Optimization of Students' Performance Prediction through an Iterative Model of Frustration Severity

Recent articles reported a massive increase in frustration among weak students due to the outbreak of COVID-19 and Massive Open Online Courses (MOOCs). These students need to be evaluated to detect possible psychological counseling and extra attention. On the one hand, the literature reports many optimization techniques focusing on existing students' performance prediction systems. On the other hand, psychological works provide insights into massive research findings focusing on various students' emotions, including frustration. However, the synchronization among these contributions is still a black box, which delays the mathematical modeling of students' frustration. Also, the literature is still limited in using insights of psychology and assumption-based datasets to provide an in-house iterative procedure for modeling students' frustration severity. This paper proposes an optimization technique called the iterative model of frustration severity (IMFS) to explore the black box. It analyzes students' performance via two modules. First, frustration is divided into four outer layers. Second, the students' performance outcome is split into 34 inner layers. The prediction results are iteratively optimized under the umbrella of frustration severity layers through the outer and inner iterations. During validation, the IMFS achieves promising results with various evaluation measures.


Introduction
e outbreak of COVID-19 and E-learning with Massive Open Online Courses (MOOCs) introduced new challenges for weak students. ey brought significant changes in students' lifestyles, academic teaching methodology, and performance evaluation procedures. COVID-19 has significantly increased students' frustration as they struggle to achieve excellent grades and good employment opportunities [1][2][3]. A student with high frustration severity is likely to perform poorly in academic activities, e.g., assignments, quizzes, workshops, and examinations [4]. Also, they made optimization of students' performance prediction systems more challenging. Such systems highlight at-risk students for psychological counseling and extra attention. Also, the prediction system needs optimized students' frustration severity modeling. Earlier studies show that distractions and frustration are the significant issues during an E-learning environment that negatively impact student engagement in the class [5]. Many research findings statistically correlated the outbreak of COVID-19 with the students' frustration severity [6]. Besides, institutions have given more liberty to the students and employees in their daily schedules. ey have changed teaching and working culture to recover from the adverse influence of COVID-19 and frustration. e current study splits earlier research contributions into two groups to provide a comprehensive picture of a few challenges, i.e., (1) psychology and data analysis findings and (2) students' performance prediction approaches. First, data analysis and psychological findings provide meaningful information and correlation between factors such as frustration, the COVID-19 pandemic, E-learning, and the performance evaluation of at-risk students [7][8][9]. Second, the prior students' performance prediction approaches used the psychological findings and data analysis contributions to optimize performance computation models [10][11][12][13][14]. ese various groups of studies are still limited in obtaining an optimized students' performance prediction system based on insightful frustration severity modeling [15][16][17][18][19].
is paper proposes an iterative model of frustration severity (IMFS) to optimize the students' performance prediction system thoroughly.
It considers students' frustration severity with two main modules, i.e., (1) digitization and quantization and (2) frustration severity module. During the in-depth quantization and digitization, the students' scores are divided into thirty-four periodic outcomes (with a period of 0.3). It ensures the in-depth consideration of students' performance under the frustration severity layers. Second, the frustration severity is split into four layers (levels) to estimate students' scores iteratively. Furthermore, the proposed model has four main iterations and thirty-four sub-iterations to predict a single student's score. It performs 136 (34 × 4) iterations to optimize the prediction result in a single round during the prediction process. e experimental study reveals that IMFS performs significantly in terms of various accuracy measures, i.e., F1 score, precision, and recall. e rest of the work depicts literature (Section 2), the proposed model, analysis, discussion, and conclusions.

