## 2 Research Methodology
### Experimental Set-Up  
To answer the research question, we develop several classification models (and not regression, as the target variable has been transformed into an ordinal variable in Section 2.1) that differ with respect to (1) the way college performance is defined, (2) the type of student's data included, (3) the machine learning algorithm applied, (4) the size of the performance window, and (5) the size of the observation window (historical data). In this study, we define the \"term performance\" of a student in two different ways. In the first representation, _by courses_, term performance is represented by a vector of size equal to the number of courses that should be taken in that term according to Table 2 with components being the numeric scores of the courses. In the second representation, _by GPA_, we represent term performance by the numeric weighted average of the courses with weights being the credit hours. Comparing the results obtained from the models _by courses_ vs the models _by GPA_ allows identifying which of the individual course grades and grade averages is more relevant for predicting student's graduation academic performance, thus answer the main research question of this study. Then, the college performance data for students is modeled using two observation window size. In the first approach, only the immediate past term performance is included in the model (either last term _by courses_, or last term _by GPA_). In the second approach, a cumulative view is adopted where all the past terms' performance is included in the analysis (either cumulative _by courses_, or cumulative _by GPA_). The first approach corresponds to using only one term as history window, while the second approach corresponds to using all past terms data since the student joined the college. The reason to consider models that include last term performance only, is to isolate the term the most impactful to the student's success. Figure 3 shows a sample student transcript data for the first 6 terms. For instance, let us consider predicting the graduation GPA class at the end of the second year, which is the end of the term 4, if we want to use one term observation history, then we use the term 4 performance alone, either as the term courses which is the vector \([2.5,2,4,2.5,4]\), or the GPA that is calculated as \((3\times 2.5+4\times 2+3\times 4+4\times 2.5+2\times 4)/16=2.84375\). On the other hand, if we want to use all past observations cumulatively, then we use all past terms performance, either as all past courses, which is to say the vector \([4.5;4.5;4;4;4;3.5;4.75;4.5;3.5;3;2.5;2.5;4.75;2.5;2;4;2.5;4;2;3;2;2.5;3;5;2;3 ;2;3;5;3;4.5]\), or the accumulated GPAs as \([4.3125;4.1;3.1;2.84375]\). For investigating the impact of the prediction window, we develop six models at different times of the curriculum, (1) as early as by the end of the first semester of the preparatory year, _term 1_, (2) by the end of preparatory year, _term 2_, (3) after the first semester of the general year, _term 3_, (4) by the end of the first general year, _term 4_, (5) after completing the first term of the second common year, _term 5_,  
Figure 2: The bar chart showing the three classes in the target variable. The GPA Classes 0, 1, and 2 represent the classes Low GPA, Average GPA, and High GPA, respectively. (6) by the end of the common general years, _term 6_. With reference to the student in Figure 3, the above described models correspond respectively to using only the term 1 data, adding one term at a time until all six terms data are used. We develop machine learning (ML) models working with the algorithm commonly used in EDM, namely Logistic Regression (LR), Random Forest (RF), and Naive Bayes (NB) with the accuracy as the performance metric. _Logistic Regression_ is a linear model used for classification. It is often the first model considered due to its simplicity and interpretability. _Random Forest_ is an ensemble method that fits number of decision trees.