library(corrplot) #easy correlation matrices
library(tidyverse) #data manipulation
library(tidymodels) #easy visualizations of clusters
library(NbClust) #determine optimal no. of clusters
library(psych) #descriptive statistics
library(standardize) #easy standardizationlibrary(haven)
engage <- read_csv("engage.xlsx - Sheet1.csv")describe(engage$behavioral_eng) vars n mean sd median trimmed mad min max range skew kurtosis se
X1 1 1000 2.75 0.97 2.61 2.71 1.12 0.55 5.29 4.75 0.31 -0.78 0.03describe(engage$affective_eng) vars n mean sd median trimmed mad min max range skew kurtosis se
X1 1 1000 3.27 0.96 3.42 3.3 1.08 0.57 5.5 4.94 -0.3 -0.79 0.03describe(engage$cognitive_eng) vars n mean sd median trimmed mad min max range skew kurtosis se
X1 1 1000 3.71 1.52 3.32 3.62 1.48 0.66 7.53 6.87 0.5 -0.94 0.05describe(engage$social_eng) vars n mean sd median trimmed mad min max range skew kurtosis se
X1 1 1000 4.39 1.39 4.5 4.42 1.67 1.2 7.2 6 -0.2 -1.01 0.04glimpse(engage)Rows: 1,000
Columns: 4
$ behavioral_eng <dbl> 2.885871, 1.707288, 4.653985, 2.786255, 1.753118, 4.340…
$ affective_eng <dbl> 5.137745, 1.956721, 3.843508, 4.226747, 4.006949, 4.640…
$ cognitive_eng <dbl> 2.203054, 2.648275, 6.171584, 3.334334, 2.324768, 4.659…
$ social_eng <dbl> 4.711175, 2.346699, 5.468555, 3.660912, 5.777080, 6.823…ggplot(data = engage, mapping = aes(x = behavioral_eng)) +
geom_density(color="black", fill="purple") +
labs(title = "Density Plot of Behavioral Engagement",
x = "Behavioral Engagement Score")
ggplot(data = engage, mapping = aes(x = affective_eng)) +
geom_density(color="black", fill="forest green") +
labs(title = "Density Plot of Affective Engagement",
x = "Affective Engagement Score")
ggplot(data = engage, mapping = aes(x = cognitive_eng)) +
geom_density(color="black", fill="red") +
labs(title = "Density Plot of Behavioral Engagement",
x = "Cognitive Engagement Score")
ggplot(data = engage, mapping = aes(x = social_eng)) +
geom_density(color="black", fill="blue") +
labs(title = "Density Plot of Social Engagement",
x = "Social Engagement Score")
engage <- engage %>%
mutate(.,
behavioral_eng_std = scale(engage$behavioral_eng),
affective_eng_std = scale(engage$affective_eng),
cognitive_eng_std = scale(engage$cognitive_eng),
social_eng_std = scale(engage$social_eng))
describe(engage$behavioral_eng_std) vars n mean sd median trimmed mad min max range skew kurtosis se
X1 1 1000 0 1 -0.14 -0.04 1.16 -2.27 2.63 4.9 0.31 -0.78 0.03describe(engage$affective_eng_std) vars n mean sd median trimmed mad min max range skew kurtosis se
X1 1 1000 0 1 0.16 0.04 1.12 -2.8 2.32 5.12 -0.3 -0.79 0.03describe(engage$cognitive_eng_std) vars n mean sd median trimmed mad min max range skew kurtosis se
X1 1 1000 0 1 -0.25 -0.06 0.97 -2 2.51 4.51 0.5 -0.94 0.03describe(engage$social_eng_std) vars n mean sd median trimmed mad min max range skew kurtosis se
X1 1 1000 0 1 0.07 0.02 1.2 -2.29 2.01 4.3 -0.2 -1.01 0.03library(ggcorrplot)
corr <- engage %>%
select(.,
behavioral_eng_std,
affective_eng_std,
cognitive_eng_std,
social_eng_std) %>%
na.omit()
corr_engage <- cor(corr)
corr_engage behavioral_eng_std affective_eng_std cognitive_eng_std
behavioral_eng_std 1.0000000 0.3587287 0.8130752
affective_eng_std 0.3587287 1.0000000 0.4136730
cognitive_eng_std 0.8130752 0.4136730 1.0000000
social_eng_std 0.5369821 0.7768180 0.6134703
social_eng_std
behavioral_eng_std 0.5369821
affective_eng_std 0.7768180
cognitive_eng_std 0.6134703
social_eng_std 1.0000000hclusts <- hclust(dist(corr, method = "euclidean"), method = "ward.D2")
hclusts
Call:
hclust(d = dist(corr, method = "euclidean"), method = "ward.D2")
Cluster method : ward.D2
Distance : euclidean
Number of objects: 1000 plot(hclusts)
wardclust <- NbClust(data = corr, method = "ward.D2") 
