Learning Analytics (LA) is a field focusing on analyzing educational data, utilizing machine learning. One of the most discussed topics is at-risk student prediction. However, the application of these methods for predicting students' academic behaviors has faced criticism due to concerns about context insensitivity, potentially leading to prejudice and discrimination against students. While some methods in explainable AI (xAI) have been proposed to address these issues, there remains uncertainty regarding the consistency of their results. In response, we incorporate two popular explainable AI (xAI) methods SHAP (Shapley Additive exPlanations) and LIME (Local Interpretable Model-agnostic Explanations), to interpret the predicting models. These methods attribute the output of these models to individual features, providing a clearer understanding of how each features contributes to the overall prediction. This approach is exemplified in the LBLS467 dataset, which includes data on 467 students' academic performance and learning behaviors in computer programming courses, encompassing a range of metrics from programming behavior to self-regulated learning and language learning strategies. Concerning the consistency of interpretations derived from SHAP and LIME, analysis via Kendall's tau coefficients reveals a moderate alignment in their feature weight rankings. Additionally, this alignment is substantiated by a highly significant confidence level, affirming that the observed alignment is not a mere coincidence.
Learning Analytics (LA) is a research field centered on measuring, collecting,
analyzing, and reporting data about learners and their contexts [
Machine learning is often criticized for being overly generalized, and overlooking the context
of the individual. Reflecting on the limitations of generalizations in understanding human
behavior, anthropologist Clifford Geertz suggests that theories and generalizations inevitably
lack deep and contextual understanding of human thought. ‘Theoretical disquisitions stand far
from the immediacies of social life,’ he notes. ‘Any generalization or theory constructed in the
absence of deep understanding, not grounded in the concrete and particular, is vacuous.’ [
RQ1: What are the successful factors in the LBLS dataset explored by SHAP and LIME? RQ2: How consistent are SHAP and LIME in interpreting a student’s learning performance?
The global community has developed an extensive variety of xAI approaches, which have been
applied across various domains to interpret a wide range of machine learning models, including
several complex models that were previously considered too intricate to interpret [
The application of xAI in education manifests primarily in two aspects: data usage and
stakeholder engagement [
Reflecting on previous studies, there was research focused on the automatic generation of
explanations in virtual learning environments. In [
According to [
LBLS467 is a dataset that collects data on 467 students’ academic performance and learning behaviors in computer programming courses. It encompasses students’ programming editing behaviors, questionnaire survey results on Self-regulated Learning (SRL) and the Strategy Inventory for Language Learning (SILL). This dataset includes a total of 208 features, covering a wide range of learning behaviors and performance indicators. The dataset is utilized to propose a series of challenging suggestions for the LBLS dataset and was used in a data challenge workshop organized by the Society for Learning Analytics Research (SoLAR) [14] [15]. 'At-risk' has diverse definition, in this study, we defined 'At-risk' students are those who fail or are on the verge of failing the course in this study. Specifically, risk students are those whose performance is comparatively worse than at least 75% of the students in their class."
In this study, we employ Principal Component Analysis (PCA) as our primary tool for feature extraction. PCA, a common preprocessing step for machine learning algorithms [16], is followed by the application of three different models, ranging from the most explainable to the least: Decision Tree, Logistic Regression, and Support Vector Machine (SVM). We create a graph to demonstrate how model accuracy relates to the number of PCA components, aiming to find the most accurate model for a given component count. The most accurate model is then further analyzed using SHAP and LIME. ("# % "&)
Accuracy = ("# % (# % "& %(& ) • • • •
TP (True Positives): The number of correct predictions that an instance is positive. TN (True Negatives): The number of correct predictions that an instance is negative. FP (False Positives): The number of incorrect predictions that an instance is positive (actually negative).
FN (False Negatives): The number of incorrect predictions that an instance is negative (actually positive).
SHAP is an xAI method grounded in game theory, designed to interpret the predictions of complex machine learning models. It employs the Shapley value to calculate the contribution of each feature to the model’s output. This approach facilitates a comprehensive understanding of how different features influence the model’s predictions. The weights of the features are derived from the following [13]:
ϕ! # ∑" ⊆%\{*}|"|!(|%||%&||!"|&')![&"∪*(( "∪*)*&"(( ")] • • • • •
F : All features. |F| : The total number of features. φ) : The SHAP value of feature i .
S : A subset of all features set F excluding the feature i. |S| : The size of subset S. (1) (2) • • f*∪)(x*∪)) : The prediction of model f when the feature set S includes the feature i. f*(x*) : The prediction of the model f with only the feature set S.
SHAP provides a method to quantify the contribution to the change in prediction when feature
i is added to the model for every possible feature set S. The idea of LIME, on the other hand, is to
approximate the behavior of a complex model near the prediction of a specific instance using a
simpler model. The formula of LIME is as follows [
,∈. g : A simple model used to approximate the behavior of the complex model f near the instance x.
