Bayesian Growth Curve Modelling of Student Academic Trajectories: The Impact of Individual-Level Characteristics and Implications for Education Policy

Abstract

This study examined the factors influencing student academic performance in the Bachelor of Science (BSc) Actuarial Science programme, focusing on Grade 12 mathematics marks, admission point (AP) scores, socioeconomic background, and progression rates. The purpose of this research was to identify the predictors of academic success and the disparities in performance related to socioeconomic factors. Data were obtained from 770 student records, with particular emphasis on admission point (AP) scores, Grade 12 mathematics marks, and progression rates over time. Bayesian hierarchical modelling was applied to analyse how these factors contribute to the students’ academic trajectories. The results revealed a strong correlation between Grade 12 mathematics marks and university success in Actuarial Science. Furthermore, students from lower SES backgrounds tended to perform less favourably than their peers, suggesting persistent disparities in academic achievement. Non-academic factors, such as personal motivation and external support systems, played a crucial role in student performance. This study concludes by recommending that universities adopt more holistic support strategies, incorporating both academic and non-academic interventions, to address the diverse needs of students in rigorous academic programmes like Actuarial Science. Educational policymakers are urged to revise admission policies and enhance support structures to foster equity and academic excellence.

1. Introduction

From engineering and economics to the natural and social sciences, mathematics is pivotal for academic success and professional careers [1]. As a foundational subject, mathematics cultivates problem-solving, analytical thinking, and logical reasoning, all of which are essential in higher education and beyond [2]. Students with a strong mathematical foundation are likelier to thrive in disciplines requiring quantitative skills [3,4]. However, in many countries, including South Africa, there has been a growing concern regarding the poor performance of students in mathematics, which poses significant challenges to their academic and professional futures [5,6].

South Africa’s performance in mathematics, particularly at the secondary school level, remains a major area of concern [7,8]. Numerous reports indicate that many learners fail to meet the minimum competency levels in mathematics, especially in Grade 12, the final year of secondary school. According to the Trends in International Mathematics and Science Study (TIMSS) and national assessments, South African students have consistently performed below the international average in mathematics [9]. This underperformance has far-reaching implications for students’ ability to succeed in higher education, particularly in fields that rely heavily on mathematics.

The South African schooling system faces significant challenges, including disparities in access to quality education, especially between urban and rural areas. Socioeconomic inequality plays a key role, with students from lower quintile schools (often under-resourced) having less access to well-trained teachers, learning materials, and support services [7]. These challenges are compounded by the historical legacy of apartheid, which continues to affect the educational opportunities available to students from disadvantaged backgrounds [5]. As a result, while South Africa produces a considerable number of matriculants each year, many of these students are underprepared for the demands of higher education, particularly in fields like Actuarial Science, where mathematical proficiency is crucial for success.

One of these fields is Actuarial Science, where mathematical proficiency is an entry requirement and a core competency for success. Actuaries use mathematics and statistics to assess risk in the financial and insurance industries, making it imperative for students in this field to have a strong grasp of mathematical concepts [10,11]. Poor performance in mathematics at the secondary school level may limit students’ ability to enter and excel in rigorous programmes like Actuarial Science, narrowing their career prospects.

This study investigates the impact of individual-level characteristics, including Grade 12 mathematics marks, school quintile (a proxy for socioeconomic background; in South Africa, schools are categorised into five quintiles based on their socioeconomic status, with quintile 1 representing the most disadvantaged and quintile 5 the most advantaged), and credits passed, on academic performance in the BSc Actuarial Science programme. In a country where mathematics proficiency is a critical bottleneck, understanding how prior performance in mathematics affects success in such a specialised and demanding field is essential. Grade 12 mathematics marks offer a valuable measure of students’ preparedness for the academic challenges they will face in higher education [12,13]. In addition to mathematics proficiency, other factors, such as the socioeconomic context in which students are educated, can further influence their academic outcomes [14]. Research suggests that students from lower quintile schools, which often lack adequate resources and support, tend to underperform compared to their peers from better-resourced schools [15,16]. This study explores how these factors, combined with the number of credits passed as a proxy for student persistence, influence academic performance trajectories in higher education. Furthermore, this study will also explore the presence of unobserved heterogeneity in student performance, considering individual differences beyond the measurable variables. The findings will have important implications for admission policies, curriculum development, and student support services, offering strategies to help bridge the gap in mathematics performance and promote academic success, particularly in fields like Actuarial Science, where mathematical competence is essential.

1.1. Theoretical Framework

This study is grounded on two theoretical frameworks: Human Capital Theory [17] and Tinto’s Model of Student Integration [18]. The frameworks provide a robust basis for examining the factors that influence academic performance, the progression of students through their academic programmes, and the broader implications for educational policy and practice.

