## 3 Results
### 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 (\(\sigma\) = 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  
Figure 2: Posterior predictive check: observed vs. predicted.  
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.