G : The set of all possible simple models. π/ : A weighting function that assigns higher weights to points closer to the instance x. Ω(g): A complexity measure that penalizes the model g. (3)
LIME begins by selecting a specific instance x (in this case, an individual student), already predicted by a complex model. It generates a series of perturbed samples around this instance to explore the model’s behavior locally. To approximate the behavior of the complex model in this localized region, a simpler model, such as linear regression, is employed. The key objective is to assess the alignment between the outputs of this simpler model, denoted as g, and the original complex model, denoted as f , within the local context. This process is represented in the formulation by minimizing the loss function between g and f, complemented by the minimization of g’s complexity measure.
In this study, the Logistic Regression model was trained using data transformed through PCA. Consequently, to maintain consistency with the training data, the data samples generated by LIME need to be transformed into the same dimensional space. A wrapper function is implemented to facilitate this process, transforming the LIME-generated data via PCA to ensure that the data is in the appropriate form for the trained model to process effectively. And the same wrapper function has been applied on SHAP.
SHAP and LIME operate on distinct principles to determine the contribution of each feature to the outcome. The critical question lies in the extent of the differences in the explanations derived from these two methods. To evaluate their consistency, our approach involved identifying features that show statistical correlation with the predicted results, as assessed by Spearman’s correlation with a significance threshold set at α = 0.05. This threshold was chosen to discern features significantly correlated with the outcomes. The next step is to compare the ranks of contributions as provided by SHAP and LIME, utilizing the Kendall’s tau for this comparative analysis.
The Kendall correlation coefficient measures the degree of similarity between two sets of rankings assigned to the same group of objects [18]. Firstly, we rank the selected features based on their influence on the prediction outcome. This process results in two sets of ranking data, each ordering the same set of features. For each pair of features, we examine their respective positions in both ranking sets and calculate their relative positions. Consequently, if a feature ranks higher than another in both sets, the pair is deemed 'consistent'; the opposite scenario indicates inconsistency. Once considers all pairs of features, calculating the difference between the number of consistent pairs and inconsistent pairs, divided by the total number of pairs. Following is the formula of Kendall correlation coefficient: 0! # 0$ τ = %&×0×(023) (4) •
n4 : The number of concordant pairs • • n5 : The number of discordant pairs.
n : The sample sizes.
The value of this coefficient ranges from -1 and 1. A value approaching 1 indicates a high level of consistency in the rankings, while a value approaching -1 signifies a substantial degree of inconsistency [19].
As illustrated in Figure 1, the accuracy assessments demonstrate that all models achieved accuracy rates around 80%. Notably, both Logistic Regression and Decision Tree models showed remarkable performance. Logistic Regression achieved an 84.6% accuracy rate with 16 components, while the Decision Tree reached a same level of accuracy with 58 components.
The final decision to focus on Logistic Regression for in-depth analysis stems from a crucial observation. Under the premise of using PCA as a method for feature extraction, the Decision Tree model becomes less interpretable. Initially, the Decision Tree was a preferred choice due to its wellknown ease of interpretability. However, it was crucial to assess whether its performance was sufficiently superior to warrant detailed explanation. Upon further analysis, it was found that its accuracy was comparable to that of the Logistic Regression model. Therefore, we decided to apply SHAP and LIME to the Logistic Regression model.
In the results, we present the explanation of SHAP’s prediction for individual instance in the form of a waterfall plot. This mode of presentation is very similar to the way data is represented in LIME results, which aids in our comparison of each instance.
This SHAP waterfall plot illustrates how feature contributions (red and blue bars) move the model prediction from a baseline value (the average output of the model) E[f(x)] to the final prediction f(x). Blue bars represent features that decrease the prediction probability, while red bars indicate those that increase it. The gray texts in front of the feature names are the value to each features.
In Figure 2, the model predicts Student A as at-risk with a probability value of 0.665, surpassing the threshold for risk. Key features like ‘ADD_MEMO’, ‘srl_s_28’, and ‘srl_s_29’’ positively influence this outcome. In contrast, ’srl_m_18’ and 192 other features collectively decrease the prediction probability by about 0.16. Figure 2 shows Student B as not at-risk with a predictive value of 0.448, influenced by features like ‘SEARCH’, ’SEARCH_JUMP’, and ‘srl_m_30’ which lower the risk probability.
LIME’s plot in Figure 3 indicates Student A as at-risk with a 0.66 predictive probability, consistent with the number displayed on SHAP analysis. Influential features include ‘LINK_CLICK’, ‘SEARCH_JUMP’, and ‘srl_s_3. Conversely, features like ‘CLEAR_HW_MEMO, and ‘OPEN_RECOMMENDATION’ contribute to a lower risk prediction. Figure 3 predicts Student B as not at-risk at 0.55 probability, significantly influenced by ‘RuntimeError’ and ‘HTTPError’.
