https://www.um.edu.mt/library/oar/handle/123456789/1034 2026-06-02T16:12:04Z 2026-06-02T16:12:04Z Camilleri, Liberato Pellicano, Milena https://www.um.edu.mt/library/oar/handle/123456789/147019 2026-06-01T13:32:33Z 2026-01-01T00:00:00Z

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.

2026-01-01T00:00:00Z Portelli, Christopher Bonnici, Maria Scerri, Claudia Camilleri, Liberato Ferry, Peter https://www.um.edu.mt/library/oar/handle/123456789/146074 2026-04-30T10:28:20Z 2026-01-01T00:00:00Z

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.

2026-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/145333 2026-04-06T09:52:34Z 2025-01-01T00:00:00Z

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.)

2025-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/145332 2026-04-06T09:40:35Z 2025-01-01T00:00:00Z

Title: Seismic source characterization in the central Mediterranean Region Abstract: The process of earthquake source characterization involves determining the key properties of an earthquake and its origin, including its location, as indicated by latitude and longitude coordinates, its depth and its magnitude. This dissertation focuses on establishing a statistical model, by combining different Neural Network (NN) architectures including the Multi-Layer Perceptron (MLP), Convolutional Neural Network (CNN) and Graph Neural Network (GNN), in order to characterize the source of the earthquakes occurring in the central Mediterranean region, particularly concentrating on the Maltese islands, Sicily and the surrounding areas. The models considered are trained and validated on earthquake data recorded between 2013 and 2024. These data were obtained from seismic stations positioned around the Maltese Islands and Sicily, which are installed and maintained by the Istituto Nazionale di Geofisica e Vulcanologia (INGV) and the University of Malta’s Seismic Monitoring and Research Group (SMRG). The objective is to predict earthquake source parameters using station coordinates and waveform features. Each earthquake is represented as a graph in which the vertices correspond to stations, and the associated features are assigned to these nodes. For each event, the model outputs latitude, longitude, depth, and magnitude. Two model architectures are considered, namely, an edgeless graph model and a dynamic edges GNN. To identify the optimal model of each architecture, a systematic series of experiments, including hyperparameter tuning, regularization techniques, restricting the analysis to a more localized region and ensemble modelling, are conducted. The best two models are then fit on test data comprising events from January 2025 to August 2025. The edgeless graph architecture emerged as the best-performing architecture. Description: M.Sc.(Melit.)

2025-01-01T00:00:00Z