edm_analysis.Rmd

---
title: "EDM Experimentation and Analysis"
author: "Eli Nimy"
date: '2022-07-18'
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```



```{r}
# Open University Learning Analytics Dataset
library(oulad)

# Data Analyis and Visualisation
library(tidyverse)
```


## Student Virtual Learning Environment: Sum Clicks Analysis
- *code_module* – an identification code for a module.
- *code_presentation* - the identification code of the module presentation.
- *id_student* – a unique identification number for the student.
- *id_site* - an identification number for the VLE material.
- *date* – the date of student’s interaction with the material measured as the number of days since the start of the - module-presentation.
- *sum_click* – the number of times a student interacts with the material in that day.
```{r}
svle_df <- student_vle
svle_df
```


### Statistical Summary
```{r}
# Percentage of missing values
sum(is.na(svle_df$sum_click))/length(svle_df$sum_click) * 100
```



```{r}
# Sum of clicks statistical summary
svle_df$sum_click %>% summary()
```



```{r}
# Sum of clicks Standard deviation
round(sd(svle_df$sum_click),3)
```



```{r}
# Sum of clicks percentiles 
quantile(svle_df$sum_click, c(.25, .50, .75, .90, .95, .97, .99, .999, .9999, 1)) 
```


## Clustering 

```{r}
# Creating a dataframe consisting of only the Sum of clicks column 
sc_kmeans_df <- select(svle_df, sum_click)
sc_gmm_df <- select(svle_df, sum_click)
```



#### Data Scaling/Standardizing for K-means
- https://www.geeksforgeeks.org/normalization-vs-standardization/
```{r}
sc_kmeans_df <- scale(sc_kmeans_df)
sc_kmeans_df %>% head()
```


The use of set. seed is to make sure that we get the same results for randomization. If we randomly select some observations for any task in R or in any statistical software it results in different values all the time and this happens because of randomization.
```{r}
set.seed(123)
```



### K-means 
- Time Measurement included in algorithm execution
- https://www.r-bloggers.com/2017/05/5-ways-to-measure-running-time-of-r-code/
```{r}
# Clustering Algorithms 
library(cluster)
# Clustering Algorithms and Data Visualization
library(factoextra)
```


```{r}
# Fit K-means Model
start_time <- Sys.time()
kmeans_model <- kmeans(sc_kmeans_df, centers = 5, nstart = 25)
end_time <- Sys.time()
```


```{r}
print(kmeans_model)
```


### K-means Model Execution Time
```{r}
end_time - start_time
```


### GMM 
- Time Measurement included in algorithm execution
- https://www.r-bloggers.com/2017/05/5-ways-to-measure-running-time-of-r-code/
```{r}
# Gaussian mixture model (GMM)
library(mclust)
```


```{r}
 # Fit a GMM model
start_time <- Sys.time()
gmm_model <- Mclust(sc_t, G=5)
end_time <- Sys.time()
```


```{r}
print(gmm_model)
```


### GMM Model Execution Time
```{r}
end_time - start_time
```



```{r}
# Summary table 
summary(gmm_fit)
```



```{r}
# GMM Plot
plot(gmm_fit, 'BIC')
```