Literature
Since the outbreak of COVID-19, the educational institutions were swapped to E-learning which brought significant changes in students' social and academic life, including weak and excellent ones [20]. e online classes, isolation, social distancing, and lockdowns considerably affected the students' attitudes. Also, educational institutions were active in overcoming the adverse impact of COVID-19 and frustration severity through significant changes in their policies [21]. ey have relaxed the policies by giving more liberty to employees' working schedules and moving students to online classes. However, these precautions are insufficient in such an alarming situation in the future. Indeed, a system that can predict students' performance for further treatment and counseling of a particular at-risk student is needed [22]. erefore, we need to work in two directions to optimize existing performance prediction systems. e first step includes data analysis findings that could correlate the factors that negatively and positively affect students' performance. e second step is to simulate (or provide a mathematical model) the correlation between students' characteristics, e.g., frustration, COVID-19 effects, performance, and so on.
2.1. Prior Analysis. COVID-19 and natural components of students' learning adversely influence students' performance 2. It is common in students during intense learning environments. So far, the literature demonstrated that only informal qualitative work had been done on students' frustration and performance. A proper systematic process needs to analyze the relationship between frustrations, severity, and the adverse influence on students' future performance. e previous studies have various models that can be replicated to optimize the existing prediction systems [23][24][25][26][27][28][29]. Moreover, the instructor usually overcomes students' frustration via collaborative assignments and class activities to provide the best opportunities for learning [30]. rough these activities, students learn how to play in frustration and an intense learning situation. ey can easily share their problems with classmates and learn better in offline mode with face-to-face interaction [31]. COVID-19 boosted the negative correlation between students' achievements and frustration severity. So, it is essential to predict students' performance and control the negative emotional impact in such an alarming situation [32]. Institutions that have transformed from offline to online are experiencing new challenges, such as technological illiteracy [33].

Prior Students' Performance Prediction Approaches.
Many scholars analyzed students' achievements and published insightful data analysis [34][35][36][37]. However, very meager work has been done in simulating the relationship between students' emotions (frustration, stress, etc.) and performance. Also, the published studies have many black boxes introducing new challenges while optimizing the current prediction system. us, the dire need is to evaluate the insightful data analysis and other opportunities to extend existing prediction approaches. Also, we need to analyze the qualitative findings of psychological literature to predict and simulate the influence of emotional factors. Excellent academic achievements are only possible with excellent cognitive skills. Usually, cognitive skills are considered the ability to perform any activity that needs reasoning and problem solving, i.e., assignments, quizzes, and written examinations [38][39][40]. ese skills evolve as students learn and forget. Effective educational policies need such systems to adapt to the dynamic nature of students' cognition. So, these challenges are the main sources of inspiration for the proposed iterative model of frustration severity (IMFS).

Preliminaries
e proposed model implements the Bayesian inference method (BIM) over different nodes. BIM achieves posterior probabilities (PPs) of the most probable score of a student. BIM is based on four basic probabilities, given by the following definitions, i.e., prior, conditional, joint, and PP of students' scores. e conditional probability in BIM is given by equation (1). It shows that the probability of event A gives event B. On the other hand, we need a joint probability for BIM to finalize the PP. A joint probability is given by equation (2).

Proposed Iterative Model of Frustration Severity
e focus of the current attempt is to predict the expected students' scores while simulating the nonlinear influence of frustration severity. us, the IMSF methodology split frustration into four severity layers (where s1 refers to the first layer and s4 refers to the fourth layer of severity). is division of frustration severity has initiated IMFS. Also, the students' performance outcomes (0.1 ≤ performanceoutcome ≤ 10) are divided into thirty-four outcomes. e in-depth quantization of students' performance has finalized the second section of the IMFS. e primary goal of these layers is to accurately predict students' scores while ensuring the computation of frustration severity influence. Moreover, the division of layers ensures significant prediction accuracy.

Probability Calculation at IMFS Layers.
To predict students' performance, the current approach selects the most probable score (out of 34) while computing each outcome's PP and the severe effects of frustration. IMFS embedded a machine learning model called BIM to calculate the most probable outcome of IMFS. IMFS embedded a machine learning model called BIM to compute the most probable outcome of IMFS. e result showed that IMFS achieved significant accuracy with the embedded BIM. BIM is easy to be embedded for the PP calculation. us, the BIM calculation finalizes the third section of the IMFS (of frustration severity).

Architecture of the Proposed Model.
e IMFS has four main umbrella iterations to estimate the PP of students' performance outcomes (with respect to frustration severities). Each iteration includes 34 sub-iterations, which produces a set of 34 performance outcome PPs. e resulting PP set is refined in the next iteration. So, the proposed IMFS iteratively produces the PP of students' scores while considering the adverse effects of frustration.

