## global_sentiment_polarity 8.185800e+00 0.1222
## global_rate_positive_words 4.507700e+00 0.2218
## global_rate_negative_words 7.763300e+00 0.1288
## rate_positive_words Inf 0.0000
## rate_negative_words 9.007199e+15 0.0000
## avg_positive_polarity 5.007500e+00 0.1997
## min_positive_polarity 1.765300e+00 0.5665
## max_positive_polarity 2.822700e+00 0.3543
## avg_negative_polarity 6.476500e+00 0.1544
## min_negative_polarity 4.344500e+00 0.2302
## max_negative_polarity 3.239400e+00 0.3087
## title_subjectivity 2.369800e+00 0.4220
## title_sentiment_polarity 1.681400e+00 0.5948
## abs_title_subjectivity 1.519200e+00 0.6583
## abs_title_sentiment_polarity 2.714300e+00 0.3684
## Wi Fi
## timedelta 7.258170e+01 7.428340e+01
## n_tokens_title 4.596800e+00 4.704600e+00
## n_tokens_content 7.266860e+01 7.437240e+01
## n_unique_tokens 4.455366e+02 4.559827e+02
## n_non_stop_words 1.424138e+17 1.457529e+17
## n_non_stop_unique_tokens 3.795974e+02 3.884974e+02
## num_hrefs 2.206690e+01 2.258420e+01
## num_self_hrefs 9.530100e+00 9.753500e+00
## num_imgs 5.917730e+01 6.056480e+01
## num_videos 3.881200e+00 3.972200e+00
## average_token_length 1.567724e+02 1.604481e+02
## num_keywords 1.545550e+01 1.581790e+01
## kw_min_min 8.857000e+01 9.064670e+01
## kw_max_min 6.259414e+02 6.406172e+02
## kw_avg_min 6.445920e+02 6.597051e+02
## kw_min_max 2.731850e+01 2.795910e+01
## kw_max_max 1.373761e+02 1.405970e+02
## kw_avg_max 1.487309e+02 1.522181e+02
## kw_min_avg 5.183000e+01 5.304520e+01
## kw_max_avg 1.946754e+02 1.992398e+02
## kw_avg_avg 2.883196e+02 2.950796e+02
## self_reference_min_shares 3.434896e+02 3.515430e+02
## self_reference_max_shares 1.044950e+03 1.069450e+03
## self_reference_avg_sharess 1.922425e+03 1.967498e+03
## is_weekend 4.173600e+00 4.271500e+00
## LDA_00 Inf Inf
## LDA_01 Inf Inf
## LDA_02 Inf Inf
## LDA_03 Inf Inf
## LDA_04 Inf Inf
## global_subjectivity 4.769130e+01 4.880950e+01
## global_sentiment_polarity 2.272298e+02 2.325575e+02
## global_rate_positive_words 1.109205e+02 1.135211e+02
## global_rate_negative_words 2.138705e+02 2.188849e+02
## rate_positive_words Inf Inf
## rate_negative_words 2.848277e+17 2.915057e+17
## avg_positive_polarity 1.267255e+02 1.296967e+02
## min_positive_polarity 2.420010e+01 2.476750e+01
## max_positive_polarity 5.763820e+01 5.898950e+01
## avg_negative_polarity 1.731792e+02 1.772395e+02
## min_negative_polarity 1.057619e+02 1.082416e+02
## max_negative_polarity 7.081520e+01 7.247550e+01
## title_subjectivity 4.331560e+01 4.433110e+01
## title_sentiment_polarity 2.154670e+01 2.205190e+01
## abs_title_subjectivity 1.641740e+01 1.680230e+01
## abs_title_sentiment_polarity 5.421080e+01 5.548190e+01
## Leamer CVIF Klein
## timedelta 0.5509 3.549700e+00 1
## n_tokens_title 0.9344 1.233800e+00 1
## n_tokens_content 0.5506 3.552700e+00 1
## n_unique_tokens 0.2574 1.625450e+01 1
## n_non_stop_words 0.0000 4.851357e+15 1
## n_non_stop_unique_tokens 0.2773 1.400830e+01 1
## num_hrefs 0.7675 1.828900e+00 1
## num_self_hrefs 0.8766 1.401900e+00 1
## num_imgs 0.5901 3.093100e+00 1
## num_videos 0.9438 1.209400e+00 1
## average_token_length 0.4097 6.417700e+00 1
## num_keywords 0.8196 1.603700e+00 1
## kw_min_min 0.5129 4.094400e+00 1
## kw_max_min 0.2193 2.240000e+01 1
## kw_avg_min 0.2162 2.303540e+01 1
## kw_min_max 0.7325 2.007800e+00 1
## kw_max_max 0.4326 5.757000e+00 1
## kw_avg_max 0.4187 6.143800e+00 1
## kw_min_avg 0.6156 2.842800e+00 1
## kw_max_avg 0.3738 7.708900e+00 1
## kw_avg_avg 0.3144 1.089890e+01 1
## self_reference_min_shares 0.2903 1.277830e+01 1
## self_reference_max_shares 0.1714 3.667370e+01 1
## self_reference_avg_sharess 