```
library(tidyverse)
library(lubridate)
library(rio)
```

# 7 Predictive Modelling in Learning Analytics: A Machine Learning Approach in R

## 1 Introduction

Prediction of students’ performance has been a central theme within the field of learning analytics (LA) since the early days [1]. In fact, the initial conceptualization of the field has highlighted the use of digital data collected from learners to predict their success —among other usages. Such predictions hold the promise to help identify those who are at risk of low achievement, in order to proactively offer early support and appropriate intervention strategies based on insights derived from learners’ data [1, 2]. Nevertheless, the prediction of students’ performance is not unique to LA and was an important theme in related fields even before LA, e.g., academic analytics [3], educational data mining [4], and even far earlier in education research at large [5].

Such widespread, longstanding and continuous centrality of early and accurate prediction of students’ performance lends itself to the premise that detection of early signs could allow a timely prevention of, e.g., dropout, low achievement, or undesired outcomes in general [6]. More importantly, identifying the predictors could help inform interventions, explain variations in outcomes and inform educators of why such outcomes happened —a form of predictive modelling that is often referred to as explanatory modelling [7]. Noticeable is the famous example of the *Signal* system at the University of Purdue, where predictions were based on digital data collected from an online learning platform [8]. *Signal* produced predictions and classified students into three categories according to “safety” and presented the students with traffic-light-inspired dashboard signs, where at-risk students get a red light. However, the influence of *Signal* on retention rates is unclear and often debated [9]. Several other systems were designed, built and applied in practice, e.g., *OU analyse* at the Open University, where the system offers informative dashboards to students and teachers as well as predictive models to forecast students' performance [10].

Successful prediction of students’ performance has been demonstrated repeatedly in several LA studies across the years [11]. In general, the majority of the published studies used features extracted from logged learning trace data (i.e., data about students’ interactions with online learning activities and resources) and achieved accurate predictions for a considerable number of students. Yet, most of such studies examined a single course or what is often referred to as a convenience sample (i.e., a course with a sufficiently large and accessible dataset) [11]. Studies that attempted to apply predictive modelling across several courses have not found similar success [12–15]. For instance, Finnegan et al. [15] examined 22 courses across three academic domains using student log-trace data recorded from the learning management system. The authors found considerable differences among predictive models developed for individual courses regarding their predictive power as well as the significance of features. Similar results were reported by Gašević et al. [12] who used data from nine undergraduate courses in different disciplines to examine how instructional variations affected the prediction of academic success. Gašević et al. [12] found that predictors were remarkably different across courses with no consistent pattern that would allow for having one model applicable across all courses. Similarly, Conijn et al. [13] examined 17 courses across several subjects and confirmed the considerable variability of the indicators and predictive models across courses.

Studies within the same domain have also found significant differences in predictors and predictive models. For instance, a recent study [14] examined 50 courses with a similar course design and homogeneous pedagogical underpinning. The authors found variations among different offerings of the same course, that is, the same predictor was statistically significantly correlated with performance in one course offering, but not in the same course offered to similar students in the next year. Furthermore, some predictors were more consistent than others e.g., the frequency of online sessions was more consistent than the frequency of lectures. In a similar vein, Jovanović et al. [16] applied mixed-effect linear modelling to data from fifty combined courses and developed several predictive models with different combinations of features. All predictive models in the work by Jovanović et al. [16] were able to explain only a limited proportion of variations in students’ grades. The intraclass correlation coefficient (a measure of source of variability) of all models revealed that the main source of variability were students themselves, that is, students’ specific features not captured in the logged data, pointing to the importance of taking students’ international conditions into account.

The goal of this chapter is to introduce the reader to predictive LA. The next section is a review of the existing literature, including the main objectives, indicators and algorithms that have been operationalized in previous works. The remainder of the chapter is a step-by-step tutorial of how to perform predictive LA using R. The tutorial describes how to predict student success using students’ online trace log data extracted from a learning management system. The reader is guided through all the required steps to perform prediction, including the data preparation and exploration, the selection of the relevant indicators (i.e., feature engineering) and the actual prediction of student success.

## 2 Predictive modelling: objectives, features, and algorithms

Extensive research in the LA field has been devoted to the prediction of different measures of student success, as proven by the existence of multiple reviews and meta-analyses on the topic [17–20]. Among the measures of student success that have been examined in the literature are student retention [21], grades [22], and course completion [23]. Predicting lack of success has also been a common target of predictive analytics, mostly in the form of dropout [24], with special interest in the early prediction of at-risk students [25, 26].

To predict student success, numerous indicators from varying data sources have been examined in the literature. Initially, indicators were derived from students’ demographic data and/or academic records. Some examples of such indicators are age, gender, and previous grades [27]. More recent research has focused on indicators derived from students’ online activity in the learning management system (LMS) [17, 20]. Many of such indicators are derived directly from the raw log data such as the number of total clicks, number of online sessions, number of clicks on the learning materials, number of views of the course main page, number of assignments completed, number of videos watched, number of forum posts [13, 14, 28–31]. Other indicators are related to time devoted to learning, rather than to the mere count of clicks, such as login time, login frequency, active days, time-on-task, average time per online session, late submissions, and periods of inactivity [13, 14, 32–35]. More complex indicators are often derived from the time, frequency, and order of online activities, such as regularity of online activities, e.g., regularity of accessing lecture materials [16, 36, 37], or regularity of active days [14, 16]. Network centrality measures derived from network analysis of interactions in collaborative learning settings were also considered, as they compute how interactions relate to each other and their importance [38]. Research has found that predictive models with generic indicators are only able to explain just a small portion of the overall variability in students’ performance [36]. Moreover, it is important to take into account learning design as well as quality and not quantity of learning [17, 20].