*** : The Hubert index is a graphical method of determining the number of clusters.
In the plot of Hubert index, we seek a significant knee that corresponds to a
significant increase of the value of the measure i.e the significant peak in Hubert
index second differences plot.
*** : The D index is a graphical method of determining the number of clusters.
In the plot of D index, we seek a significant knee (the significant peak in Dindex
second differences plot) that corresponds to a significant increase of the value of
the measure.
*******************************************************************
* Among all indices:
* 5 proposed 2 as the best number of clusters
* 5 proposed 3 as the best number of clusters
* 10 proposed 4 as the best number of clusters
* 1 proposed 9 as the best number of clusters
* 1 proposed 10 as the best number of clusters
* 1 proposed 15 as the best number of clusters
***** Conclusion *****
* According to the majority rule, the best number of clusters is 4
******************************************************************* plot(hclusts)
rect.hclust(hclusts,k=4, border="purple")
wardclust <- NbClust(data = corr, method = "average") 
*** : The Hubert index is a graphical method of determining the number of clusters.
In the plot of Hubert index, we seek a significant knee that corresponds to a
significant increase of the value of the measure i.e the significant peak in Hubert
index second differences plot.
*** : The D index is a graphical method of determining the number of clusters.
In the plot of D index, we seek a significant knee (the significant peak in Dindex
second differences plot) that corresponds to a significant increase of the value of
the measure.
*******************************************************************
* Among all indices:
* 4 proposed 2 as the best number of clusters
* 10 proposed 3 as the best number of clusters
* 2 proposed 4 as the best number of clusters
* 4 proposed 5 as the best number of clusters
* 1 proposed 6 as the best number of clusters
* 1 proposed 9 as the best number of clusters
* 1 proposed 15 as the best number of clusters
***** Conclusion *****
* According to the majority rule, the best number of clusters is 3
******************************************************************* Approach # 2 Kmeans clustering
library(tidymodels)
kclusts <-
tibble(k = 2:4) %>%
mutate(
kclust = map(k, ~kmeans(corr, .x)),
tidied = map(kclust, tidy),
glanced = map(kclust, glance),
augmented = map(kclust, augment, corr)
)clusters <-
kclusts %>%
unnest(cols = c(tidied))
assignments <-
kclusts %>%
unnest(cols = c(augmented))
clusterings <-
kclusts %>%
unnest(cols = c(glanced))p1 <-
ggplot(assignments, aes(x = affective_eng_std, y = cognitive_eng_std)) +
geom_jitter(aes(color = .cluster), alpha = 0.8) +
facet_wrap(~ k)
p1
p2 <- p1 + geom_point(data = clusters, size = 10, shape = "x")
p2
kmeansclust <- NbClust(data = corr, method = "kmeans")
*** : The Hubert index is a graphical method of determining the number of clusters.
In the plot of Hubert index, we seek a significant knee that corresponds to a
significant increase of the value of the measure i.e the significant peak in Hubert
index second differences plot.
*** : The D index is a graphical method of determining the number of clusters.
In the plot of D index, we seek a significant knee (the significant peak in Dindex
second differences plot) that corresponds to a significant increase of the value of
the measure.
*******************************************************************
* Among all indices:
* 1 proposed 2 as the best number of clusters
* 8 proposed 3 as the best number of clusters
* 11 proposed 4 as the best number of clusters
* 1 proposed 7 as the best number of clusters
* 2 proposed 15 as the best number of clusters
***** Conclusion *****
* According to the majority rule, the best number of clusters is 4
*******************************************************************