0.1272 6.656500e+01 1
## is_weekend 0.9399 1.219400e+00 1
## LDA_00 0.0000 Inf 1
## LDA_01 0.0000 Inf 1
## LDA_02 0.0000 Inf 1
## LDA_03 0.0000 Inf 1
## LDA_04 0.0000 Inf 1
## global_subjectivity 0.6314 2.701800e+00 1
## global_sentiment_polarity 0.3495 8.817900e+00 1
## global_rate_positive_words 0.4710 4.855700e+00 1
## global_rate_negative_words 0.3589 8.362800e+00 1
## rate_positive_words 0.0000 Inf 1
## rate_negative_words 0.0000 9.702715e+15 1
## avg_positive_polarity 0.4469 5.394100e+00 1
## min_positive_polarity 0.7526 1.901600e+00 1
## max_positive_polarity 0.5952 3.040700e+00 1
## avg_negative_polarity 0.3929 6.976600e+00 1
## min_negative_polarity 0.4798 4.680000e+00 1
## max_negative_polarity 0.5556 3.489600e+00 1
## title_subjectivity 0.6496 2.552800e+00 1
## title_sentiment_polarity 0.7712 1.811200e+00 1
## abs_title_subjectivity 0.8113 1.636500e+00 1
## abs_title_sentiment_polarity 0.6070 2.923900e+00 1
## IND1 IND2
## timedelta 0.0092 0.9615
## n_tokens_title 0.0263 0.1752
## n_tokens_content 0.0091 0.9618
## n_unique_tokens 0.0020 1.2889
## n_non_stop_words 0.0000 1.3804
## n_non_stop_unique_tokens 0.0023 1.2742
## num_hrefs 0.0178 0.5673
## num_self_hrefs 0.0232 0.3197
## num_imgs 0.0105 0.8996
## num_videos 0.0269 0.1509
## average_token_length 0.0051 1.1487
## num_keywords 0.0203 0.4532
## kw_min_min 0.0079 1.0172
## kw_max_min 0.0015 1.3140
## kw_avg_min 0.0014 1.3158
## kw_min_max 0.0162 0.6398
## kw_max_max 0.0056 1.1221
## kw_avg_max 0.0053 1.1383
## kw_min_avg 0.0114 0.8573
## kw_max_avg 0.0042 1.1875
## kw_avg_avg 0.0030 1.2439
## self_reference_min_shares 0.0025 1.2640
## self_reference_max_shares 0.0009 1.3398
## self_reference_avg_sharess 0.0005 1.3580
## is_weekend 0.0267 0.1609
## LDA_00 0.0000 1.3804
## LDA_01 0.0000 1.3804
## LDA_02 0.0000 1.3804
## LDA_03 0.0000 1.3804
## LDA_04 0.0000 1.3804
## global_subjectivity 0.0120 0.8300
## global_sentiment_polarity 0.0037 1.2117
## global_rate_positive_words 0.0067 1.0741
## global_rate_negative_words 0.0039 1.2025
## rate_positive_words 0.0000 1.3804
## rate_negative_words 0.0000 1.3804
## avg_positive_polarity 0.0060 1.1047
## min_positive_polarity 0.0171 0.5984
## max_positive_polarity 0.0107 0.8913
## avg_negative_polarity 0.0047 1.1672
## min_negative_polarity 0.0069 1.0626
## max_negative_polarity 0.0093 0.9542
## title_subjectivity 0.0127 0.7979
## title_sentiment_polarity 0.0179 0.5594
## abs_title_subjectivity 0.0199 0.4717
## abs_title_sentiment_polarity 0.0111 0.8718
##
## 1 --> COLLINEARITY is detected by the test
## 0 --> COLLINEARITY is not detected by the test
##
## n_tokens_title , n_tokens_content , n_unique_tokens , n_non_stop_unique_tokens , num_hrefs , num_self_hrefs , average_token_length , num_keywords , kw_min_min , kw_max_min , kw_avg_min , kw_min_max , kw_max_max , kw_avg_max , kw_min_avg , self_reference_max_shares , self_reference_avg_sharess , LDA_00 , LDA_01 , LDA_02 , LDA_03 , LDA_04 , global_subjectivity , global_sentiment_polarity , global_rate_positive_words , global_rate_negative_words , rate_positive_words , avg_positive_polarity , min_positive_polarity , max_positive_polarity , avg_negative_polarity , min_negative_polarity , max_negative_polarity , title_subjectivity , title_sentiment_polarity , coefficient(s) are non-significant may be due to multicollinearity
##
## R-square of y on all x: 0.1038
##
## * use method argument to check which regressors may be the reason of collinearity
## ===================================Looking at all of the VIF values, we are going to start by removing all of the LDA Values, and the positive word rate to remove all “infinite” VIF values.
