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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 | 2227 | 6305 | 1100 | 954 |
| monday | 2284 | 5829 | 1100 | 984 |
| saturday | 2913 | 5393 | 1600 | 1600 |
| sunday | 2357 | 2774 | 1400 | 1200 |
| thursday | 2211 | 4870 | 1100 | 914 |
| tuesday | 2127 | 4741 | 1100 | 937 |
| wednesday | 1891 | 2995 | 1100 | 911 |
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_imgs" "average_token_length"
## [3] "avg_negative_polarity" "LDA_02"
## [5] "LDA_01"
## Number of terminal nodes: 7
## Residual mean deviance: 21430000 = 1.262e+11 / 5891
## Distribution of residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -32680.0 -1167.0 -848.2 0.0 -201.1 138100.0plot(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
## -3.4318 -0.4428 -0.1150 0.2926 4.5366
##
## Coefficients: (4 not defined because of singularities)
## Estimate Std. Error
## (Intercept) 6.929e+00 1.725e-01
## timedelta 4.249e-05 7.046e-05
## n_tokens_title 1.207e-02 5.196e-03
## n_tokens_content -1.022e-05 4.431e-05
## n_unique_tokens 4.999e-01 3.946e-01
## n_non_stop_words 1.183e+00 3.180e-01
## n_non_stop_unique_tokens -5.029e-01 3.300e-01
## num_hrefs 7.042e-03 1.351e-03
## num_self_hrefs 4.730e-03 4.290e-03
## num_imgs 1.274e-02 2.317e-03
## num_videos 1.907e-02 7.274e-03
## average_token_length -3.665e-01 4.905e-02
## num_keywords -3.081e-03 6.790e-03
## kw_min_min 1.297e-03 3.770e-04
## kw_max_min 3.305e-06 1.292e-05
## kw_avg_min -9.782e-06 8.535e-05
## kw_min_max -8.005e-07 7.249e-07
## kw_max_max 2.864e-07 1.358e-07
## kw_avg_max -5.764e-07 1.916e-07
## kw_min_avg -6.469e-05 1.836e-05
## kw_max_avg -4.243e-05 6.333e-06
## kw_avg_avg 3.263e-04 3.319e-05
## self_reference_min_shares -8.470e-06 2.961e-06
## self_reference_max_shares -4.066e-06 1.574e-06
## self_reference_avg_sharess 1.427e-05 4.305e-06
## weekday_is_monday -2.499e-01 4.636e-02
## weekday_is_tuesday -3.062e-01 4.561e-02
## weekday_is_wednesday -3.002e-01 4.560e-02
## weekday_is_thursday -2.886e-01 4.556e-02
## weekday_is_friday -2.440e-01 4.680e-02
## weekday_is_saturday 4.363e-02 5.642e-02
## weekday_is_sunday NA NA
## is_weekend NA NA
## LDA_00 3.419e-01 1.145e-01
## LDA_01 -2.132e-01 1.361e-01
## LDA_02 -2.464e-01 6.690e-02
## LDA_03 -4.818e-02 1.119e-01
## LDA_04 NA NA
## global_subjectivity 5.229e-01 1.594e-01
## global_sentiment_polarity -1.723e-01 3.677e-01
## global_rate_positive_words 7.561e-02 1.706e+00
## global_rate_negative_words 1.707e+00 2.903e+00
## rate_positive_words 2.455e-01 2.145e-01
## rate_negative_words NA NA
## avg_positive_polarity -3.594e-02 2.522e-01
## min_positive_polarity 7.066e-02 2.270e-01
## max_positive_polarity -8.266e-02 7.502e-02
## avg_negative_polarity 1.368e-01 2.140e-01
## min_negative_polarity 2.276e-02 7.355e-02
## max_negative_polarity -3.293e-01 2.044e-01
## title_subjectivity 8.410e-02 5.207e-02
## title_sentiment_polarity 1.349e-01 4.491e-02
## abs_title_subjectivity 1.483e-01 6.785e-02
## abs_title_sentiment_polarity 4.200e-02 7.478e-02
## t value Pr(>|t|)
## (Intercept) 40.178 < 2e-16 ***
## timedelta 0.603 0.546503
## n_tokens_title 2.323 0.020232 *
## n_tokens_content -0.231 0.817517
## n_unique_tokens 1.267 0.205259
## n_non_stop_words 3.720 0.000201 ***
## n_non_stop_unique_tokens -1.524 0.127576
## num_hrefs 5.213 1.92e-07 ***
## num_self_hrefs 1.102 0.270303