Posterior Probability Estimation.
During the training process, we randomly initiated the prior probabilities of students' performance outcomes, i.e., Figure 1 shows nodes of IMFS, which calculate PP under the influence of frustration. It depicts that the PP of students' performance outcomes is iteratively computed in each layer of the IMFS. During prior probability distribution, a probability weight is assigned from the interval of [0, 1].
Equations (3) and (4) show mutually exclusive and collectively exhaustive events. Moreover, SP prior reveals the weight of prior probabilities (prior � 1 to 34), while 1 − SP prior depicts the probabilities of various events, also referred to as mutually exclusive events. So, the probability of the first outcome of students' performance is depicted by SP prior . Also, the remaining thirty-three outcomes' probabilities are represented by 1 − SP prior . If we summarize the probability distribution in simple words, we can say that the probability [0, 1] is split into two sets. e probability of the first set is represented by equation (3) and the second set of probabilities is illustrated by equation (4). ese both probabilities are mutually exclusive and collectively exhaustive. Furthermore, SP c prior shows the probability of students' scores (where prior � 1 to 34) and SP c prior illustrates the summation of thirty-three outcomes' probabilities. Additionally, the IMFS achieves the prior probabilities of frustration layers, which are shown by sev prior (where prior � 1 to 4). Such probabilities are achieved for the computation of different students' score probabilities (joint and conditional).
Equations (5) and (6) compute the conditional probabilities of students' performance, which are demonstrated by PS cp and PS c m . Moreover, cp and m show various iterations for the computation of conditional probabilities. On the one hand, SP prior and 1−SP prior illustrate the single frustration severity layers (also referred to as prior probabilities), and on the other hand sev k depicts the remaining 4 layers of severity (where k = 1 to 4). Finally, SP prior c depicts students' performance. In every computation round of m, the frustration probability (conditional) is analyzed. Also, p and m illustrated 68 iterations (sub-iterations) in each round of p.
Computational Intelligence and Neuroscience 3 In equations (7) and (8), the variables SP joint xy and SP joint c s represent the probability (joint) of students' outcome and the four layers of frustration, respectively. xy and s depict two rounds of iterations. e iterative model of frustration severity needs various types of probabilities to compute the final PP. In equation (9), the variable SP post mn shows the final probabilities of students' performance, also referred to as PP. Also, the range of m � 1 to 4 and n � 1 to 34. IMFS has four iterations for severity, while in each round of iteration, IMFS has thirty-four sub-iterations. Also, it should be noted that the obtained PP is considered before the next round of iteration. Every round of iteration produces a refined set of probabilities. Finally, IMFS chooses the most probable outcome of students' performance. Algorithm 1 illustrates the iterative procedure of the proposed IMFS. As an input, it takes three sets of data; (1) sev consists of the information about frustration severity layers (F1 to F4), and (2) sp1 and sp2 consist of 34 prior probabilities of students' performance. e first loop initiates the principal iterations in which i chooses severity from sev (one by one). Furthermore, the algorithm starts an inner loop for the element of sp1. So, the variable j selects each element from sp1 (34 elements one by one) and calculates its PP under the influence of frustration severity. Each sub-iteration of the nested loop produces a PP of J with respect to the selected frustration severity (i). ese PPs are achieved using equations (3)- (7). At the end of each step of the inner loop, the prior probability of a student's score is replaced by the PP of j of sp1. us, this process continues until the PP of the 34th performance outcome is calculated. e probabilities of 34 outcomes are re-estimated under the influence of four severity layers. Eventually, the first loop produces a set of refined PP.
Furthermore, Algorithm 1 consists of another module that compares the estimated values with actual values of students' performance outcomes, i.e., calculates prediction loss by (PL � (Actual − Measured)). is process evaluates the final PP of a student's performance outcome to enhance the accuracy of the proposed model. It compares the actual score with the most probable student's score (out of 34 PPs).

Statistical Algebraic Model for IMFS.
e IMFS mathematically models the relationship among different frustration levels during various cognitive tasks, such as assignments, quizzes, final examinations, class activities, and group assignments. e following module shows the mathematical modulation of the proposed IMFS.
where A is the coefficient matrix representing students' scores while B is called augmented matrix. Furthermore, the existence and uniqueness of such system are derived as Let x ∈ R + 4 and x∈ R + 4; then, we have the following equation.
Lastly, we have achieved ‖A‖ ≤ 1. It shows that system (1) has unique solution.