First Multicolinearity Trim
The mctest package was used to calculate the VIF values of multicolinearity.
toRemove<-c( "LDA_01", "LDA_02", "LDA_03", "LDA_04", "rate_positive_words")
trimTrain1 <- newTrain[, ! names(newTrain) %in% toRemove, drop = F]
lmNewTest3<-lmNewTest[, ! names(newTrain) %in% toRemove, drop = F]
#Repeat linear Model process
lm3<- lm(log(shares)~., trimTrain1)
yhat_lm3<-predict(lm3,lmNewTest3)
RMSE_lm3<-sqrt(mean((lmNewTest3$shares - exp(yhat_lm3))^2))
imcdiag(lm3)##
## Call:
## imcdiag(mod = lm3)
##
##
## All Individual Multicollinearity Diagnostics Result
##
## VIF TOL Wi
## timedelta 3.2699 0.3058 81.0364
## n_tokens_title 1.1414 0.8761 5.0475
## n_tokens_content 3.2836 0.3045 81.5259
## n_unique_tokens 14.8633 0.0673 494.9185
## n_non_stop_words 8.7883 0.1138 278.0435
## n_non_stop_unique_tokens 12.9177 0.0774 425.4610
## num_hrefs 1.6628 0.6014 23.6631
## num_self_hrefs 1.2777 0.7826 9.9150
## num_imgs 2.6940 0.3712 60.4747
## num_videos 1.1015 0.9079 3.6218
## average_token_length 5.8274 0.1716 172.3376
## num_keywords 1.4467 0.6912 15.9478
## kw_min_min 3.7898 0.2639 99.5961
## kw_max_min 20.5350 0.0487 697.3991
## kw_avg_min 21.0562 0.0475 716.0054
## kw_min_max 1.8457 0.5418 30.1913
## kw_max_max 5.1766 0.1932 149.1035
## kw_avg_max 5.4687 0.1829 159.5309
## kw_min_avg 2.5959 0.3852 56.9745
## kw_max_avg 6.9219 0.1445 211.4109
## kw_avg_avg 9.4362 0.1060 301.1732
## self_reference_min_shares 11.8401 0.0845 386.9910
## self_reference_max_shares 34.0382 0.0294 1179.4627
## self_reference_avg_sharess 61.7741 0.0162 2169.6349
## is_weekend 1.1259 0.8881 4.4959
## LDA_00 1.0808 0.9252 2.8848
## global_subjectivity 2.4784 0.4035 52.7806
## global_sentiment_polarity 8.1764 0.1223 256.1982
## global_rate_positive_words 4.4920 0.2226 124.6634
## global_rate_negative_words 7.7206 0.1295 239.9259
## rate_negative_words 10.4657 0.0956 337.9239
## avg_positive_polarity 5.0049 0.1998 142.9765
## min_positive_polarity 1.7589 0.5685 27.0922
## max_positive_polarity 2.8101 0.3559 64.6221
## avg_negative_polarity 6.4400 0.1553 194.2086
## min_negative_polarity 4.3363 0.2306 119.1073
## max_negative_polarity 3.2259 0.3100 79.4645
## title_subjectivity 2.3690 0.4221 48.8717
## title_sentiment_polarity 1.6788 0.5956 24.2347
## abs_title_subjectivity 1.5120 0.6614 18.2782
## abs_title_sentiment_polarity 2.7087 0.3692 61.0014
## Fi Leamer CVIF
## timedelta 83.1724 0.5530 3.4432
## n_tokens_title 5.1806 0.9360 1.2019
## n_tokens_content 83.6749 0.5519 3.4576
## n_unique_tokens 507.9642 0.2594 15.6507
## n_non_stop_words 285.3725 0.3373 9.2539
## n_non_stop_unique_tokens 436.6759 0.2782 13.6020
## num_hrefs 24.2869 0.7755 1.7509
## num_self_hrefs 10.1764 0.8847 1.3454
## num_imgs 62.0688 0.6093 2.8367
## num_videos 3.7172 0.9528 1.1598
## average_token_length 176.8803 0.4143 6.1361
## num_keywords 16.3682 0.8314 1.5234
## kw_min_min 102.2214 0.5137 3.9906
## kw_max_min 715.7820 0.2207 21.6229
## kw_avg_min 734.8788 0.2179 22.1717
## kw_min_max 30.9871 0.7361 1.9435
## kw_max_max 153.0338 0.4395 5.4508
## kw_avg_max 163.7360 0.4276 5.7584
## kw_min_avg 58.4763 0.6207 2.7335
## kw_max_avg 216.9836 0.3801 7.2886
## kw_avg_avg 309.1119 0.3255 9.9361
## self_reference_min_shares 397.1918 0.2906 12.4674
## self_reference_max_shares 1210.5524 0.1714 35.8415
## self_reference_avg_sharess 2226.8249 0.1272 65.0468
## is_weekend 4.6145 0.9424 1.1856
## LDA_00 2.9609 0.9619 1.1381