## num_imgs 5.500 3.96e-08 ***
## num_videos 2.621 0.008787 **
## average_token_length -7.471 9.14e-14 ***
## num_keywords -0.454 0.650037
## kw_min_min 3.441 0.000583 ***
## kw_max_min 0.256 0.798128
## kw_avg_min -0.115 0.908759
## kw_min_max -1.104 0.269505
## kw_max_max 2.109 0.034950 *
## kw_avg_max -3.008 0.002638 **
## kw_min_avg -3.523 0.000430 ***
## kw_max_avg -6.699 2.29e-11 ***
## kw_avg_avg 9.830 < 2e-16 ***
## self_reference_min_shares -2.860 0.004250 **
## self_reference_max_shares -2.583 0.009822 **
## self_reference_avg_sharess 3.316 0.000920 ***
## weekday_is_monday -5.391 7.28e-08 ***
## weekday_is_tuesday -6.715 2.06e-11 ***
## weekday_is_wednesday -6.584 4.97e-11 ***
## weekday_is_thursday -6.335 2.55e-10 ***
## weekday_is_friday -5.212 1.93e-07 ***
## weekday_is_saturday 0.773 0.439344
## weekday_is_sunday NA NA
## is_weekend NA NA
## LDA_00 2.988 0.002824 **
## LDA_01 -1.566 0.117319
## LDA_02 -3.684 0.000232 ***
## LDA_03 -0.431 0.666708
## LDA_04 NA NA
## global_subjectivity 3.280 0.001044 **
## global_sentiment_polarity -0.469 0.639317
## global_rate_positive_words 0.044 0.964645
## global_rate_negative_words 0.588 0.556626
## rate_positive_words 1.145 0.252434
## rate_negative_words NA NA
## avg_positive_polarity -0.143 0.886667
## min_positive_polarity 0.311 0.755630
## max_positive_polarity -1.102 0.270595
## avg_negative_polarity 0.639 0.522729
## min_negative_polarity 0.309 0.756976
## max_negative_polarity -1.611 0.107229
## title_subjectivity 1.615 0.106337
## title_sentiment_polarity 3.004 0.002673 **
## abs_title_subjectivity 2.185 0.028924 *
## abs_title_sentiment_polarity 0.562 0.574392
## ---
## Signif. codes:
## 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7771 on 5848 degrees of freedom
## Multiple R-squared: 0.1161, Adjusted R-squared: 0.1087
## F-statistic: 15.67 on 49 and 5848 DF, p-value: < 2.2e-16yhat_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: NaN NA
## Red Indicator: 1.835000e-01 0
## Sum of Lambda Inverse: -2.117766e+14 0
## Theil's Method: 2.692120e+01 1
## Condition Number: 1.170127e+09 1
##
## 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 2.024200e+00 0.4940
## n_tokens_title 1.128600e+00 0.8861
## n_tokens_content 3.397500e+00 0.2943
## n_unique_tokens 2.308410e+01 0.0433
## n_non_stop_words 9.007199e+15 0.0000
## n_non_stop_unique_tokens 2.240020e+01 0.0446
## num_hrefs 1.527600e+00 0.6546
## num_self_hrefs 1.246800e+00 0.8021
## num_imgs 1.419700e+00 0.7044
## num_videos 1.101100e+00 0.9082
## average_token_length 1.733450e+01 0.0577
## num_keywords 1.613700e+00 0.6197
## kw_min_min 4.319200e+00 0.2315
## kw_max_min 1.823890e+01 0.0548
## kw_avg_min 1.727100e+01 0.0579
## kw_min_max 1.660100e+00 0.6024
## kw_max_max 5.385300e+00 0.1857
## kw_avg_max 2.790900e+00 0.3583
## kw_min_avg 2.385500e+00 0.4192
## kw_max_avg 7.479000e+00 0.1337
## kw_avg_avg 7.769400e+00 0.1287
## self_reference_min_shares 1.641230e+01 0.0609
## self_reference_max_shares 1.451010e+01 0.0689
## self_reference_avg_sharess 4.460790e+01 0.0224
## is_weekend 1.020600e+00 0.9798
## 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 2.818700e+00 0.3548
## global_sentiment_polarity 8.898600e+00 0.1124
## global_rate_positive_words 5.861800e+00 0.1706
## global_rate_negative_words 6.808500e+00 0.1469
## rate_positive_words 9.007199e+15 0.0000
## rate_negative_words 