IMFS Prediction Result
e proposed approach was evaluated during the experiment using state-of-the-art measures such as precision, recall, accuracy, and F1 score. It automated the association between students' performance and frustration. us, the empirical result section is split into the following sections to evaluate the accuracy.

Data Collection Process.
e proposed IMFS was analyzed with a students' score dataset during the experiment.
is particular dataset is a new version of the dataset, which was collected during an interview [41].

Population and Sampling.
e data were collected in seven universities around different provinces of Pakistan. e particular universities are given below.
According to the Yamane sampling formula (using population), the minimum sample size is 15700; however, we have oversampled the data up to 20000 to ensure the Yamane standard.

Data Collection Methodology.
We conducted 21 prank-based interviews in the institutions mentioned above to collect enough qualitative students' score data. Students were frustrated by negatively commenting on their performance. Such comments were made by the concerned teacher of the course in different universities. A student can be frustrated by negative comments on his future grades, performance, job opportunity, and family attributes [42]. Also, state-of-the-art findings were used to frustrate these students during the interview. Students' performances were evaluated on course-related quizzes. Psychological literature-based tactics were used to discourage the participants [43][44][45][46][47][48][49]. Also, we have developed various quizzes to assess the students' performance in different frustration severity. e performance outcome in the test depends on different factors, such as the amount of time taken during the test, their mistakes, and the logic of the solution. After the test, the particular student was informed about the nature of the ongoing experiment to sign the consent. e frustration severity was ensured via participants' self-assessment basis. We have assessed the performance of 451 students. So, 1804 samples were collected. To efficiently train IMFS, we oversampled the dataset to 20000 records based on psychological findings and theoretical data analysis contributions. Such assumption-based datasets pave the way for efficient training and testing of a deep model. Moreover, the correlation between different levels of frustration severity is highlighted by the Pearson correlation in Table 1, which is self-explanatory with Pearson correlation values and confidence intervals.

Training of IMFS.
e training process was initiated with 10-fold cross-validations. Also, the study has five partitions of students' score outcomes, such as very low performance (at-risk students), low (still at-risk), average performance, good, and excellent (with outstanding performance). e IMFS achieved significant performance in terms of ten-fold cross-validation processes. Furthermore, 150 distinct tests were performed using ten samples of data. So, training and testing were carried out on various pairs (i.e., 90% training set and 10% test set). is section achieved a final set of prior probabilities [33] during IMFS training.

IMFS Prediction Assessment.
e performance outcomes are distributed into five different partitions to show the performance results. On the one hand, the first four partitions consist of 28 students' score outcomes. On the other hand, the last partition consists of six score outcomes. Moreover, the study divided the performance range into various intervals, which are demonstrated as follows: Here, SP means students' performance. During the experiment, the PP of each partition is evaluated separately, i.e., PPs of the five partitions are estimated using the severity layer umbrella. During the method validation, we selected five random data samples. Each sample consists of thirty values. e IMFS receives a set of thirty-four probabilities along with the highest probability. In addition, the performance of IMFS was assessed with various validation models, such as recall, F1 score, and precision, while the training and testing have true positive, true negative, false negative, and false positive, represented by the following variables.
e prediction results of IMFS (with P1 partition) are illustrated in Figure 2. e PP is shown in a red line graph depicting the actual PP of students' performance outcomes. e prior probabilities of the proposed technique are described in Table 2, working as coefficients to obtain the PP of the given inputs (frustration severity). To achieve the accuracy for P1, we have used equation (10) for performance calculation (where i = 1 to 5). TP denotes true positive, FP reveals false positive, TN represents true negative, and the FN manifests a false negative of the model. e list of stateof-the-art performance measures is given in Table 3. Eventually, the IMFS obtained significant performance in terms of validation models.
Equation (11) measures the accuracy of students' performance outcome as a precision measurement. e parameters of equation (11) are explained earlier. e IMFS has received an excellent precision value for P1, i.e., see Table 3. Moreover, the recall measure (equation (12)) is used to calculate the accuracy of the proposed technique. Resultantly, the IMFS achieved a significant accuracy in terms of recall measure for P1, i.e., see Table 3. 6 Computational Intelligence and Neuroscience Recall � e proposed model achieved a significant result via the F1 score illustrated by equation (13), i.e., F1 scores in Table 3 and Figure 3. e red graph depicts predicted values, while the blue graph represents the original values of students' performance. e empirical analyses demonstrated significant results in every dataset partition. In addition, Figure 4 shows the accuracy of IMFS in P3 (partition three). e results have shown that the IMFS thoroughly simulated the correlation between frustration severity and P3. Also, the study examined the performance of IMFS (in terms of the validation measures as mentioned earlier) to validate its preciseness. So, it performed satisfactorily in different validation measures (see results in Table 3). Figure 5 shows the result of IMFS for P4 (partition four), which depicted significant accuracy in terms of precision, recall, F1, and accuracy measures. Also, in Table 3, the study demonstrated the performance of IMFS for P4. Lastly, IMFS was thoroughly investigated in terms of P5 partition (prediction results are shown in Figure 6). On the one hand, the red graph illustrates the predicted values, while on the other hand, the blue graph shows original values of the students' scores. e proposed IMFS has iteratively modulated the nonlinear links among partition five and the severity of frustration. e result via validation models depicted significant results in terms of different parameters (for more information, see Table 3).