## global_subjectivity 54.1719 0.6352 2.6098
## global_sentiment_polarity 262.9514 0.3497 8.6096
## global_rate_positive_words 127.9495 0.4718 4.7300
## global_rate_negative_words 246.2502 0.3599 8.1296
## rate_negative_words 346.8313 0.3091 11.0201
## avg_positive_polarity 146.7453 0.4470 5.2701
## min_positive_polarity 27.8063 0.7540 1.8521
## max_positive_polarity 66.3255 0.5965 2.9590
## avg_negative_polarity 199.3278 0.3941 6.7812
## min_negative_polarity 122.2469 0.4802 4.5661
## max_negative_polarity 81.5591 0.5568 3.3968
## title_subjectivity 50.1599 0.6497 2.4945
## title_sentiment_polarity 24.8735 0.7718 1.7678
## abs_title_subjectivity 18.7600 0.8133 1.5921
## abs_title_sentiment_polarity 62.6093 0.6076 2.8522
## Klein IND1 IND2
## timedelta 1 0.0086 1.0529
## n_tokens_title 1 0.0245 0.1879
## n_tokens_content 1 0.0085 1.0549
## n_unique_tokens 1 0.0019 1.4148
## n_non_stop_words 1 0.0032 1.3442
## n_non_stop_unique_tokens 1 0.0022 1.3994
## num_hrefs 1 0.0168 0.6046
## num_self_hrefs 1 0.0219 0.3297
## num_imgs 1 0.0104 0.9538
## num_videos 0 0.0254 0.1397
## average_token_length 1 0.0048 1.2565
## num_keywords 1 0.0194 0.4684
## kw_min_min 1 0.0074 1.1166
## kw_max_min 1 0.0014 1.4430
## kw_avg_min 1 0.0013 1.4448
## kw_min_max 1 0.0152 0.6950
## kw_max_max 1 0.0054 1.2238
## kw_avg_max 1 0.0051 1.2395
## kw_min_avg 1 0.0108 0.9325
## kw_max_avg 1 0.0040 1.2977
## kw_avg_avg 1 0.0030 1.3561
## self_reference_min_shares 1 0.0024 1.3887
## self_reference_max_shares 1 0.0008 1.4723
## self_reference_avg_sharess 1 0.0005 1.4923
## is_weekend 1 0.0249 0.1697
## LDA_00 0 0.0259 0.1134
## global_subjectivity 1 0.0113 0.9048
## global_sentiment_polarity 1 0.0034 1.3313
## global_rate_positive_words 1 0.0062 1.1791
## global_rate_negative_words 1 0.0036 1.3204
## rate_negative_words 1 0.0027 1.3719
## avg_positive_polarity 1 0.0056 1.2138
## min_positive_polarity 1 0.0159 0.6544
## max_positive_polarity 1 0.0100 0.9771
## avg_negative_polarity 1 0.0043 1.2813
## min_negative_polarity 1 0.0065 1.1670
## max_negative_polarity 1 0.0087 1.0466
## title_subjectivity 1 0.0118 0.8765
## title_sentiment_polarity 1 0.0167 0.6133
## abs_title_subjectivity 1 0.0185 0.5136
## abs_title_sentiment_polarity 1 0.0103 0.9568
##
## 1 --> COLLINEARITY is detected by the test
## 0 --> COLLINEARITY is not detected by the test
##
## n_tokens_title , n_tokens_content , n_unique_tokens , n_non_stop_unique_tokens , num_hrefs , num_self_hrefs , average_token_length , num_keywords , kw_min_min , kw_max_min , kw_avg_min , kw_min_max , kw_max_max , kw_avg_max , kw_min_avg , self_reference_max_shares , self_reference_avg_sharess , LDA_00 , global_subjectivity , global_sentiment_polarity , global_rate_positive_words , global_rate_negative_words , rate_negative_words , avg_positive_polarity , max_positive_polarity , avg_negative_polarity , min_negative_polarity , max_negative_polarity , title_subjectivity , title_sentiment_polarity , abs_title_subjectivity , abs_title_sentiment_polarity , coefficient(s) are non-significant may be due to multicollinearity
##
## R-square of y on all x: 0.102
##
## * use method argument to check which regressors may be the reason of collinearity
## ===================================This improves the model multicolinearity, but we are still left with some. We then pare down and select those models with the next highest VIF removed one at a time, until all values are below 5.