1.1.1. Human Capital Theory

Human Capital Theory, introduced by Gary S. Becker in 1964, postulates that individuals and societies benefit economically from investing in education, training, and skills development. Education is seen as an investment in human capital, increasing individuals’ productivity and potential economic returns. Becker argued that differences in educational attainment, skills, and training could largely explain differences in income. The key tenets include the following: Education as an Investment: individuals invest in their education to improve their economic opportunities and personal development; Skills Development: education and training enhance the productive capacity of individuals, making them more valuable in the labour market; Returns to Education: the returns on educational investments are reflected in improved labour market outcomes, such as higher wages, job stability, and economic mobility.

The Human Capital Theory aligns with this study’s research focus on individual-level characteristics (such as Grade 12 mathematics marks, AP scores, and school quintile) and their relationship with academic performance. This theory supports the notion that students with stronger pre-university qualifications, which represent prior investments in human capital, are likely to perform better in the BSc Actuarial Science programme. This study aims to quantify the impact of these prior investments on academic success, thus contributing to understanding how human capital factors influence student trajectories in higher education.

1.1.2. Tinto’s Model of Student Integration

Vincent Tinto’s Model of Student Integration, developed in 1975, offers a framework for understanding how students’ academic and social integration within an institution affects their persistence and success. Tinto suggested that students are more likely to persist and succeed in their studies when they are academically and socially integrated into the institutional environment. The model emphasises the importance of academic performance and engagement in social aspects of university life for student retention and success. The key tenets of Tinto’s student integration model include academic integration—successful students must feel integrated into the institution’s academic life, have strong relationships with faculty, and engage in academic activities; social integration—social relationships with peers and extracurricular activities foster a sense of belonging, contributing to student retention and success; and institutional support—the institution’s role in providing adequate academic and social support structures is critical in ensuring students’ persistence and success.

Tinto’s model is relevant to this study’s exploration of student performance trajectories and the unobserved heterogeneity in performance across different modules (courses) and individual factors. The model underscores the importance of academic support services, curriculum design, and student engagement as key factors influencing academic success, which directly connects to the research question about the implications of the study’s findings for admission policies, curriculum development, and student support services. Tinto’s Model of Student Integration provides a useful framework for interpreting the implications of this study’s findings. Although this study primarily examines individual-level factors such as Grade 12 mathematics marks, school quintile, and credits passed, Tinto’s model helps contextualise how institutions can use these findings to enhance student integration and success. The model underscores the importance of academic support services, curriculum design, and student engagement as potential strategies to mitigate disparities identified in this study. While institutional support was not a primary focus of our analysis, our results suggest that such support structures could play a pivotal role in addressing unobserved heterogeneity in student performance and improving academic outcomes.

The combination of Human Capital Theory and Tinto’s Model of Student Integration provides a holistic framework for this study. While the Human Capital Theory focuses on the individual-level characteristics that students bring to the university (such as prior academic performance and socioeconomic background), Tinto’s model emphasises the role of institutional factors and student engagement in shaping academic outcomes. Together, these theories enabled a comprehensive examination of how pre-university qualifications, academic trajectories, and institutional support influence student performance in the BSc Actuarial Science programme.

1.2. Reviewed Literature

This research reviewed studies that explored factors influencing student academic performance, focusing on themes of admission point scores, socioeconomic background, progression rates, and variability across academic programmes. A particular emphasis is placed on the Bachelor of Science (BSc) Actuarial Science programme to identify gaps in the existing research and set the context for the present study.

Admission point (AP) scores and prior academic achievements, such as Grade 12 mathematics marks, are commonly used predictors of university success. Studies have shown a strong association between these criteria and students’ academic trajectories. For instance, ref. [19] found that general high school knowledge predicted success more reliably than programme-specific entrance exams at the Budapest University of Technology and Economics. Their findings indicate that high school performance provides a broad measure of academic ability, which is beneficial for success in university programmes that require rigorous quantitative skills, such as Actuarial Science. Similarly, ref. [20] explored predictive validity in medical education, demonstrating that high school grades and standardised test scores significantly correlate with university cumulative grade point average (GPA). The implications for Actuarial Science are significant given the quantitative nature of the field, suggesting that a solid performance in high school mathematics could serve as a strong predictor of university achievement.

However, there are limitations to using AP scores and standardised tests as the sole basis for admission. Ref. [21] noted that students with lower placement exam scores but high school averages still performed well in coursework, highlighting the limitations of standardised assessments in capturing the complete picture of a student’s potential. This suggests a need for a more nuanced approach that incorporates multiple indicators, such as learning strategies, socioeconomic background, and foundational preparation.