Assessment of the Most Probable Outcome of Students'
Performance.
e thirty-four outcomes of students' scores are split into five partitions to validate the proposed iterative      Computational Intelligence and Neuroscience model, i.e., very low, low, average, good, and finally, excellent performance outcome, as illustrated earlier. e technique separately simulated the relationship between frustration severity and students' scores during the second experiment. Also, each partition of students' scores has a probability interval [0, 1] distributed between seven outcomes. ese particular distributions depend on the prior probabilities of students' performance outcomes. Before the prediction experiment, we hypothesized the relationship between students' performance and frustration severity. According to the hypothesis, the PP of the first three partitions (P1, P2, and P3) must be increased with severity. In comparison, the PP of the last two partitions (P4 and P5) might be decreased with an inevitable increase in frustration severity. e technique has achieved excellent prediction accuracy on students' datasets. ese results illustrated that the PPs of the first three partitions (P1 to P3) are increasing under the intense influence of frustration severity. Figures 7-9 show P1 (very low), P2 (low), and P3 (average) students' scores, respectively. e increased rate in PP of P1 (Figure 7) is comparatively higher than P2 (Figure 8).

Computational Intelligence and Neuroscience
On the one hand, Figure 9 demonstrates that an increase in PP of P3 is comparatively higher than the increase in PP of P2. e first three partitions have revealed an increase in students' score probabilities under the influence of the four layers (s1 to s4). On the other hand, we have investigated the prediction results of the last two partitions (good � P4 and excellent � P5), which are shown in Figures 10 and 11. ese two partitions' PPs are decreasing because frustration severity layers thoroughly influence P4 and P5 partitions. Also, the decrease rate of PP in P5 ( Figure 11) is higher than that in P4 ( Figure 10). ese surprising results depicted that the proposed approach efficiently predicted the expected performance of students during cognitive tasks.

Comparative Analysis.
As it can be seen from Table 4, the proposed IMFS is compared with three prior studies based on 11 significant features. ey highlighted many technical challenges and efforts toward optimizing students' performance prediction systems; however, they could not achieve the 11 essential features mentioned in Table 4.

Relevant Factor-Based Comparison.
Earlier studies are saturated with many contributions that correlate students' performance with different levels of frustration severity (see section literature review). Also, state-of-the-art methods are insufficient to compute the adverse influence of frustration severity. As far as we know, the literature lacks algorithms that quantize frustration severity into multiple layers. It also lacks in splitting students' scores into thirty-four components to compute performance under the umbrella of the adverse impact of frustration severity. e quantization of performance outcomes and frustration severity is illustrated in Table 3.