Second Mulitcolinearity Trim
toRemove<-c("self_reference_avg_sharess", "kw_avg_min", "n_unique_tokens", "rate_negative_words", "kw_avg_avg", "n_non_stop_words", "global_sentiment_polarity", "avg_negative_polarity", "kw_max_max")
trimTrain2 <- trimTrain1[, ! names(trimTrain1) %in% toRemove, drop = F]
#Repeat linear Model process
lm4<- lm(log(shares)~., trimTrain2)
imcdiag(lm4)##
## Call:
## imcdiag(mod = lm4)
##
##
## All Individual Multicollinearity Diagnostics Result
##
## VIF TOL Wi
## timedelta 3.1261 0.3199 98.5571
## n_tokens_title 1.1293 0.8855 5.9946
## n_tokens_content 2.1811 0.4585 54.7488
## n_non_stop_unique_tokens 2.5044 0.3993 69.7360
## num_hrefs 1.6451 0.6079 29.9020
## num_self_hrefs 1.2170 0.8217 10.0603
## num_imgs 2.0991 0.4764 50.9478
## num_videos 1.0844 0.9221 3.9146
## average_token_length 2.0090 0.4978 46.7702
## num_keywords 1.3784 0.7255 17.5397
## kw_min_min 2.0783 0.4812 49.9863
## kw_max_min 1.8482 0.5411 39.3180
## kw_min_max 1.8004 0.5554 37.1028
## kw_avg_max 4.1915 0.2386 147.9433
## kw_min_avg 1.8070 0.5534 37.4063
## kw_max_avg 1.9736 0.5067 45.1306
## self_reference_min_shares 1.4124 0.7080 19.1161
## self_reference_max_shares 1.3616 0.7344 16.7635
## is_weekend 1.1131 0.8984 5.2415
## LDA_00 1.0769 0.9286 3.5627
## global_subjectivity 2.0956 0.4772 50.7878
## global_rate_positive_words 1.4562 0.6867 21.1460
## global_rate_negative_words 1.4788 0.6762 22.1926
## avg_positive_polarity 3.1148 0.3210 98.0319
## min_positive_polarity 1.6464 0.6074 29.9648
## max_positive_polarity 2.6356 0.3794 75.8169
## min_negative_polarity 1.7657 0.5663 35.4938
## max_negative_polarity 1.2841 0.7788 13.1680
## title_subjectivity 2.3469 0.4261 62.4332
## title_sentiment_polarity 1.6307 0.6133 29.2339
## abs_title_subjectivity 1.5049 0.6645 23.4056
## abs_title_sentiment_polarity 2.6650 0.3752 77.1814
## Fi Leamer CVIF
## timedelta 101.9132 0.5656 3.2184
## n_tokens_title 6.1987 0.9410 1.1626
## n_tokens_content 56.6132 0.6771 2.2454
## n_non_stop_unique_tokens 72.1107 0.6319 2.5783
## num_hrefs 30.9203 0.7797 1.6936
## num_self_hrefs 10.4029 0.9065 1.2529
## num_imgs 52.6826 0.6902 2.1610
## num_videos 4.0479 0.9603 1.1164
## average_token_length 48.3628 0.7055 2.0682
## num_keywords 18.1370 0.8518 1.4190
## kw_min_min 51.6884 0.6937 2.1397
## kw_max_min 40.6569 0.7356 1.9027
## kw_min_max 38.3663 0.7453 1.8535
## kw_avg_max 152.9812 0.4884 4.3152
## kw_min_avg 38.6801 0.7439 1.8603
## kw_max_avg 46.6674 0.7118 2.0318
## self_reference_min_shares 19.7671 0.8414 1.4541
## self_reference_max_shares 17.3343 0.8570 1.4018
## is_weekend 5.4200 0.9478 1.1459
## LDA_00 3.6840 0.9637 1.1086
## global_subjectivity 52.5173 0.6908 2.1575
## global_rate_positive_words 21.8661 0.8287 1.4991
## global_rate_negative_words 22.9483 0.8223 1.5224
## avg_positive_polarity 101.3701 0.5666 3.2067
## min_positive_polarity 30.9851 0.7793 1.6950
## max_positive_polarity 78.3986 0.6160 2.7133
## min_negative_polarity 36.7025 0.7526 1.8178
## max_negative_polarity 13.6164 0.8825 1.3220
## title_subjectivity 64.5592 0.6528 2.4161
## title_sentiment_polarity 30.2294 0.7831 1.6788
## abs_title_subjectivity 24.2026 0.8152 1.5493