4.503600e+15 0.0000
## avg_positive_polarity 5.694400e+00 0.1756
## min_positive_polarity 1.857400e+00 0.5384
## max_positive_polarity 3.110900e+00 0.3215
## avg_negative_polarity 5.690900e+00 0.1757
## min_negative_polarity 4.228700e+00 0.2365
## max_negative_polarity 2.200900e+00 0.4544
## title_subjectivity 2.579500e+00 0.3877
## title_sentiment_polarity 1.134200e+00 0.8817
## abs_title_subjectivity 1.454300e+00 0.6876
## abs_title_sentiment_polarity 2.275700e+00 0.4394
## Wi Fi
## timedelta 1.331925e+02 1.362429e+02
## n_tokens_title 1.672010e+01 1.710310e+01
## n_tokens_content 3.117792e+02 3.189196e+02
## n_unique_tokens 2.871921e+03 2.937693e+03
## n_non_stop_words 1.171336e+18 1.198162e+18
## n_non_stop_unique_tokens 2.782976e+03 2.846711e+03
## num_hrefs 6.860640e+01 7.017760e+01
## num_self_hrefs 3.209010e+01 3.282500e+01
## num_imgs 5.458440e+01 5.583450e+01
## num_videos 1.315170e+01 1.345290e+01
## average_token_length 2.124213e+03 2.172862e+03
## num_keywords 7.981220e+01 8.164000e+01
## kw_min_min 4.316426e+02 4.415281e+02
## kw_max_min 2.241826e+03 2.293169e+03
## kw_avg_min 2.115948e+03 2.164407e+03
## kw_min_max 8.584380e+01 8.780980e+01
## kw_max_max 5.702837e+02 5.833444e+02
## kw_avg_max 2.329030e+02 2.382370e+02
## kw_min_avg 1.801806e+02 1.843071e+02
## kw_max_avg 8.425625e+02 8.618588e+02
## kw_avg_avg 8.803243e+02 9.004855e+02
## self_reference_min_shares 2.004283e+03 2.050186e+03
## self_reference_max_shares 1.756919e+03 1.797156e+03
## self_reference_avg_sharess 5.670968e+03 5.800845e+03
## is_weekend 2.676000e+00 2.737300e+00
## LDA_00 Inf Inf
## LDA_01 Inf Inf
## LDA_02 Inf Inf
## LDA_03 Inf Inf
## LDA_04 Inf Inf
## global_subjectivity 2.365149e+02 2.419316e+02
## global_sentiment_polarity 1.027165e+03 1.050690e+03
## global_rate_positive_words 6.322449e+02 6.467246e+02
## global_rate_negative_words 7.553682e+02 7.726677e+02
## rate_positive_words 1.171336e+18 1.198162e+18
## rate_negative_words 5.856681e+17 5.990811e+17
## avg_positive_polarity 6.104825e+02 6.244638e+02
## min_positive_polarity 1.115049e+02 1.140585e+02
## max_positive_polarity 2.745077e+02 2.807945e+02
## avg_negative_polarity 6.100199e+02 6.239906e+02
## min_negative_polarity 4.198798e+02 4.294959e+02
## max_negative_polarity 1.561745e+02 1.597512e+02
## title_subjectivity 2.054049e+02 2.101091e+02
## title_sentiment_polarity 1.744680e+01 1.784630e+01
## abs_title_subjectivity 5.907720e+01 6.043020e+01
## abs_title_sentiment_polarity 1.658955e+02 1.696949e+02
## Leamer CVIF Klein
## timedelta 0.7029 2.26130e+00 1
## n_tokens_title 0.9413 1.26070e+00 0
## n_tokens_content 0.5425 3.79530e+00 1
## n_unique_tokens 0.2081 2.57875e+01 1
## n_non_stop_words 0.0000 1.00620e+16 1
## n_non_stop_unique_tokens 0.2113 2.50234e+01 1
## num_hrefs 0.8091 1.70640e+00 1
## num_self_hrefs 0.8956 1.39280e+00 1
## num_imgs 0.8393 1.58600e+00 1
## num_videos 0.9530 1.23010e+00 0
## average_token_length 0.2402 1.93645e+01 1
## num_keywords 0.7872 1.80270e+00 1
## kw_min_min 0.4812 4.82500e+00 1
## kw_max_min 0.2342 2.03748e+01 1
## kw_avg_min 0.2406 1.92935e+01 1
## kw_min_max 0.7761 1.85450e+00 1
## kw_max_max 0.4309 6.01600e+00 1
## kw_avg_max 0.5986 3.11780e+00 1
## kw_min_avg 0.6475 2.66490e+00 1
## kw_max_avg 0.3657 8.35490e+00 1
## kw_avg_avg 0.3588 8.67930e+00 1
## self_reference_min_shares 0.2468 1.83343e+01 1
