# Predicting Student Academic Performance by Means of Associative Classification
## 3 Materials and Methods
### Associative Model Learning
An association rule is represented in the form \(R:X\to Y\), where \(X\) and \(Y\) are the body and the head of the rule respectively._  
\(X\) and \(Y\) are also denoted as antecedent and consequent of rule \(X\to Y\). For example, {(_Entry test_, [60, 70]), (_Video-lectures accessed_, \(<\)5%)} \(\rightarrow\) (_Success rate_, _fail_) is an association rule. It indicates that the co-occurrence of two specific conditions, i.e., passing the entry test with a grade between 60 and 70 and accessing less than 5% of the video-lectures, is correlated with an exam fail. Association rule extraction is commonly driven by support (sup), confidence (conf), and correlation (corr) quality indexes [37]. The support of the rule indicates the frequency of occurrence of the implication in the source dataset, while the confidence index represents the rule strength. Definition 5: **Support of an association rule. **_Let \(\mathcal{D}\) be a relational dataset. The support (sup) of an association rule \(R:X\to Y\) is defined as the support of \(X\cup Y\) in \(\mathcal{D}\)._  
Definition 6: **Confidence of an association rule. **_Let \(\mathcal{D}\) be a relational dataset. The confidence (conf) of an association rule \(R:X\to Y\) is the conditional probability of occurrence in \(\mathcal{D}\) of itemset \(Y\) given itemset \(X\), i.e., \(conf(R)=\frac{sup(X\cup Y)}{sup(X)}\)._  
For example, the association rule {(_Entry test_, [60, 70]), (_Video-lectures accessed_, \(<\)5%)} \(\rightarrow\) (_Success rate_, _fail_) has support equal to 33% and confidence equal to 100%, because in all the records in which the antecedent occurs the consequent occurs as well. In our context, the confidence index indicates that in all the cases in which the entry test grade is between 60 and 70 and the number of video-lectures accessed is very low the success rate is _fail_. In some cases, measuring the strength of a rule in terms of support and confidence may be misleading [42]. When the rule consequent is characterized by relatively high support value, the corresponding rule may be characterized by a high confidence even if its actual strength is relatively low. To overcome this issue, the correlation (or lift) index [42] may be used to measure the (symmetric) correlation between body and head of the extracted rules. Definition 7: **Correlation of an association rule. **_Let \(X\to Y\) be an association rule. Its correlation index (corr) is given by \(\mathrm{corr(X,Y)}=\frac{\mathrm{conf(X\to Y)}}{\mathrm{sup(Y)}}= \frac{\mathrm{sup(X\to Y)}}{\mathrm{sup(X)sup(Y)}}\), where \(\mathrm{sup(X\to Y)}\) and \(\mathrm{conf(X\to Y)}\) are, respectively, the rule support and confidence, and \(\mathrm{sup(X)}\) and \(\mathrm{sup(Y)}\) are the support counts of the rule antecedent and consequent._  
If corr(X,Y) is equal to or close to 1, itemsets \(X\) and \(Y\) are not correlated with each other. Correlation values significantly below 1 show negative correlation, whereas values significantly above 1 indicate a positive correlation between itemsets \(X\) and \(Y\), i.e., \(X\) and \(Y\) co-occur more than expected. For example, the correlation of rule {(_Entry test_, [60, 70]), (_Fraction of video-lectures accessed_, \(<\)5%)} \(\rightarrow\) {(_Success rate_, _fail_)} is \(\frac{\frac{\pi}{2}}{\frac{\pi}{8}+\frac{\pi}{8}}=2\). Hence, the rule correlation is positive. **Classification rules. ** The \(L^{3}\) classifier consists of a subset of high-quality association rules, hereafter denoted as _strong classification rules_. A classification rule [13] is an association rule whose consequent is a class item. For example, rule {(_Entry test_, [60, 70]), (_Fraction of video-lectures accessed_, \(<\)5%)} \(\rightarrow\) {(_Success rate_, _fail_)} is a classification rule. Classification rules are selected because they can be directly applied to label test records whose non-class feature values match those appearing in the rule antecedent. A classification rule is _strong_ if its support, confidence, and correlation values are above (analyst-provided) thresholds.