Despite evidence supporting the predictive power of AP scores, there is a lack of research examining how these scores interact with other factors, such as course-specific demands or the impact of varying instructional quality across modules. This study uses Bayesian hierarchical modelling to fill this gap by exploring the influence of AP scores in conjunction with other characteristics, such as socioeconomic background and module-level variability.

Socioeconomic status (SES) and related indicators, like school quintile and parental education, significantly influence academic outcomes. Ref. [22] demonstrated the impact of sociodemographic factors on student performance across various countries using data from the Programme for International Student Assessment (PISA). The study found significant differences between the schools in outcomes such as achievement and learning strategies, with sociodemographic factors accounting for a considerable portion of the variation. This variability poses challenges when generalising academic expectations across diverse populations.

Furthermore, ref. [23] identified persistent achievement gaps among students from different racial, socioeconomic, and geographic backgrounds, particularly in mathematics. Students from high-poverty schools and underrepresented racial groups tended to show lower academic growth during the school year and higher learning loss over the summer compared to their more advantaged peers. These disparities underscore the need for tailored interventions to bridge the gap in academic readiness, especially for demanding fields like Actuarial Science, where a solid mathematical foundation is critical.

While the literature has extensively documented the effects of SES on academic achievement, limited attention has been given to how these factors influence specific academic trajectories within quantitative fields like Actuarial Science. Additionally, few studies have explored the role of SES in combination with other academic indicators, such as AP scores or credit accumulation. This study addresses these gaps by examining how socioeconomic background interacts with academic preparedness to shape students’ performance trajectories.

Student progression rates are key indicators of academic success and retention, reflecting how well students can navigate university courses. Ref. [24] found a positive relationship between GPA, science GPA, and progression in graduate education. Such relationships highlight that early academic success is a foundation for continued achievement, suggesting that monitoring students’ GPA and credit accumulation could provide insights into their future academic trajectories. In nursing education, ref. [25] explored the relationship between progression examination scores and academic success in capstone courses. The results showed that higher progression scores were associated with better academic outcomes, implying that formative assessments could serve as tools for predicting student success in later stages of their academic programmes. This approach can be applied to Actuarial Science, where a strong foundation in earlier mathematics courses may predict success in more advanced topics. Ref. [26] emphasised the critical role of remedial support in improving student progression, particularly during the first year. Their findings showed that students who participated in remedial programmes exhibited improved academic performance and lower dropout rates. This points to the importance of addressing gaps early in foundational knowledge, which could benefit students in challenging quantitative programmes like Actuarial Science.

While previous research has highlighted the importance of progression examinations and remedial interventions, limited studies have applied these insights to actuarial programmes. There is a need to investigate how progression rates within specific courses impact long-term academic trajectories and how early identification of struggling students can help tailor support mechanisms to improve retention and completion rates.

Variability in academic outcomes can occur due to differences in programme structures, instructional quality, and the characteristics of student cohorts. Ref. [27] examined graduation rates across institutions and found that these rates were more influenced by students’ entering characteristics and stable institutional factors than by variables that institutions could directly control, such as expenditures. Their results show that while institutional policies and investments matter, student-level factors remain more critical in predicting outcomes.

In a multi-level analysis, Ref. [28] explored the relationship between student evaluations of teaching (SET) and academic achievement. The findings indicated that prior academic performance was a more consistent predictor of outcomes than SET scores, which showed variability across the class and individual levels. This suggests that academic success may be more closely tied to students’ foundational knowledge and learning strategies than perceived teaching quality. Ref. [29] focused on community college transfers, revealing that larger institutions and proximity to public universities positively affected student outcomes, while university size was associated with lower first-year grades and persistence. These findings highlight the importance of contextual factors, such as institutional size and support structures, in shaping academic trajectories.

There is a lack of research examining the variability in academic outcomes across different modules within a single programme, particularly in Actuarial Science. Additionally, few studies have considered how individual-level characteristics interact with module-level factors to influence academic trajectories. This study aims to fill this gap by using Bayesian hierarchical growth curve modelling to assess the variability in student performance across modules and over time.

The reviewed literature demonstrates the complex interplay between admission criteria, socioeconomic factors, progression rates, and programme-specific variability in influencing academic success. However, significant gaps remain, particularly in understanding how these factors interact in quantitative and demanding fields like Actuarial Science. This study examines the impact of individual-level characteristics on the academic performance trajectories of students in the Bachelor of Science (BSc) Actuarial Science programme. Using a Bayesian hierarchical growth curve model, this study explores how factors such as admission point (AP) scores, Grade 12 mathematics marks, socioeconomic background (school quintile), and the number of credits passed influence students’ academic outcomes. Additionally, this study aims to investigate student performance variability over time and assess unobserved heterogeneity at the student and module levels.