## self_reference_max_shares 0.2625 1.62094e+01 1
## self_reference_avg_sharess 0.1497 4.98318e+01 1
## is_weekend 0.9899 1.14010e+00 0
## 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 0.5956 3.14880e+00 1
## global_sentiment_polarity 0.3352 9.94070e+00 1
## global_rate_positive_words 0.4130 6.54820e+00 1
## global_rate_negative_words 0.3832 7.60590e+00 1
## rate_positive_words 0.0000 1.00620e+16 1
## rate_negative_words 0.0000 5.03100e+15 1
## avg_positive_polarity 0.4191 6.36130e+00 1
## min_positive_polarity 0.7337 2.07500e+00 1
## max_positive_polarity 0.5670 3.47520e+00 1
## avg_negative_polarity 0.4192 6.35730e+00 1
## min_negative_polarity 0.4863 4.72400e+00 1
## max_negative_polarity 0.6741 2.45870e+00 1
## title_subjectivity 0.6226 2.88160e+00 1
## title_sentiment_polarity 0.9390 1.26700e+00 1
## abs_title_subjectivity 0.8292 1.62460e+00 1
## abs_title_sentiment_polarity 0.6629 2.54220e+00 1
## IND1 IND2
## timedelta 0.0036 0.7250
## n_tokens_title 0.0065 0.1632
## n_tokens_content 0.0022 1.0111
## n_unique_tokens 0.0003 1.3708
## n_non_stop_words 0.0000 1.4329
## n_non_stop_unique_tokens 0.0003 1.3689
## num_hrefs 0.0048 0.4949
## num_self_hrefs 0.0059 0.2836
## num_imgs 0.0052 0.4236
## num_videos 0.0067 0.1316
## average_token_length 0.0004 1.3502
## num_keywords 0.0046 0.5449
## kw_min_min 0.0017 1.1011
## kw_max_min 0.0004 1.3543
## kw_avg_min 0.0004 1.3499
## kw_min_max 0.0044 0.5697
## kw_max_max 0.0014 1.1668
## kw_avg_max 0.0026 0.9195
## kw_min_avg 0.0031 0.8322
## kw_max_avg 0.0010 1.2413
## kw_avg_avg 0.0009 1.2484
## self_reference_min_shares 0.0004 1.3456
## self_reference_max_shares 0.0005 1.3341
## self_reference_avg_sharess 0.0002 1.4007
## is_weekend 0.0072 0.0289
## LDA_00 0.0000 1.4329
## LDA_01 0.0000 1.4329
## LDA_02 0.0000 1.4329
## LDA_03 0.0000 1.4329
## LDA_04 0.0000 1.4329
## global_subjectivity 0.0026 0.9245
## global_sentiment_polarity 0.0008 1.2718
## global_rate_positive_words 0.0013 1.1884
## global_rate_negative_words 0.0011 1.2224
## rate_positive_words 0.0000 1.4329
## rate_negative_words 0.0000 1.4329
## avg_positive_polarity 0.0013 1.1812
## min_positive_polarity 0.0040 0.6614
## max_positive_polarity 0.0024 0.9723
## avg_negative_polarity 0.0013 1.1811
## min_negative_polarity 0.0017 1.0940
## max_negative_polarity 0.0033 0.7818
## title_subjectivity 0.0028 0.8774
## title_sentiment_polarity 0.0065 0.1695
## abs_title_subjectivity 0.0051 0.4476
## abs_title_sentiment_polarity 0.0032 0.8032
##
## 1 --> COLLINEARITY is detected by the test
## 0 --> COLLINEARITY is not detected by the test
##
## timedelta , n_tokens_content , n_unique_tokens , n_non_stop_unique_tokens , num_self_hrefs , num_keywords , kw_max_min , kw_avg_min , kw_min_max , LDA_01 , LDA_03 , global_subjectivity , global_sentiment_polarity , global_rate_positive_words , global_rate_negative_words , rate_positive_words , rate_negative_words , avg_positive_polarity , min_positive_polarity , max_positive_polarity , avg_negative_polarity , min_negative_polarity , title_sentiment_polarity , coefficient(s) are non-significant may be due to multicollinearity
##
## R-square of y on all x: 0.1152
##
## * 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 1.9793 0.5052 143.3981
## n_tokens_title 1.1269 0.8874 18.5752
## n_tokens_content 3.3895 0.2950 349.8795
## n_unique_tokens 22.9825 0.0435 3218.7912
