https://www.um.edu.mt/library/oar/handle/123456789/1034 Wed, 24 Jun 2026 21:23:08 GMT 2026-06-24T21:23:08Z https://www.um.edu.mt/library/oar/handle/123456789/147185 Title: Using robust non-parametric and semi parametric survival techniques to analyze student dropout in university courses Authors: Fenech, Mireille; Camilleri, Liberato; Karagoz, Derya Abstract: The Kaplan Meier (KM) estimator and the Cox Proportional Hazards(CPH) model have been used extensively to analyze survival data in educational settings, however, these statistical techniques are vulnerable to outliers. This paper explores the robust KM estimator and the robust CPH model to analyze durations of students in university courses before dropout in the presence of influential observations. These outliers can severely impact the parameter estimates and lead to incorrect inferences. The bias-adjusted KM estimator is the first technique used in this paper to overcome the impact of outlier. The estimator uses an empirical likelihood weighting to enforce the equality of the covariate distributions, more specifically the equality of the moments of the covariates between comparison groups. The robust CPR model is the second technique used in this paper to overcome the impact of influential observation. This method, proposed by Bednarski(1993), is based on a smooth modification of the partial likelihood (PL)which yields reliable estimates of the effect sizes of different predictors on survival durations in the presence of data contamination. These robust techniques are used to investigate student dropouts in undergraduate courses at the Faculty of Science in the University of Malta (UOM). Using the student cohort that commenced their studies in 2022, the study examines the impact of a number of predictors on student dropout rates using the bias-adjusted KM estimator and the robust CPR model.The predictors include gender, admission score, and selected subjects. Moreover, the study compares the results obtained from traditional Kaplan Meier and Cox regression analysis with their robust alternative approaches to assess the stability of hazard ratio (HR) estimates. This paper demonstrates that in the presence of outliers and influential observations, the robust KM estimator and the robust CPR approach yield robust parameter estimates without a notable loss of efficiency. One of the findings shows that the number of dropouts peak at the end of the first year of tertiary education but then reduces gradually in subsequent years. Other findings show that pre tertiary academic achievement and the selection of course subjects have a huge impact on dropout rates. Mon, 01 Jun 2026 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/147185 2026-06-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/147019 Title: Analyzing ordinal categorical responses using multilevel models with an application related to dancing Authors: Camilleri, Liberato; Pellicano, Milena Abstract: Ordinal categorical outcomes frequently arise in applied research, particularly in settings where responses are recorded using rating scores rather than continuous measurements. In many practical applications, the data may be nested in higher level structures, with observations clustered within higher-level units, leading to dependence that cannot be adequately handled by standard regression models. This paper analyses ordinal categorical responses within a multilevel modelling framework, with particular emphasis on likelihood-based estimation methods for generalized mixed-effects models and their practical application to dance competition data. The study first develops the theoretical foundation of two-level models for ordinal responses assuming a multinomial distribution and a logit link function. Particular attention is given to random intercept and random coefficient structures, the interpretation of between-cluster variation, and the role of intra-class correlation in assessing dependence within hierarchical data. The paper then discusses the estimation and inferential techniques used for multilevel ordinal models and explores procedure to overcome difficulties that arise when the marginal likelihood involves integrals over random effects that do not have a closed-form solution. The study examines various numerical integration methods used in marginal likelihood estimation, with emphasis on Gaussian quadrature and Gauss-Hermite quadrature. The construction of quadrature rules and their role in approximating intractable integrals are discussed in detail, together with the use of modified Newton-Raphson procedures for maximising the approximated likelihood. In addition, Bayesian ideas are introduced in the context of predicting random effects, where empirical Bayes estimates (posterior means) are used to obtain cluster-specific predictions within the fitted models. These modelling methods are applied to a dance competition dataset. Since the dancing performance scores awarded by judges had a left skewed non-normal distribution, it was decided to categorise these scores to five ordinal response categories and analysed using multilevel logit models. The hierarchical structure is represented by individual performers (level-1 units) nested within dance types (level-2 units) allowing two-level models to be fitted. The models are implemented in Stata using the GLLAMM software, which provides flexible likelihood-based estimation for multilevel models with ordinal responses using numerical integration. The analysis demonstrates how multilevel models for ordinal responses can be used to account for clustering, estimate random-effects variability, compare alternative model structures, and interpret the effects of explanatory variables in a practically meaningful way. Overall, the paper provides a methodological and applied examination of multilevel modelling for ordinal categorical data. It shows that when ordinal responses are analysed within a hierarchical framework, likelihood-based estimation supported by quadrature methods offers a rigorous and practical approach for modelling complex dependence structures and obtaining interpretable statistical inferences. Thu, 01 Jan 2026 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/147019 2026-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/146074 Title: Improving discharge summary documentation of older adults in a rehabilitation hospital with an electronic discharge template Authors: Portelli, Christopher; Bonnici, Maria; Scerri, Claudia; Camilleri, Liberato; Ferry, Peter Abstract: Background: During past quality improvement projects at our rehabilitation hospital, inconsistencies were observed in the inclusion of essential information in discharge notes. The introduction of an electronic discharge summary template (EDST) aimed to address this by providing guidance to clinicians for comprehensive documentation. Methods: The EDST was developed through feedback from healthcare professionals using the Delphi method. 100 discharge letters were audited against the EDST criteria before and after implementation, following formal training for foundation year doctors. Results: Initial analysis revealed areas requiring improvement, particularly the Barthel score, patient weight, and cognitive assessment. Following implementation of the EDST, significant improvements were observed in these areas. Conclusion: The introduction of the EDST resulted in improved documentation and overall discharge summary completeness, supporting ongoing improvements in patient care continuity. Thu, 01 Jan 2026 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/146074 2026-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/145333 Title: Solving the inverse shortest path problem for earthquakes’ motion Abstract: According to Fermat’s principle, seismic waves follow paths of least travel time. Thus, shortest path algorithms such as Dijkstra’s can be used to determine these paths. Conversely, inferring the parameters of a mathematical program from an observed optimal path defines the inverse shortest path problem, an area within inverse optimisation. With its wide range of applicability, inverse optimisation has attracted considerable interest. One of the earliest topics in this field was the inverse shortest path problem, with Burton and Toint (1992) laying its foundations. Since then, this problem has been explored across several domains, with various mathematical formulations and algorithms proposed. This dissertation examines the inverse shortest path problem in depth, reviews its theoretical foundations, and applies it to a seismological case study. Three algorithms are employed to solve the problem: the column generation algorithm, a quadratic programming algorithm, and a deep inverse optimisation algorithm using a modern deep learning framework. The aim is to estimate the weight vector using these algorithms, thereby reconstructing the mathematical program that defines the shortest paths taken by seismic waves. To the best of the author’s knowledge, this is the first study to apply the inverse shortest path problem to local seismic data from the Maltese Islands and Sicily. Description: M.Sc.(Melit.) Wed, 01 Jan 2025 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/145333 2025-01-01T00:00:00Z