1.3. Research Questions

• Do individual-level characteristics (AP scores, Grade 12 mathematics marks, school quintile, and credits passed) have a statistically significant influence on students’ academic performance in the BSc Actuarial Science programme?
• Do socioeconomic factors, such as school quintile, have a statistically significant influence on academic performance in the BSc Actuarial Science programme?
• What is the relationship between the number of credits passed and students’ academic performance in the BSc Actuarial Science programme?
• Is there significant unobserved heterogeneity in student performance that varies across modules, and what are the implications for admission policies, curriculum development, and student support services in higher education?

1.4. Hypotheses

• Higher Grade 12 mathematics marks are positively associated with improved academic performance in the BSc Actuarial Science programme.
• Students from higher socioeconomic backgrounds (as proxied by school quintile) will exhibit better academic performance than those from lower socioeconomic backgrounds.
• The number of credits passed during the academic year is positively associated with students’ final marks in the programme.
• There is significant unobserved heterogeneity in student performance due to individual factors not captured by the included covariates, and this unobserved heterogeneity varies across modules.

2. Materials and Methods

2.1. Research Design

This study employs a longitudinal quantitative research design using a Bayesian hierarchical growth curve model to analyse student academic performance trajectories over time. The model allows for estimating fixed and random effects, accounting for individual and module levels of variability. By integrating individual-level characteristics (e.g., AP scores, Grade 12 mathematics marks, school quintile) and module-level variability, the model comprehensively analyses the factors influencing students’ academic outcomes in the BSc Actuarial Science programme.

2.2. Participants

The participants in this study consisted of 770 students enrolled in the BSc Actuarial Science programme at a South African university. Due to the nature of this study, direct interaction with students was not required. Instead, we analysed archival academic records, including their Grade 12 mathematics marks, admission point (AP) scores, socioeconomic background, and progression rates within the programme. These records were used to evaluate the relationship between prior academic performance, socioeconomic status, and academic success within the Actuarial Science programme. Personal identifiers were anonymised to ensure confidentiality and protect the participants’ privacy.

2.3. Data Collection

The data were collected from institutional records, including students’ admission point (AP) scores, Grade 12 mathematics marks, and school quintile classification (used as a proxy for socioeconomic background). Student academic performance was measured using the final marks in individual modules, which were tracked across multiple academic years to analyse changes in performance over time. For this study, academic success is primarily assessed using the final marks in individual modules, and for a longitudinal analysis, the GPA across the years was also considered. Additionally, the number of credits passed each academic year was also included to provide a comprehensive picture of academic progress and achievement.

2.4. Analytical Approach

The Bayesian hierarchical growth curve model was used to estimate individual-level characteristics’ impact and model student academic trajectories over time. The model accounted for the following:

• Fixed effects: These were included to estimate the direct relationships between covariates (e.g., AP scores and Grade 12 mathematics marks) and academic outcomes;
• Random effects: These were included to capture unobserved heterogeneity at both the student and module levels, allowing for individual differences in starting performance and growth trajectories.

The analysis was conducted using four Markov chains with 4000 post-warmup draws. Convergence was achieved with a Rhat value of 1.00, ensuring the reliability of the posterior estimates. Posterior predictive checks (PPCs) were employed to evaluate the model’s adequacy, particularly in predicting the distribution of final marks.

2.5. Data Analysis

In this study, the data analysis was informed using the theoretical frameworks of Human Capital Theory and Tinto’s Model of Student Integration. The fixed effects in the model were analysed to examine the relationship between individual-level characteristics (AP scores, Grade 12 mathematics marks, school quintile, and credits passed) and academic performance, as measured by final marks. These factors reflect the concepts outlined in Human Capital Theory, which suggests that students with stronger prior academic performance (e.g., Grade 12 marks, AP scores) are likely to achieve better academic outcomes.

Additionally, the random effects were modelled to assess the unobserved heterogeneity in student and module performance, which aligns with Tinto’s Model of Student Integration. Tinto’s model emphasises that unobserved factors, such as students’ academic and social integration into the institution, can significantly impact their academic success. By modelling random effects, we were able to capture individual differences in performance across modules and account for variability in student success that may be influenced by institutional factors not directly observed in the data, such as support services, social integration, and curriculum design.

This approach enables us to tie the theoretical concepts of both frameworks to the empirical analysis of student performance in the BSc Actuarial Science programme. The results from the fixed and random effects provide critical perspectives into how individual-level characteristics and unobserved institutional factors interact to shape student success.