## n_non_stop_words 26.3429 0.0380 3710.8314
## n_non_stop_unique_tokens 22.3663 0.0447 3128.5657
## num_hrefs 1.5255 0.6555 76.9500
## num_self_hrefs 1.2448 0.8033 35.8503
## num_imgs 1.4006 0.7140 58.6572
## num_videos 1.0725 0.9324 10.6180
## average_token_length 17.1660 0.0583 2367.1050
## num_keywords 1.5785 0.6335 84.7110
## kw_min_min 4.3129 0.2319 485.0978
## kw_max_min 18.1931 0.0550 2517.4927
## kw_avg_min 17.2177 0.0581 2374.6711
## kw_min_max 1.6536 0.6048 95.6964
## kw_max_max 5.2773 0.1895 626.2994
## kw_avg_max 2.6523 0.3770 241.9374
## kw_min_avg 2.2501 0.4444 183.0446
## kw_max_avg 7.2032 0.1388 908.3108
## kw_avg_avg 6.9730 0.1434 874.6032
## self_reference_min_shares 16.3887 0.0610 2253.2967
## self_reference_max_shares 14.5006 0.0690 1976.8238
## self_reference_avg_sharess 44.5629 0.0224 6378.7009
## is_weekend 1.0199 0.9805 2.9096
## LDA_00 1.0289 0.9719 4.2282
## global_subjectivity 2.8137 0.3554 265.5692
## global_sentiment_polarity 8.8797 0.1126 1153.7901
## global_rate_positive_words 5.8543 0.1708 710.7860
## global_rate_negative_words 6.7969 0.1471 848.8054
## rate_negative_words 11.7807 0.0849 1578.5581
## avg_positive_polarity 5.6867 0.1759 686.2439
## min_positive_polarity 1.8556 0.5389 125.2824
## max_positive_polarity 3.1106 0.3215 309.0474
## avg_negative_polarity 5.6671 0.1765 683.3843
## min_negative_polarity 4.2227 0.2368 471.8794
## max_negative_polarity 2.1978 0.4550 175.3920
## title_subjectivity 2.5780 0.3879 231.0624
## title_sentiment_polarity 1.1327 0.8828 19.4326
## abs_title_subjectivity 1.4489 0.6902 65.7319
## abs_title_sentiment_polarity 2.2733 0.4399 186.4417
## Fi Leamer CVIF
## timedelta 147.1001 0.7108 2.1098
## n_tokens_title 19.0547 0.9420 1.2011
## n_tokens_content 358.9120 0.5432 3.6129
## n_unique_tokens 3301.8880 0.2086 24.4974
## n_non_stop_words 3806.6307 0.1948 28.0793
## n_non_stop_unique_tokens 3209.3332 0.2114 23.8406
## num_hrefs 78.9365 0.8096 1.6261
## num_self_hrefs 36.7758 0.8963 1.3269
## num_imgs 60.1715 0.8450 1.4929
## num_videos 10.8921 0.9656 1.1432
## average_token_length 2428.2145 0.2414 18.2975
## num_keywords 86.8979 0.7959 1.6826
## kw_min_min 497.6212 0.4815 4.5972
## kw_max_min 2582.4847 0.2344 19.3922
## kw_avg_min 2435.9760 0.2410 18.3526
## kw_min_max 98.1669 0.7777 1.7625
## kw_max_max 642.4680 0.4353 5.6251
## kw_avg_max 248.1833 0.6140 2.8271
## kw_min_avg 187.7701 0.6667 2.3984
## kw_max_avg 931.7599 0.3726 7.6780
## kw_avg_avg 897.1821 0.3787 7.4327
## self_reference_min_shares 2311.4682 0.2470 17.4690
## self_reference_max_shares 2027.8578 0.2626 15.4564
## self_reference_avg_sharess 6543.3744 0.1498 47.5003
## is_weekend 2.9847 0.9902 1.0871
## LDA_00 4.3373 0.9859 1.0967
## global_subjectivity 272.4251 0.5962 2.9991
## global_sentiment_polarity 1183.5765 0.3356 9.4650
## global_rate_positive_words 729.1357 0.4133 6.2401
## global_rate_negative_words 870.7183 0.3836 7.2449
## rate_negative_words 1619.3103 0.2914 12.5572
## avg_positive_polarity 703.9600 0.4193 6.0615
## min_positive_polarity 128.5167 0.7341 1.9779
## max_positive_polarity 317.0259 0.5670 3.3157
## avg_negative_polarity 701.0266 0.4201 6.0407
## min_negative_polarity 484.0615 0.4866 4.5010
## max_negative_polarity 179.9199 0.6745 2.3427
## title_subjectivity 237.0275 0.6228 2.7480
## title_sentiment_polarity 19.9343 0.9396 1.2074
## abs_title_subjectivity 