To identify the key features contributing to succeed in the LBLS dataset, we assess the contribution of features to the prediction. For SHAP analysis, we employed global explanation to find out the top five features with the highest contribution values. Since LIME lacks a global explanation mechanism, we aggregated the top five features with the most significant impact from each predictions. The five most influential features in the global explanation of SHAP were ADD_RECOMMENDATION, ADD_HW_MEMO, s_41, s_26, and TabError; whereas, for LIME, they were LINK_CLICK, HTTPError, ZeroDivisionError, RecursionError, and s_32.
We select 93 features that are statistically correlated to the result using Spearman’s correlation coefficient. In the next step of the analysis, we will employ SHAP and LIME to evaluate the prediction concerning student A. Our focus will be on capturing the rankings of all 93 features. Following this, using Kendall’s tau coefficient to assess the similarity between these rankings. *p < .05 **p < .01 ***p < .001
Opened the book.
Jumped to a particular page.
Number of times a student copy codes.
Number of times a student execute codes.
ρ -0.11* -0.12** 0.17*** 0.33*** 0.28***
Each blue dot on the graph represents a unique feature. When a dot aligns with the diagonal, it signifies that SHAP and LIME assign the same ranking to that feature’s weight. For the interpretative analysis of Student A and Student B, the Kendall’s tau are 0.66 and 0.64, respectively, suggesting a moderate but noticeable positive correlation between the two datasets. This implies that an increase in one dataset’s values is generally mirrored by an increase in the other, although the relationship is not exceptionally strong. The analysis yields remarkably low P-values for the weight rankings, all of which are below 0.001, reinforce the significance of this correlation.
The graph reveals a tendency for the features’ weight rankings, as determined by both interpretation methods, to cluster near the diagonal, particularly those with higher (towards the start) and lower weights (towards the end). This pattern suggests a greater consistency in how both methods evaluate these features. Conversely, the rankings of features in the central region of the graph tend to be more dispersed.
In the two prediction points, SHAP and LIME show a moderate level of consistency in assessing feature importance, with a tendency for feature rankings to cluster near the diagonal line indicating higher consistency in evaluating the most and least important features. The dispersion of feature rankings in the central area of the graph suggests greater variability in interpreting features of medium importance. The low P-values enhance the credibility of the results, suggesting that the observed correlations are not random but reflect the underlying patterns in the data.
Finally, we compared the feature weight rankings explained by SHAP and LIME for each prediction point pairwise, calculating the average of Kendall's tau and p-value. We obtained an average Kendall's tau of 0.623 and an average p-value of 0.000979. This suggests that there is also a moderate to strong correlation in the feature importance rankings between the two methods for each prediction point. In other words, the rankings of feature importance are relatively consistent between the two methods, and the p-value being far below 0.05 shows that the correlation in rankings between SHAP and LIME is statistically significant.
In this study, we emphasize the importance of xAI in preventing over-generalization of machine learning algorithms, especially in fields of learning analytics. We use PCA for feature extraction, comparing accuracies of multiple models, and selected one that is both simple to use and highly accurate. We then combine various statistical methods to check if SHAP and LIME explanations of feature weight rankings are consistent. The results show moderate consistency in SHAP and LIME rankings among 93 selected features related to prediction outcomes, with high confidence. In learning analytics, divergent results from xAI in predicting at-risk students can complicate strategy formulation for stakeholders. Our study has analyzed explanations for two students predicted with different labels. Future research could explore which explanation is more trustable when there is a lack of consistency, whether to sacrifice model accuracy for higher consistency, or to involve more human intuition in assessing the reasonableness of explanations. As for key feature identification for student learning performance and strategy formulation for adaptive development, it undoubtedly requires involvement from school teachers, educators, and psychologists.
This study is supported in part by the National Science and Technology Council of Taiwan under contract numbers NSTC 112-2410-H-004 -063 -. [12] Liu, B., & Udell, M. (2020). Impact of accuracy on model interpretations. arXiv preprint arXiv:2011.09903 . [13] Lundberg, S. M., & Lee, S.-I. (2017). A unified approach to interpreting model predictions.
Advances in neural information processing systems, 30 [14] Lu, O. H., Huang, A. Y., Flang, B., Ogata, H., & Yang, S. J. (2022). A quality data set for data challenge: Featuring 160 students’ learning behaviors and learning strategies in a programming course. In 2022 30th International Conference on Computers in Education.
ICCE. [15] Flanagan, B., Ogata, H. (2018). Learning Analytics Platform in Higher Education in Japan,
Knowledge Management & E-Learning (KM&EL), Vol.10, No.4, pp.469-484. [16] Wold, S., Esbensen, K., & Geladi, P. (1987). Principal component analysis. Chemometrics and intelligent laboratory systems, 2 (1-3), 37–52. [17] DW, G. D. A. (2019). Darpa’s explainable artificial intelligence program. AI Mag, 40 (2), 44 [18] Kendall, M. G. (1938). A new measure of rank correlation. Biometrika, 30 (1/2), 81 93. [19] Abdi, H. (2007). The kendall rank correlation coefficient. Encyclopedia of Measurement and Statistics. Sage, Thousand Oaks, CA, 508–510.