3. Results

A Bayesian hierarchical growth curve model was employed to investigate the academic performance trajectories of students enrolled in the Bachelor of Science programme with a specialisation in Actuarial Science. The model accounted for individual-level characteristics, module-level variability, and time-dependent factors, comprehensively analysing the determinants influencing final marks. Both fixed and random effects were incorporated to estimate the direct relationships between covariates and academic outcomes and to capture unobserved heterogeneity at the student and module levels. The analysis was based on 4000 post-warmup draws from four Markov chains, all demonstrating effective convergence (Rhat = 1.00), ensuring the reliability of the posterior estimates.

3.1. Impact of Individual-Level Characteristics on Academic Performance

The first research question sought to determine the impact of individual-level characteristics. The fixed effects in the model represented the influence of these individual-level characteristics on students’ final marks. These individual-level characteristics include admission point (AP) scores, Grade 12 mathematics marks, school quintile (as a proxy for socioeconomic status), and the number of credits passed during the academic year.

Table 1. Posterior estimates for individual-level characteristics.

Covariate	M	SE	95% CI (Lower, Upper)
AP Score (β1)	0.10	0.06	[−0.03, 0.22]
Grade 12 Math (β2)	0.42	0.03	[0.37, 0.49]
School Quintile (β3)	1.69	0.19	[1.33, 2.07]
Credits Passed (β4)	0.15	0.01	[0.14, 0.16]

presents the posterior estimates for the fixed effects, including posterior means, standard deviations, and 95% credible intervals.

The analysis revealed varying degrees of influence exerted by individual-level characteristics on academic performance. The AP score exhibited a relatively weak and uncertain relationship with final marks (β = 0.10, SE = 0.06, 95% CI [−0.03, 0.22]). Although the positive point estimate suggests that higher AP scores may predict better academic performance, the credible interval encompassing zero indicates that this effect is not consistently significant. This finding suggests that within the BSc Actuarial Science programme, where high AP scores are a prerequisite for admission, the variation in AP scores may not be substantial enough to differentiate student performance meaningfully.

In contrast, Grade 12 mathematics marks demonstrated a strong and consistent positive effect on final marks (β = 0.42, SE = 0.03, 95% CI [0.37, 0.49]). For every unit increase in Grade 12 mathematics marks, the final university module marks increased by approximately 0.42 units. This relationship underscores the critical role of mathematic proficiency as a foundational skill essential for success in actuarial science. The narrow credible interval indicates a high confidence in this estimate, aligning with prior studies that emphasise the importance of mathematics achievement in predicting success in science, technology, engineering, and mathematics (STEM) disciplines.

Furthermore, the school quintile, serving as a proxy for socioeconomic background, exhibited a relatively substantial effect on final marks (β = 1.69, SE = 0.19, 95% CI [1.33, 2.07]). Students from higher quintile schools (indicative of relatively wealthier backgrounds) significantly outperformed their peers from lower quintile schools, with an estimated difference of 1.69 units in final marks in the modules. This finding highlights the persistent impact of socioeconomic disparities on academic achievement, even at the higher education level, and suggests that factors associated with higher socioeconomic status, such as access to quality educational resources and supportive learning environments, continue to confer advantages in higher education settings.

Lastly, regarding fixed effects, this study considered the number of credits passed during the academic year. The result revealed that credits passed were positively associated with final marks (β = 0.15, SE = 0.01, 95% CI [0.14, 0.16]). Each additional credit passed corresponded to a 0.15 unit increase in final marks, indicating that academic engagement and persistence are critical determinants of success in the programme. The precision of this estimate, as evidenced by the narrow credible interval, reinforces the significance of continuous academic progress and the accumulation of credits as indicators of student success in academic performance.

3.2. Student Academic Performance Trajectories over Time

The second research question explored how students’ academic performances change over time in the BSc Actuarial Science programme and what factors influence these trajectories. The model’s inclusion of random slopes for students allowed for the examination of individual academic performance trajectories over time. The variability in these random slopes indicates that students exhibit different academic growth or decline rates throughout the programme. Some students demonstrated a consistent improvement every year, while others experienced stagnation or decline. This heterogeneity suggests that factors beyond the measured covariates, such as motivation, study habits, and time management skills, may influence individual academic trajectories [30]. These findings underscore the importance of providing longitudinal support and early interventions tailored to individual student needs to promote sustained academic growth.

The plot of average student academic trajectories by quintile group reveals two distinct patterns. Students from the low quintile (1–3) group generally maintain a relatively stable trajectory, with only minor declines in predicted final marks throughout the programme. On the other hand, students from the high quintile (4–5) group, who initially started with higher predicted marks, show a more pronounced decline in academic performance over time.