67.4289 0.8308 1.5444
## abs_title_sentiment_polarity 191.2549 0.6632 2.4231
## Klein IND1 IND2
## timedelta 1 0.0035 0.7843
## n_tokens_title 0 0.0061 0.1784
## n_tokens_content 1 0.0020 1.1175
## n_unique_tokens 1 0.0003 1.5162
## n_non_stop_words 1 0.0003 1.5250
## n_non_stop_unique_tokens 1 0.0003 1.5143
## num_hrefs 1 0.0045 0.5461
## num_self_hrefs 1 0.0055 0.3118
## num_imgs 1 0.0049 0.4534
## num_videos 0 0.0064 0.1072
## average_token_length 1 0.0004 1.4928
## num_keywords 1 0.0043 0.5809
## kw_min_min 1 0.0016 1.2176
## kw_max_min 1 0.0004 1.4980
## kw_avg_min 1 0.0004 1.4931
## kw_min_max 1 0.0041 0.6265
## kw_max_max 1 0.0013 1.2848
## kw_avg_max 1 0.0026 0.9875
## kw_min_avg 1 0.0030 0.8807
## kw_max_avg 1 0.0009 1.3651
## kw_avg_avg 1 0.0010 1.3578
## self_reference_min_shares 1 0.0004 1.4884
## self_reference_max_shares 1 0.0005 1.4758
## self_reference_avg_sharess 1 0.0002 1.5496
## is_weekend 0 0.0067 0.0309
## LDA_00 0 0.0066 0.0445
## global_subjectivity 1 0.0024 1.0218
## global_sentiment_polarity 1 0.0008 1.4066
## global_rate_positive_words 1 0.0012 1.3144
## global_rate_negative_words 1 0.0010 1.3519
## rate_negative_words 1 0.0006 1.4506
## avg_positive_polarity 1 0.0012 1.3064
## min_positive_polarity 1 0.0037 0.7309
## max_positive_polarity 1 0.0022 1.0755
## avg_negative_polarity 1 0.0012 1.3054
## min_negative_polarity 1 0.0016 1.2097
## max_negative_polarity 1 0.0031 0.8639
## title_subjectivity 1 0.0026 0.9703
## title_sentiment_polarity 1 0.0060 0.1857
## abs_title_subjectivity 1 0.0047 0.4911
## abs_title_sentiment_polarity 1 0.0030 0.8878
##
## 1 --> COLLINEARITY is detected by the test
## 0 --> COLLINEARITY is not detected by the test
##
## timedelta , n_tokens_content , n_unique_tokens , n_non_stop_unique_tokens , num_self_hrefs , num_keywords , kw_max_min , kw_avg_min , kw_min_max , global_sentiment_polarity , global_rate_positive_words , global_rate_negative_words , rate_negative_words , avg_positive_polarity , min_positive_polarity , max_positive_polarity , avg_negative_polarity , min_negative_polarity , max_negative_polarity , title_subjectivity , abs_title_sentiment_polarity , coefficient(s) are non-significant may be due to multicollinearity
##
## R-square of y on all x: 0.1129
##
## * 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 1.7739 0.5637 146.4432
## n_tokens_title 1.1057 0.9044 20.0000
## n_tokens_content 2.2194 0.4506 230.7345
## n_non_stop_unique_tokens 4.5488 0.2198 671.5243
## num_hrefs 1.4165 0.7060 78.8137
## num_self_hrefs 1.2176 0.8213 41.1765
## num_imgs 1.3162 0.7598 59.8364
## num_videos 1.0530 0.9497 10.0208
## average_token_length 4.1121 0.2432 588.8884
## num_keywords 1.4795 0.6759 90.7326
## kw_min_min 1.8596 0.5378 162.6550
## kw_max_min 2.0424 0.4896 197.2479
## kw_min_max 1.6281 0.6142 118.8556
## kw_avg_max 2.0572 0.4861 200.0526
## kw_min_avg 1.4678 0.6813 88.5134
## kw_max_avg 2.0913 0.4782 206.5000
## self_reference_min_shares 1.5139 0.6606 97.2348
## self_reference_max_shares 1.5342 0.6518 101.0794
## is_weekend 1.0163 0.9839 3.0888
## LDA_00 1.0217 0.9788 4.0997
## global_subjectivity 2.4836 0.4026 280.7339
## global_rate_positive_words 1.8660 0.5359 163.8656
## global_rate_negative_words 1.4861 0.6729 91.9893
## avg_positive_polarity 3.5263 0.2836 478.0412
## min_positive_polarity 1.7280 0.5787 137.7648
## max_positive_polarity 