## abs_title_sentiment_polarity 79.8096 0.6126 2.7436
## Klein IND1 IND2
## timedelta 1 0.0069 1.6528
## n_tokens_title 1 0.0191 0.2783
## n_tokens_content 1 0.0099 1.3160
## n_non_stop_unique_tokens 1 0.0086 1.4598
## num_hrefs 1 0.0131 0.9529
## num_self_hrefs 1 0.0177 0.4334
## num_imgs 1 0.0103 1.2725
## num_videos 0 0.0199 0.1892
## average_token_length 1 0.0107 1.2205
## num_keywords 1 0.0157 0.6671
## kw_min_min 1 0.0104 1.2609
## kw_max_min 1 0.0117 1.1153
## kw_min_max 1 0.0120 1.0804
## kw_avg_max 1 0.0051 1.8504
## kw_min_avg 1 0.0119 1.0853
## kw_max_avg 1 0.0109 1.1989
## self_reference_min_shares 1 0.0153 0.7096
## self_reference_max_shares 1 0.0158 0.6454
## is_weekend 1 0.0194 0.2469
## LDA_00 0 0.0200 0.1734
## global_subjectivity 1 0.0103 1.2706
## global_rate_positive_words 1 0.0148 0.7613
## global_rate_negative_words 1 0.0146 0.7868
## avg_positive_polarity 1 0.0069 1.6500
## min_positive_polarity 1 0.0131 0.9542
## max_positive_polarity 1 0.0082 1.5081
## min_negative_polarity 1 0.0122 1.0539
## max_negative_polarity 1 0.0168 0.5376
## title_subjectivity 1 0.0092 1.3947
## title_sentiment_polarity 1 0.0132 0.9399
## abs_title_subjectivity 1 0.0143 0.8154
## abs_title_sentiment_polarity 1 0.0081 1.5183
##
## 1 --> COLLINEARITY is detected by the test
## 0 --> COLLINEARITY is not detected by the test
##
## n_tokens_title , n_tokens_content , n_non_stop_unique_tokens , num_self_hrefs , average_token_length , num_keywords , kw_min_min , kw_max_min , kw_min_max , kw_avg_max , kw_min_avg , kw_max_avg , self_reference_max_shares , LDA_00 , global_subjectivity , global_rate_positive_words , global_rate_negative_words , avg_positive_polarity , max_positive_polarity , max_negative_polarity , title_subjectivity , title_sentiment_polarity , abs_title_subjectivity , abs_title_sentiment_polarity , coefficient(s) are non-significant may be due to multicollinearity
##
## R-square of y on all x: 0.0813
##
## * use method argument to check which regressors may be the reason of collinearity
## ===================================After removing 15 more variables for obvious multicolinearity via VIF (>5), we need to replot the correlation matrix, which shows a much lower clustering rate of high correlations.
Replot Correlation
#Remove the predictor
train_cor<-trimTrain2[1:31]
res <- cor(train_cor)
palette = colorRampPalette(c("green", "white", "red")) (20)
heatmap(x = res, col = palette, symm = TRUE, cexRow=0.5, cexCol = 0.5)
The new heatmap appears to have less prominent clustering values.
Final Model Fit Prediction
#trim the testing data
newTest1<-test[ -c(25:31) ]
toRemove<-c( "LDA_01", "LDA_02", "LDA_03", "LDA_04", "rate_positive_words", "self_reference_avg_sharess", "kw_avg_min", "n_unique_tokens", "rate_negative_words", "kw_avg_avg", "n_non_stop_words", "global_sentiment_polarity", "avg_negative_polarity", "kw_max_max")
trimTest4 <- newTest1[, ! names(newTest1) %in% toRemove, drop = F]
yhat_lm4<-predict(lm4,trimTest4)
RMSE_lm4<-sqrt(mean((trimTest4$shares - exp(yhat_lm4))^2))Backward Regression Selection
Transform the response with log, then fit a linear regression model with the variables after backward selection.