The confidence intervals displayed in Figure 1 highlight the variation within each group. For the low quintile group, the confidence intervals remain relatively narrow, indicating relatively less variability in performance. However, for the high quintile group, the confidence intervals widen over time, suggesting increasing variability in performance as the programme progresses. This widening suggests that students in this group experience more diverse academic outcomes—some continue to perform well, while others experience sharper declines.

3.3. Unobserved Heterogeneity in Student Performance

The third research question aimed to determine whether significant unobserved heterogeneity in student performance can be attributed to random effects at the student and module levels. Specifically, the question asked the following:

“Is there significant unobserved heterogeneity in student performance that can be attributed to random effects at the student and module levels?”

Analysing the random effects in the Bayesian hierarchical growth curve model provided evidence of unobserved heterogeneity in student performance at both levels. The student-level random intercepts showed variation in baseline academic performance, with values ranging from −0.08 to 0.04 (M = −0.01; see

Table 2. Summary of random effects and residual variability.

Random Effect	Minimum	1st Quartile	Median	Mean	3rd Quartile	Maximum
Student Intercepts	−0.08	−0.04	−0.00	−0.01	0.02	0.04
Student Slopes	−4.02	−3.53	−3.04	−2.45	−1.66	−0.28
Module Intercepts	−1.96	−0.08	0.18	0.00	0.34	0.78

). This indicates that individual students differ in their starting performance, suggesting the presence of latent factors beyond the included covariates, such as cognitive abilities, psychological factors, or prior educational experiences, all of which influence students’ academic performance. On average, students did not systematically deviate from the group mean, but the variation suggests that some students started significantly above or below the expected level.

Furthermore, the student-level random slopes demonstrated considerable variability, ranging from −4.02 to −0.28 (M = −2.45; see Table 2), reflecting differences in academic growth rates over time. This variability indicates that some students experience a steeper decline in performance compared to others, suggesting that unobserved factors such as motivation, study habits, or external support might influence their academic trajectories throughout the programme.

The random intercepts indicated variability across modules at the module level, ranging from −1.96 to 0.78 (M = 0.00; see Table 2). This suggests that some modules are systematically more difficult or lenient than others, even after controlling for student characteristics. These differences could be due to various factors, such as the complexity of the content, instructional quality, or variations in assessment methods and grading standards across modules. Understanding and addressing this variability is essential for ensuring equity in assessments and academic standards across the curriculum.

3.4. Model Adequacy and Posterior Predictive Check

A PPC was performed to evaluate the fit of the Bayesian hierarchical growth curve model to the observed data. The PPC compared the observed distribution of final marks with the posterior predictive distribution generated by the model. The results indicated that the model accurately captured the central tendency of the data, particularly for students achieving average performances (see Figure 2). However, the model exhibited slightly wider uncertainty in the distribution’s tails, especially for students with very low or very high marks. This suggests that the model may underfit the extreme ends of the performance distribution, potentially due to the influence of unmeasured factors or the need for additional covariates that specifically account for outlier performances.

The residual standard deviation (σ = 12.10, 95% CI [11.78, 12.44]) indicates that while the model explains a substantial proportion of the variance in final marks, there remains an unexplained variability. This residual variance suggests that additional factors, possibly related to student engagement, psychosocial attributes, learning environments, or external influences, may affect academic performance. Future research could further explore these dimensions to refine the model’s explanatory power and improve its fit, particularly for students at the extremes of the performance spectrum.

These findings highlight several critical factors influencing the academic success of BSc Actuarial Science students, with clear implications for admission policies, curriculum development, and student support systems. The strong effect of Grade 12 mathematics marks suggests that mathematics preparedness is a key predictor of success in Actuarial Science, aligning with existing research on the importance of prior math achievement for STEM fields. The significant impact of the school quintile underscores the ongoing challenge of socioeconomic inequality in higher education, suggesting that targeted interventions may be required to level the playing field for students from lower socioeconomic backgrounds.

The random effects demonstrate that individualised support is crucial, as students exhibit different growth trajectories not fully explained by their prior achievements. Additionally, the variability in module-level performance highlights the importance of maintaining equity in assessment practices across curriculums. This research contributes to the broader literature on student retention and success, reinforcing the importance of academic preparedness and institutional support in fostering positive outcomes in rigorous academic programmes such as BSc Actuarial Science. The study’s use of a Bayesian hierarchical growth curve model allows for exploring individual academic trajectories and identifying unobserved heterogeneity. This methodological approach provides nuanced insights into the factors influencing student performance over time and highlights the complexity of academic success determinants. By explicitly modelling random effects at the student and module levels, this research captures the multi-level nature of educational data and contributes to methodological advancements in educational research.