3.0311 0.3299 384.3438
## min_negative_polarity 1.7947 0.5572 150.3777
## max_negative_polarity 1.2328 0.8111 44.0551
## title_subjectivity 2.5720 0.3888 297.4680
## title_sentiment_polarity 1.1194 0.8933 22.6000
## abs_title_subjectivity 1.4455 0.6918 84.3000
## abs_title_sentiment_polarity 2.2647 0.4416 239.3212
## Fi Leamer CVIF
## timedelta 151.3504 0.7508 1.8198
## n_tokens_title 20.6702 0.9510 1.1343
## n_tokens_content 238.4663 0.6713 2.2767
## n_non_stop_unique_tokens 694.0267 0.4689 4.6664
## num_hrefs 81.4548 0.8402 1.4531
## num_self_hrefs 42.5563 0.9062 1.2491
## num_imgs 61.8415 0.8716 1.3502
## num_videos 10.3566 0.9745 1.0802
## average_token_length 608.6217 0.4931 4.2184
## num_keywords 93.7730 0.8221 1.5177
## kw_min_min 168.1054 0.7333 1.9077
## kw_max_min 203.8576 0.6997 2.0952
## kw_min_max 122.8384 0.7837 1.6702
## kw_avg_max 206.7562 0.6972 2.1104
## kw_min_avg 91.4795 0.8254 1.5057
## kw_max_avg 213.4197 0.6915 2.1453
## self_reference_min_shares 100.4931 0.8128 1.5530
## self_reference_max_shares 104.4665 0.8074 1.5738
## is_weekend 3.1923 0.9919 1.0426
## LDA_00 4.2371 0.9893 1.0481
## global_subjectivity 290.1411 0.6345 2.5478
## global_rate_positive_words 169.3567 0.7321 1.9142
## global_rate_negative_words 95.0719 0.8203 1.5246
## avg_positive_polarity 494.0602 0.5325 3.6175
## min_positive_polarity 142.3812 0.7607 1.7727
## max_positive_polarity 397.2229 0.5744 3.1095
## min_negative_polarity 155.4168 0.7465 1.8411
## max_negative_polarity 45.5314 0.9006 1.2647
## title_subjectivity 307.4360 0.6235 2.6385
## title_sentiment_polarity 23.3573 0.9452 1.1484
## abs_title_subjectivity 87.1249 0.8317 1.4829
## abs_title_sentiment_polarity 247.3407 0.6645 2.3233
## Klein IND1 IND2
## timedelta 1 0.0030 1.1119
## n_tokens_title 1 0.0048 0.2436
## n_tokens_content 1 0.0024 1.4002
## n_non_stop_unique_tokens 1 0.0012 1.9883
## num_hrefs 1 0.0037 0.7494
## num_self_hrefs 1 0.0043 0.4555
## num_imgs 1 0.0040 0.6123
## num_videos 0 0.0050 0.1282
## average_token_length 1 0.0013 1.9288
## num_keywords 1 0.0036 0.8260
## kw_min_min 1 0.0028 1.1781
## kw_max_min 1 0.0026 1.3007
## kw_min_max 1 0.0032 0.9832
## kw_avg_max 1 0.0026 1.3097
## kw_min_avg 1 0.0036 0.8122
## kw_max_avg 1 0.0025 1.3299
## self_reference_min_shares 1 0.0035 0.8651
## self_reference_max_shares 1 0.0034 0.8874
## is_weekend 0 0.0052 0.0409
## LDA_00 0 0.0052 0.0540
## global_subjectivity 1 0.0021 1.5224
## global_rate_positive_words 1 0.0028 1.1828
## global_rate_negative_words 1 0.0036 0.8337
## avg_positive_polarity 1 0.0015 1.8259
## min_positive_polarity 1 0.0031 1.0738
## max_positive_polarity 1 0.0017 1.7078
## min_negative_polarity 1 0.0029 1.1285
## max_negative_polarity 1 0.0043 0.4813
## title_subjectivity 1 0.0021 1.5577
## title_sentiment_polarity 1 0.0047 0.2719
## abs_title_subjectivity 1 0.0037 0.7855
## abs_title_sentiment_polarity 1 0.0023 1.4233
##
## 1 --> COLLINEARITY is detected by the test
## 0 --> COLLINEARITY is not detected by the test
##
## timedelta , n_tokens_content , n_non_stop_unique_tokens , num_self_hrefs , kw_max_min , kw_min_max , kw_avg_max , self_reference_min_shares , global_rate_negative_words , avg_positive_polarity , min_positive_polarity , max_positive_polarity , title_subjectivity , abs_title_sentiment_polarity , coefficient(s) are non-significant may be due to multicollinearity