#backward selection after log transformation
library(leaps)
backward<- regsubsets(log(shares)~., trimTrain1, nvmax = 31, method = "backward")
backward_summary<-summary(backward)
#backward_summary[["which"]][size, ]
par(mfrow=c(1,3))
plot(backward_summary$cp, xlab = "Size", ylab = "backward Cp", type = "l")
plot(backward_summary$bic, xlab = "Size", ylab = "backward bic", type = "l")
plot(backward_summary$adjr2, xlab = "Size", ylab = "backward adjR2", type = "l")
coef(backward, which.min(backward_summary$cp))## (Intercept) timedelta
## 7.484522e+00 6.530856e-04
## n_non_stop_words num_hrefs
## -9.269018e-01 5.345769e-03
## num_imgs num_videos
## 1.063025e-02 4.352489e-02
## kw_max_avg kw_avg_avg
## -2.646323e-05 1.914506e-04
## self_reference_min_shares is_weekend
## 7.230813e-06 2.108812e-01
## global_sentiment_polarity global_rate_positive_words
## -1.392669e+00 5.976567e+00
## min_positive_polarity title_sentiment_polarity
## 6.126773e-01 -1.434343e-01coef(backward, which.max(backward_summary$adjr2))## (Intercept) timedelta
## 7.227471e+00 6.894014e-04
## n_unique_tokens n_non_stop_words
## -1.081231e+00 -2.016536e+00
## n_non_stop_unique_tokens num_hrefs
## 1.135138e+00 4.220366e-03
## num_imgs num_videos
## 1.185756e-02 4.047826e-02
## average_token_length num_keywords
## 1.701021e-01 2.298952e-02
## kw_max_avg kw_avg_avg
## -2.869676e-05 2.016231e-04
## self_reference_min_shares self_reference_avg_sharess
## 1.084693e-05 -3.029088e-06
## is_weekend LDA_00
## 2.230891e-01 1.266156e-01
## global_sentiment_polarity global_rate_positive_words
## -1.170166e+00 5.246845e+00
## min_positive_polarity min_negative_polarity
## 8.984881e-01 -1.477351e-01
## title_sentiment_polarity
## -1.508617e-01#get best subset of the specified size with min cp.
sub <- backward_summary$which[which.min(backward_summary$cp), ]
# Create test model matrix, predcition, test error
test_model <- model.matrix(log(shares)~ ., data = lmNewTest3)
model <- test_model[, sub]
yhat_back<-model %*% coef(backward, which.min(backward_summary$cp))
RMSE_back<-sqrt(mean((test$shares - exp(yhat_back))^2))Random Forests
As previously mentioned in the regression trees section, the random forest builds an entire forest of these trees, and merges them together to get a more accurate and stable predictions than one off trees. It is usually trained using the bagging method. Unlike regression trees, which are prone to overfitting, only a random subset of the features is taken into consideration by the algorithm for splitting a node (used CV to find the perfect amount of variables to use). This builds in additional error and makes a more robust prediction.
The manual dimensional reduction was necessary to have the processing speeds to handle the random forests model.
library(randomForest)
#single bagged model
tree.train<-randomForest(shares~., data=trimTrain1, mtry=32, importance=TRUE)
tree.train##
## Call:
## randomForest(formula = shares ~ ., data = trimTrain1, mtry = 32, importance = TRUE)
## Type of random forest: regression
## Number of trees: 500
## No. of variables tried at each split: 32
##
## Mean of squared residuals: 113382819
## % Var explained: -20.57#single bagged regression tree error prediction
tree.test<-lmNewTest3["shares"]
yhat.bag<-predict(tree.train, newdata=lmNewTest3)
yhat.bag<-as.data.frame(yhat.bag)
yhat_bag<-mean((yhat.bag$yhat.bag-tree.test$shares)^2)
RMSE_bag<-sqrt(yhat_bag)
#random forests model
tree.trainRF<-randomForest(shares~., data=trimTrain1, mtry=12, importance=TRUE)
tree.trainRF##
## Call:
## randomForest(formula = shares ~ ., data = trimTrain1, mtry = 12, importance = TRUE)
## Type of random forest: regression
## Number of trees: 500
## No. of variables tried at each split: 12
##
## Mean of squared residuals: 101170138
## % Var explained: -7.58#random forest error prediction
yhat.rf<-predict(tree.trainRF, newdata = lmNewTest3)
yhat.rf<-as.data.frame(yhat.rf)
yhat_rf<-mean((yhat.rf$yhat.rf-tree.test$shares)^2)
RMSE_rfTrimmed<-sqrt(yhat_rf)
varImpPlot(tree.trainRF)
Boosted Tree
Boosting is a general approach that can be applied to many statistical learning methods for regression or classification. The trees in boosting are grown sequentially : each tree is grown using information from previously grown trees. Boosting does not involve bootstrap sampling; instead each tree is fit on a modified version of the original data set.