## Stratified Sampling
```{r}
db_df <- svle_df %>% 
  filter(code_presentation %in% "2014J")
db_df
```



```{r}
library(tigerstats)
```



```{r}
# 2014J Data 
favstats(db_df$sum_click)
```



```{r}
set.seed(1937)
AAA=subset(db_df,code_module == "AAA")
AAA_samp=popsamp(2500,AAA)
AAA_samp
```



```{r}
set.seed(1837)
BBB = subset(db_df,code_module == "BBB")
BBB_samp = popsamp(2500,BBB)
BBB_samp
```



```{r}
set.seed(1737)
CCC = subset(db_df,code_module == "CCC")
CCC_samp = popsamp(2500,CCC)
CCC_samp
```



```{r}
set.seed(1637)
DDD = subset(db_df,code_module == "DDD")
DDD_samp = popsamp(2500,DDD)
DDD_samp
```



```{r}
set.seed(1537)
EEE = subset(db_df,code_module == "EEE")
EEE_samp = popsamp(2500,EEE)
EEE_samp
```



```{r}
set.seed(1437)
FFF = subset(db_df,code_module == "FFF")
FFF_samp = popsamp(2500,FFF)
FFF_samp
```



```{r}
set.seed(1337)
GGG = subset(db_df,code_module == "GGG")
GGG_samp = popsamp(2500,GGG)
GGG_samp
```



```{r}
strat_samp = rbind(AAA_samp, BBB_samp, CCC_samp, DDD_samp, EEE_samp, FFF_samp, GGG_samp)
strat_samp
```



```{r}
favstats(db_df$sum_click)
```



```{r}
favstats(strat_samp$sum_click)
```



```{r}
object.size(strat_samp)
```


### GMM Model 
```{r}
ss_gmm_df <- select(strat_samp, sum_click)
```



```{r}
gmm_model <- Mclust(ss_gmm_df, G=8)
```



```{r}
print(gmm_model)
```



```{r}
summary(gmm_model)
```



```{r}
strat_samp$cluster <- gmm_model$classification
strat_samp$uncertainty <- gmm_model$uncertainty
```



```{r}
# Obtain used cluster averages and number of observations in each cluster. 
strat_samp %>%
  group_by(cluster) %>%
  summarise(sum_clicks = mean(sum_click),
            Number_of_students = n())
```



```{r}
# Exclude scientific outputs
view(format(strat_samp, scientific = FALSE))
```



```{r}
# Plot our results.
plot(gmm_model, what = "classification", main = "Mclust Classification")
```



```{r}
# Cluster means (output this in a transposed form)
gmm_model$parameters$mean
```


- https://www.rdocumentation.org/packages/mclust/versions/5.4.7/topics/Mclust
```{r}
# Probability of belonging to each cluster
format(round(gmm_model$z, 5), scientific = FALSE)
```



```{r}
gmm_model$parameters$pro
```



```{r}
student_clicks <- svle_df %>% 
  group_by(id_student) %>% 
  summarise(sum_clicks = sum(sum_click))
```



```{r}
favstats(svle_df$date)
```



```{r}
favstats(student_clicks$sum_clicks)
```



```{r}
view(student_clicks)
```



```{r}
student_clicks_gmm <- select(student_clicks, sum_clicks)
```



```{r}
gmm_model2 <- Mclust(student_clicks_gmm, G=8)
```



```{r}
summary(gmm_model2)
```



```{r}
svle_df %>% 
  group_by(id_site) %>% 
  summarise(n = n())
```



```{r}
gmm_model2$parameters$mean
```



```{r}
hist(student_clicks$sum_clicks, breaks = 50)
```


```{r}
favstats(svle_df$date)
```


```{r}
svle_df %>% 
  filter(date >=-25 & date <= 269) %>% 
  group_by(id_student) %>% 
  summarise(sum_clicks = sum(sum_click))
```



```{r}
student_clicks$cluster <- gmm_model2$classification
student_clicks$uncertainty <- gmm_model2$uncertainty
```



```{r}
# Exclude scientific outputs
view(format(student_clicks, scientific = FALSE))
```



```{r}
options(scipen=999)
View(student_clicks) 
```


### Cluster Mean Table
```{r}
cluster_mean_df <- as.data.frame(gmm_model2$parameters$mean)
colnames(cluster_mean_df) <- "cluster_mean"
cluster_mean_df
# Rename rownames to date in R
cluster_mean_df <- cbind(cluster = rownames(cluster_mean_df), cluster_mean_df)
# Remove rownames 
rownames(cluster_mean_df) <- NULL
cluster_mean_df
```



```{r}
# Obtain number of observations in each cluster. 
student_clicks %>%
  group_by(cluster) %>%
  summarise(Number_of_students = n())
```



```{r}
summary(gmm_model2)
```



```{r}
gmm_model2
```



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