The variety of predictive algorithms that have been operationalized in LA research is also worth discussing. Basic algorithms, such as linear and logistic regression, or decision trees, have been used for their explainability, which allows teachers to make informed decisions and interventions related to the students “at risk” [37]. Other machine learning algorithms have also been operationalized such as kNN or random forest [39, 40], although their interpretability is less straightforward. Lastly, the most cutting-edge techniques in the field of machine learning have also made their way to LA, such as XGBoost [41] or Neural Networks [42]. Despite the fact that the accuracy achieved by these complex algorithms is often high, their lack of interpretability is often pointed out as a reason for teachers to avoid making decisions based on their outcomes [7, 43].

It is beyond the scope of this review to offer a comprehensive coverage of the literature. Interested readers are encouraged to read the cited literature and the literature reviews on the topics [11, 14, 17–20]

## 3 Predicting students’ course success early in the course

### 3.1 Prediction objectives and methods

The overall objective of this section is to illustrate predictive modelling in LA through a typical LA task of making early-in-the-course predictions of the students’ course outcomes based on the logged learning-related data (e.g., making predictions of the learners’ course outcomes after log data has been gathered for the first 2-3 weeks). The course outcomes will be examined and predicted in two distinct ways: i) as success categories (high vs. low achievement), meaning that the prediction task is approached with classification models; ii) as success score (final grades), in which case the development of regression models is required.

To meet the stated objectives, the following overall approach will be applied: create several predictive models, each one with progressively more learning trace data (i.e., logged data about the learners’ interactions with course resources and activities), as they become available during the course. In particular, the first model will be built using the learning traces available at the end of the first week of the course; the second model will be built using the data available after the completion of the second week of the course (i.e., the data logged over the first two weeks); then, the next one will be built by further accumulating the data, so that we have learning traces for the first three weeks, and so on. In all these models, the outcome variable will be the final course outcome (high/low achievement for classification models, that is, the final grade for regression models). We will evaluate all the models on a small set of properly chosen evaluation metrics and examine when (that is, how early in the course) we can make reasonably good predictions of the course outcome. In addition, we will examine which learning-related indicators (i.e., features of the predictive models) had the highest predictive power.

### 3.2 Context

The context of the predictive modelling presented in this chapter is a postgraduate course on learning analytics (LA), taught at University of Eastern Finland. The course was 6 weeks long, though some assignments were due in the week after the official end of the course. The course covered several LA themes (e.g., Introductory topics, Learning theories, Applications, Ethics), and each theme was covered roughly in one week of the course. Each theme had a set of associated learning materials, mostly slides, and reading resources. The course reading resources included seminal articles, book chapters, and training materials for practical work. The course also contained collaborative project work (referred to as group projects). In the group project, students worked together in small groups to design an LA system. The group project was continuous all over the course and was designed to align with the course themes. For instance, when students learned about LA data collection, they were required to discuss the data collection of their own project. The group project has two grades, one for the group project as a whole and another for the individual contribution to the project. It is important to note here that the dataset is based on a synthetic anonymized version of the original dataset and was augmented to three times the size of the original dataset. For more details on the course and the dataset, please refer to the dataset chapter [44] of the book.

### 3.3 An overview of the required tools (R packages)

In addition to a set of tidyverse packages that facilitate general purpose data exploration, wrangling, and analysis tasks (e.g., `dplyr`

, `tidyr`

, `ggplot2`

, `lubridate`

), in this chapter, we will also need a few additional R packages relevant for the prediction modelling tasks:

- The
(Classification And REgression Training) package [45] offers a wide range of functions that facilitate the overall process of development and evaluation of prediction models. In particular, it includes functions for data pre-processing, feature selection, model tuning through resampling, estimation of feature importance, and the like. Comprehensive documentation of the package, including tutorials, is available online`caret`

^{1}.

The

package [46] provides an implementation of the Random Forest prediction method [47] that can be used both for the classification and regression tasks.`randomForest`

The

package [48] offers utilities for computing indices of model quality and goodness of fit for a range of regression models. In this chapter, it will be used for estimating the quality of linear regression models. The package documentation, including usage examples, is available online`performance`

^{2}.

### 3.4 Data preparation and exploration

The data that will be used for predictive modelling in this chapter originates from the LMS of a blended course on LA. The dataset is publicly available in a GitHub repository^{4}, while its detailed description is given in the book’s chapter on datasets [44]. In particular, we will make use of learning trace data (stored in the `Events.xlsx`

file) and data about the students’ final grades (available in the `Results.xlsx`

file).

We will start by familiarising ourselves with the data through exploratory data analysis.

After loading the required packages, we will load the data from the two aforementioned data files:

```
= import("https://github.com/lamethods/data/raw/main/1_moodleLAcourse/Events.xlsx")
events = import("https://github.com/lamethods/data/raw/main/1_moodleLAcourse/Results.xlsx") results
```

We will start by exploring the events data, and looking first into its structure:

` events`