##
## R-square of y on all x: 0.0856
##
## * 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) n_tokens_title
## 6.402754e+00 1.258547e-02
## n_unique_tokens n_non_stop_words
## 7.475270e-01 1.439049e+00
## n_non_stop_unique_tokens num_hrefs
## -5.830464e-01 7.030187e-03
## num_imgs num_videos
## 1.276199e-02 2.061951e-02
## average_token_length kw_min_min
## -3.837005e-01 1.327585e-03
## kw_max_max kw_avg_max
## 2.969066e-07 -7.210723e-07
## kw_min_avg kw_max_avg
## -8.348655e-05 -4.614613e-05
## kw_avg_avg self_reference_min_shares
## 3.617624e-04 -8.186538e-06
## self_reference_max_shares self_reference_avg_sharess
## -3.723456e-06 1.375061e-05
## is_weekend LDA_00
## 2.968016e-01 5.153536e-01
## global_subjectivity rate_negative_words
## 5.066961e-01 -1.684708e-01
## max_positive_polarity title_subjectivity
## -1.097451e-01 1.056518e-01
## title_sentiment_polarity abs_title_subjectivity
## 1.312288e-01 1.455139e-01coef(backward, which.max(backward_summary$adjr2))## (Intercept) n_tokens_title
## 6.409383e+00 1.235084e-02
## n_unique_tokens n_non_stop_words
## 6.398954e-01 1.395293e+00
## n_non_stop_unique_tokens num_hrefs
## -5.287521e-01 6.892278e-03
## num_self_hrefs num_imgs
## 4.304481e-03 1.260402e-02
## num_videos average_token_length
## 2.051658e-02 -3.808777e-01
## kw_min_min kw_max_max
## 1.320596e-03 2.933964e-07
## kw_avg_max kw_min_avg
## -7.206657e-07 -8.445304e-05
## kw_max_avg kw_avg_avg
## -4.597711e-05 3.616949e-04
## self_reference_min_shares self_reference_max_shares
## -8.416760e-06 -4.019270e-06
## self_reference_avg_sharess is_weekend
## 1.427997e-05 2.969454e-01
## LDA_00 global_subjectivity
## 5.147310e-01 5.531846e-01
## rate_negative_words max_positive_polarity
## -1.238529e-01 -9.722964e-02
## avg_negative_polarity max_negative_polarity
## 1.376864e-01 -3.175778e-01
## title_subjectivity title_sentiment_polarity
## 1.087234e-01 1.288545e-01
## abs_title_subjectivity
## 1.449588e-01#get best subset of the specified size with min cp.
sub <- backward_summary$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$shares - exp(yhat_back))^2))Random Forests
As previously mentioned in the regression trees section, the random forest builds an entire forest of these trees, and merges them together to get a more accurate and stable predictions than one off trees. It is usually trained using the bagging method. Unlike regression trees, which are prone to overfitting, only a random subset of the features is taken into consideration by the algorithm for splitting a node (used CV to find the perfect amount of variables to use). This builds in additional error and makes a more robust prediction.
The manual dimensional reduction was necessary to have the processing speeds to handle the random forests model.
library(randomForest)
#single bagged model
tree.train<-randomForest(shares~., data=trimTrain1, mtry=32, importance=TRUE)
tree.train##
## Call:
## randomForest(formula = shares ~ ., data = trimTrain1, mtry = 32, importance = TRUE)
## Type of random forest: regression
## Number of trees: 500
## No. of variables tried at each split: 32
##
## Mean of squared residuals: 25689972
## % Var explained: -6.26#single bagged regression tree error prediction
tree.test<-lmNewTest3["shares"]
yhat.bag<-predict(tree.train, newdata=lmNewTest3)
yhat.bag<-as.data.frame(yhat.bag)
yhat_bag<-mean((yhat.bag$yhat.bag-tree.test$shares)^2)
RMSE_bag<-sqrt(yhat_bag)
#random forests model
tree.trainRF<-randomForest(shares~., data=trimTrain1, mtry=12, importance=TRUE)
tree.trainRF##
## Call:
## randomForest(formula = shares ~ ., data = trimTrain1, mtry = 12, importance = TRUE)
## Type of random forest: regression
## Number of trees: 500
## No. of variables tried at each split: 12
##
## Mean of squared residuals: 24336624
## % Var explained: -0.66#random forest error prediction
yhat.rf<-predict(tree.trainRF, newdata = lmNewTest3)
yhat.rf<-as.data.frame(yhat.rf)
yhat_rf<-mean((yhat.rf$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
##
## 5898 samples
## 53 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 5309, 5309, 5307, 5309, 5309, 5309, ...
## Resampling results across tuning parameters:
##
## shrinkage interaction.depth n.trees
## 0.01 1 1000
## 0.01 1 1500
## 0.01 2 1000
## 0.01 2 1500
## 0.01 3 1000
## 0.01 3 1500
## 0.05 1 1000
## 0.05 1 1500
## 0.05 2 1000
## 0.05 2 1500
## 0.05 3 1000
## 0.05 3 1500
## 0.10 1 1000
## 0.10 1 1500
## 0.10 2 1000
## 0.10 2 1500
## 0.10 3 1000
## 0.10 3 1500
## RMSE Rsquared MAE
## 0.7704382 0.1253222 0.5444390
## 0.7677343 0.1292380 0.5425947
## 0.7643665 0.1370172 0.5405721
## 0.7622319 0.1408862 0.5398244
## 0.7617169 0.1424937 0.5392324
## 0.7600554 0.1455175 0.5391943
## 0.7658797 0.1328486 0.5446494
## 0.7662343 0.1330982 0.5464222
## 0.7658943 0.1350531 0.5460199
## 0.7679272 0.1333796 0.5485868
## 0.7619294 0.1449790 0.5442774
## 0.7655236 0.1414328 0.5487261
## 0.7681046 0.1305679 0.5491781
## 0.7722241 0.1251168 0.5525444
## 0.7727992 0.1287123 0.5536598
## 0.7789730 0.1230637 0.5601528
## 0.7833594 0.1176739 0.5637165
## 0.7919707 0.1128793 0.5737120
##
## 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 = 1500, 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
## 1 8250.091 8257.97 8260.785 8229.648
## RMSE_back RMSE_bag RMSE_rfTrimmed RMSE_boost
## 1 8259.882 8220.41 8129.113 8199.403
## RMSE_regTree
## 1 8299.325which.min(comparison)## RMSE_rfTrimmed
## 7The 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.