Procedure (for regression trees):
1.Initialize predictions as 0,
2.Find the residuals (observed-predicted), call the set of them
3.Fit a tree with splits (d+1 terminal nodes) treating the residuals as the response (which they are for the first fit)
4.Update predictions
5.Update residuals for new predictions and repeat B times
Tune parameters must be chosen shrinkage, B and d in the boosting tree model.
cvcontrol <- trainControl(method="repeatedcv", number = 10,
allowParallel=TRUE)
grid <- expand.grid(n.trees = c(1000,1500),
interaction.depth=c(1:3),
shrinkage=c(0.01,0.05,0.1),
n.minobsinnode=c(20))
capture<-capture.output(train.gbm <- train(log(shares) ~ .,
data=train,
method="gbm",
trControl=cvcontrol,
tuneGrid = grid))
train.gbm## Stochastic Gradient Boosting
##
## 1469 samples
## 53 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 1323, 1322, 1323, 1321, 1323, 1322, ...
## Resampling results across tuning parameters:
##
## shrinkage interaction.depth n.trees RMSE
## 0.01 1 1000 0.9237667
## 0.01 1 1500 0.9258402
## 0.01 2 1000 0.9250762
## 0.01 2 1500 0.9281214
## 0.01 3 1000 0.9231966
## 0.01 3 1500 0.9261154
## 0.05 1 1000 0.9412686
## 0.05 1 1500 0.9485568
## 0.05 2 1000 0.9528973
## 0.05 2 1500 0.9642633
## 0.05 3 1000 0.9638626
## 0.05 3 1500 0.9771778
## 0.10 1 1000 0.9564422
## 0.10 1 1500 0.9688196
## 0.10 2 1000 0.9856722
## 0.10 2 1500 1.0017541
## 0.10 3 1000 0.9971562
## 0.10 3 1500 1.0110305
## Rsquared MAE
## 0.03977513 0.7003342
## 0.03912668 0.7001502
## 0.04119647 0.6992808
## 0.04153391 0.7003171
## 0.04693402 0.6962659
## 0.04812201 0.6978224
## 0.03803374 0.7120079
## 0.03745736 0.7163856
## 0.03907406 0.7185559
## 0.03754556 0.7305598
## 0.03744277 0.7295671
## 0.03547716 0.7425868
## 0.03795484 0.7248907
## 0.03629342 0.7354428
## 0.03275410 0.7517526
## 0.03016025 0.7629391
## 0.03346575 0.7585675
## 0.03276467 0.7713565
##
## Tuning parameter 'n.minobsinnode' was held constant at
## a value of 20
## RMSE was used to select the optimal model using
## the smallest value.
## The final values used for the model were n.trees =
## 1000, interaction.depth = 3, shrinkage = 0.01
## and n.minobsinnode = 20.boostPred <- predict(train.gbm, newdata = test)
RMSE_boost <- sqrt(mean((test$shares - exp(boostPred))^2))Comparison
Generally, the model with the lowest RMSE is the best on comparison.
comparison<-data.frame(RMSE_lm, RMSE_lm2, RMSE_lm3, RMSE_lm4, RMSE_back, RMSE_bag, RMSE_rfTrimmed, RMSE_boost, RMSE_regTree)
comparison ## RMSE_lm RMSE_lm2 RMSE_lm3 RMSE_lm4 RMSE_back RMSE_bag
## 1 6715.992 6694.652 6665.73 6709.166 6726.546 8423.705
## RMSE_rfTrimmed RMSE_boost RMSE_regTree
## 1 7197.748 6644.584 7352.023which.min(comparison)## RMSE_boost
## 8The overall prediction error rate for this data set is very high. This is likely due to the high values of outlier articles with freakishly high shares, that are timely AND viral. These values were NOT removed from analysis, as these are the share metrics that a company would likely want to evaluate for emulation.