Iterative Prediction.
e related work focused on student interaction with LMS, academic scores, and different family attributes; however, an optimized educational model is needed to mathematically model the frustration severity. So, the proposed IMFS computes students' performance under the umbrella of frustration severity clusters. Also, it addresses various challenges, such as optimization of prediction results with four outer layers and thirty-four inner layers. e current study optimizes students' performance prediction with in-depth frustration severity layers. e proposed system was trained and validated on an assumption-based and real-world dataset. ese data were collected from seven different institutions to consider the additional demographic background data. Later, the dataset was extended based on psychological findings and theoretical data analysis discoveries. Nevertheless, the dataset used by state-of-the-art techniques is comparatively not sufficient for frustration severity challenges.

Discussion
Students' performance prediction has emerged as an exciting domain for many cognitive computing researchers and education-focused scientists. It has massive applications for critical cognitive tasks, such as performance prediction during students' class activities, written examinations, and quizzes. e study illustrated earlier that frustration severity continuously declines the performance of students. erefore, it proposed an optimization method called the iterative model of frustration severity (IMFS) to predict students' scores while mathematically modeling the adverse influence of frustration severity. It has manipulated the nonlinear statistical relationship between the students' performance and frustration severity. is network consists of two main modules. First, frustration severity is split into four layers (s1 to s4). Second, the study digitized and quantized students' performance outcomes with a unique range (0.1 ≤ StudentPerformance ≤ 10) to ensure prediction accuracy. Also, the range of students' scores was split into 34 periodic discrete outcomes (with a period of 0.3). It manifests that the IMFS has two sets of layers, i.e., outer layers (frustration severities s1 to s4) and inner layers (34 layers of students' performance outcomes). During the prediction process, the first outer layer of the network produces a set of 34 unique posterior probabilities using equations (1)- (7). ese posterior probabilities are optimized in the remaining three layers of frustration severity. Hence, the model produces an optimized set of posterior probabilities in each layer. Finally, the IMFS predicts students' performance by picking the score with the highest posterior probability. e proposed IMFS was tested on the students' scores dataset, which produced a significant accuracy in terms of various measures (results are presented in Table 3). Also, all the important abbreviations are shown in Table 5 and the parameter values of prior probabilities are depicted in Table 5. e proposed model solves three challenges with the iterative procedure but also reports a few limitations. First, the proposed IMFS is instead a journey than a destination; therefore, the main loophole is the lack of extensive comparison based on prediction accuracy. Such comparison is planned in the future work (see Table 4 for novelty). Second, we have yet to perform extensive empirical tests using extended assumption-based and real-world datasets to ensure prediction accuracy. We also plan to add comprehensive quantization modules to optimize students' performance prediction process. Such a module will pave the way to assess the influence of other emotional attributes, such as various levels of frustration severity (instead of only four), depression, stress, and anxiety.
ird, the severe effects of frustration are yet to be investigated by thoroughly examining the existing psychological work. Also, the study needs to explore the factors such as frustration and frustration severity by electroencephalography (EEG) because an

Features
Proposed IMFS Prior study [50] Prior study [51] Prior study [52]   individual's emotional status is always sensitive to the aforementioned emotional attributes. In addition, the following statement should be noted for future consideration.
A series of experiments were conducted to validate the network's performance, and finally, we have chosen the average prediction results (i.e., see Table 3). e proposed model can produce different results in achieving different sets of prior probabilities for the intervals of students' scores and frustration severities. e performance outcomes are partitioned into five groups (P1 to P5) due to the nonlinear statistical correlation between students' performance and frustration severity; however, in future work, the study will simulate the relationship between frustration severity and each outcome of students' scores.

Conclusions
In this paper, we presented an iterative model of frustration severity (IMFS) to optimize the prediction of students' performance while modeling the influence of frustration severity. e IMFS has three main contributions. First, the student frustration severity was divided into four outer layers (s1, s2, s3, and s4) to model the severity influence. Second, the study divided the range of students' scores into thirty-four discrete periodic outcomes (periodic distance � 0.3), forming the IMFS inner layers. ird, it predicted students' performance with the two sets of layers. Finally, the IMFS was evaluated on students' score datasets. It achieved significant performance in terms of various accuracy measures, i.e., F1 score, precision, and recall.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon reasonable request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.