## 3 Results
### 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 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 (\(\beta\) = 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 (\(\beta\) = 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  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Covariate** & **M** & **SE** & **95\% CI (Lower, Upper)** \\ \hline AP Score (\(\beta_{1}\)) & 0.10 & 0.06 & [\(-\)0.03, 0.22] \\ \hline Grade 12 Math (\(\beta_{2}\)) & 0.42 & 0.03 & [0.37, 0.49] \\ \hline School Quintile (\(\beta_{3}\)) & 1.69 & 0.19 & [1.33, 2.07] \\ \hline Credits Passed (\(\beta_{4}\)) & 0.15 & 0.01 & [0.14, 0.16] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Posterior estimates for individual-level characteristics.  
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 (\(\beta\) = 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 (\(\beta\) = 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.