4. Discussion

This study explored the impact of individual-level characteristics, such as Grade 12 mathematics marks, socioeconomic background, and credits passed on students’ academic performance in the BSc Actuarial Science programme. The findings reveal several important insights that are supported by the existing literature and align with Human Capital Theory and Tinto’s Model of Student Integration.

The results indicate that higher Grade 12 mathematics marks significantly correlate with improved academic performance in the programme, supporting Hypothesis 1. This finding aligns with the existing literature, emphasising the foundational role of mathematics in actuarial studies. For instance, ref. [19] found that general high school knowledge, particularly mathematics, predicted university success more reliably than programme-specific entrance exams. This supports the notion that excelling in mathematics at the secondary level enhances preparedness for the rigorous curriculum of the Actuarial Science programme. Similarly, ref. [20] demonstrated a strong correlation between high school grades and university GPA in medical education, reinforcing the critical role of foundational knowledge in navigating complex quantitative fields. This finding aligns with the Human Capital Theory [17], which posits that education is an investment in human capital. Grade 12 mathematics marks represent an early investment in this human capital, and the positive correlation with academic success in university shows the returns on this investment. Students who excelled in mathematics in high school were better prepared for the rigorous demands of the Actuarial Science programme, validating the notion that prior investments in education lead to greater productivity and success.

Furthermore, the study revealed that socioeconomic factors, as indicated by the school quintile, significantly impact academic performance, confirming Hypothesis 2. Students from higher socioeconomic backgrounds tend to perform better than their counterparts from lower socioeconomic backgrounds. This finding corroborates with the work by [22], which highlights the persistent educational inequalities influenced by socioeconomic status. The disparities indicate the need for targeted interventions to support students from disadvantaged backgrounds, ensuring that all students have an equitable opportunity to succeed in mathematics-intensive programmes. Ref. [23] also highlighted that students from high-poverty schools faced greater challenges in achieving academic success, further emphasising the importance of addressing these inequalities in the context of Actuarial Science. This finding also aligns with Human Capital Theory, as students from higher socioeconomic backgrounds may have had more resources to invest in their education, leading to better academic outcomes. The disparities in performance between students from different socioeconomic backgrounds reflect unequal opportunities for human capital development, where students from wealthier families have access to better educational resources, enabling them to achieve greater academic success.

Addressing Hypothesis 3, the analysis of the number of credits passed during the academic year demonstrated a positive association with students’ final marks in the programme. This finding is consistent with the study by [26], who emphasised the importance of course engagement and completion as critical indicators of student success. Engaging in coursework and successfully passing modules correlate with better academic outcomes, underscoring institutions’ need to foster student engagement in their academic journeys. Furthermore, ref. [24] found that monitoring students’ GPA and credit accumulation could provide valuable insights into their future academic trajectories, suggesting that a proactive approach to tracking student progress may enhance retention rates. This finding aligns with Tinto’s Model of Student Integration, which emphasises the importance of academic engagement for student success. Passing more credits suggests that students are academically integrated into their institution, which includes actively participating in and completing their coursework. This integration leads to better academic outcomes; students will likely persist and succeed in their studies as they engage more in their academic activities.

Examining unobserved heterogeneity in student performance (Hypothesis 4) revealed significant variability across modules and student demographics. This finding points to individual factors that influence student outcomes beyond the measured covariates, such as personal motivation, study habits, and support systems. The variability observed is consistent with [27], who noted that student characteristics and stable institutional factors play critical roles in predicting outcomes. The variability in student performance highlights the importance of institutional support, as emphasised in Tinto’s Model of Student Integration. Students who are academically and socially supported within their institutions are more likely to succeed. The presence of unmeasured factors, such as personal motivation or social support systems, suggests that social integration and the institution’s role in fostering a supportive environment are crucial for academic success beyond academic integration.

5. Conclusions

This study provides critical insights into the factors influencing academic performance in the BSc Actuarial Science programme. First, it confirms the significant role of Grade 12 mathematics marks in predicting student success, reinforcing the importance of strong mathematical foundations for rigorous, quantitatively demanding fields like Actuarial Science. Socioeconomic factors, such as school quintile, were also shown to impact academic outcomes, with students from higher socioeconomic backgrounds generally outperforming those from disadvantaged backgrounds. This result highlights ongoing inequalities in access to quality education and the need for targeted interventions to support underprivileged students. A notable finding is the relatively weak and uncertain relationship between AP scores and final marks, with the credible interval encompassing zero, indicating that high AP scores, while a prerequisite for admission, may not meaningfully differentiate student performance in this programme. Moreover, the positive relationship between credit accumulation and final marks emphasises the importance of student engagement in coursework and progression through academic programmes. The study also identified unobserved individual factors such as personal motivation, study habits, and external support systems that contribute to academic performance beyond the measured covariates. These findings suggest that universities must adopt a holistic view of student success, factoring in both academic preparedness and individual support needs.

One of the primary strengths of this study is its comprehensive analysis of multiple factors including academic preparedness (as indicated by Grade 12 mathematics marks), socioeconomic background, student engagement (credit accumulation), and their combined influence on academic performance in a highly demanding programme. Using a large, representative sample and rigorous statistical methods, including exploring unobserved heterogeneity, adds robustness to the findings. Additionally, the study’s ability to highlight measured and unmeasured variables provides a more holistic understanding of student performance, which can inform institutional policies on admissions and student support services. These strengths make the findings highly relevant for shaping interventions to improve academic success, especially for students from diverse backgrounds and varying levels of preparedness.

5.1. Educational Implications

The findings of this study have significant implications for educational policy, especially concerning university admissions, curriculum development, and student support services. First, the strong link between Grade 12 mathematics performance and success in quantitative fields like Actuarial Science suggests that institutions should prioritise mathematics skills in their admissions criteria or introduce bridging programmes for underprepared students. This would help align student readiness with the demands of rigorous programmes. However, the relatively weak and uncertain relationship between AP scores and final marks highlights critical considerations for admissions policies. Institutions that rely heavily on high AP scores as a prerequisite may overlook other predictors of academic success, such as non-cognitive skills, personal motivation, and resilience. This calls for a re-evaluation of admissions processes to adopt a more holistic approach. Incorporating additional assessments or metrics could help identify students with the potential to succeed in demanding environments beyond their prior academic achievements. Furthermore, the limited differentiation in performance among students admitted with high AP scores suggests that universities should provide tailored academic support and resources to help all students thrive, regardless of their initial admissions profiles.

The disparities in academic performance based on socioeconomic status also highlight the need for policies that address inequality, such as improving access to quality education in under-resourced schools and expanding financial aid and mentorship programmes for disadvantaged students. This would ensure equal opportunities for success regardless of background. Additionally, policies should emphasise continuous student engagement through strategies like formative assessments, peer tutoring, and academic advising. Expanding access to support services, such as academic counselling and study skills workshops, would help students stay on track. Finally, recognising non-academic factors like personal motivation, study habits, and external support systems is crucial. A holistic approach, including mentorship and mental health support, would better address the diverse needs of students in demanding academic environments.

5.2. Limitations

This study has several limitations that warrant consideration. First, the analysis is based on data from a single academic programme (BSc Actuarial Science) at one institution, which may limit the generalizability of the findings to other disciplines or universities. Future studies should extend this research to multiple institutions and a broader range of academic programmes to provide a more comprehensive understanding. Second, while this study highlights Grade 12 mathematics performance and socioeconomic factors as key influences, it does not fully account for other critical variables, such as individual student motivations, teaching quality, and peer influence, which may significantly impact academic outcomes. Future research could integrate these variables to build a more holistic model of academic performance. Third, this study does not explore the potential mediating role of socioeconomic status (SES) in the relationship between pre-university mathematics performance and academic success. This is a notable gap given SES’s well-documented influence on education. Investigating SES as a mediating or moderating factor could provide deeper insights into the dynamics of academic success. Fourth, while the methodological approach used effectively captures variability in academic performance, the slight underfitting observed at the extremes of the performance distribution suggests that additional covariates or more complex models might better account for outlier performances. Future studies should consider these enhancements to improve the precision of predictions. Lastly, the cross-sectional design limits the ability to assess long-term academic trajectories, as the data reflect a snapshot of performance rather than changes over time. Employing a longitudinal design in future research could provide insights into how the observed factors influence academic outcomes across different stages of higher education.

5.3. Recommendations

Based on the findings of this study, several recommendations are suggested as follows:

• Higher education institutions should place a stronger emphasis on Grade 12 mathematics marks during the admission process and consider introducing bridging programmes for students who need additional mathematical preparation. This would ensure that students entering demanding programmes are adequately prepared;
• Policies aimed at reducing educational inequalities should be strengthened. These include increasing access to quality education in under-resourced schools and expanding financial aid and mentorship opportunities for disadvantaged students;
• Universities should implement continuous academic engagement strategies, including frequent formative assessments, peer tutoring, and academic advising, to ensure students remain on track throughout their studies;
• Support services personnel should work closely with the faculty and students to offer targeted interventions that address emotional, psychological, and motivational challenges. This should involve regular mental health check-ins, counselling, and workshops on personal development alongside academic tutoring.