OAR@UM Collection:
https://www.um.edu.mt/library/oar/handle/123456789/30457
2024-03-28T11:01:59ZAnalyzing longitudinal count data related to re-sits in the faculty of science using GLMs and hierarchical poisson random coefficient models
https://www.um.edu.mt/library/oar/handle/123456789/93463
Title: Analyzing longitudinal count data related to re-sits in the faculty of science using GLMs and hierarchical poisson random coefficient models
Abstract: The GLM family subsumes a large number of statistical models that are widely used in
practical applications for prediction purposes. GLMs overcome the limitations of
traditional Regression models, which assume a Normal distribution for the responses. In
this thesis, we present three GLMs to forecast the number of ECTS resits for students in
the Faculty of Science. The first model is a Normal regression model that is plagued by
model misspecifications. The second and third models improve the model fit by
assuming a Poisson and Gamma distribution that respectively lead to the logarithmic and
reciprocal canonical link functions. Three predictors were identified that were thought to
contribute considerably in explaining the variability in the responses. These include the
University entry qualification score, the subjects studied and the year in which the ECTS
resit count was recorded.
A limitation of GLMs is that they assume independence for the responses. It is very
implausible that responses from longitudinal data are independent. An approach that
overcomes this limitation is based on considering the hierarchical structure of the study
design. Multilevel models, also known as random coefficient models, focus on nested
sources of variability and involve measurements of variables for more than one level of
hierarchy. Our data set comprise responses (number of ECTS resits) that are nested
within the students (level-2 units) and students that are nested within departments (level 3 units). The data is appropriate for multilevel modelling.
In this dissertation, we present four multilevel models to forecast the number of ECTS
resits for B.Sc.(Hons.) students. These include a random intercept and a random
coefficient model each with two and three levels of nesting.
Description: B.SC.(HONS)STATS.&OP.RESEARCH2017-01-01T00:00:00ZNonparametric density estimation concerning social benefits in Malta
https://www.um.edu.mt/library/oar/handle/123456789/72988
Title: Nonparametric density estimation concerning social benefits in Malta
Abstract: Nonparametric density estimation involves obtaining an estimate for the unknown
probability density function given a sample of size đť‘› but without having any prior knowledge
on the form of the function. We shall consider the wavelet and kernel density estimation
methods to obtain the estimate of the unknown density function. Since this density function
is unknown, we shall work in an infinite dimensional space. However, in practice we are not
able to work in this space, thus we shall use the method of sieves to approximate our infinite
dimensional space with a sequence of finite dimensional spaces. We shall use wavelets as
our orthonormal bases which will then be used to obtain the required wavelet density
estimator. On the other hand, the kernel density estimator is based on the choice on the
smoothing parameter and the kernel function. We shall compare the two nonparmateric
methods by applying both techniques to a sample of Maltese individuals who were entitled
to receive different types of social benefits.
Description: B.SC.(HONS)STATS.&OP.RESEARCH2017-01-01T00:00:00ZAn overview of ROC analysis
https://www.um.edu.mt/library/oar/handle/123456789/72977
Title: An overview of ROC analysis
Abstract: The Receiver Operating Characteristic (ROC) curve is considered to be one of the
best developed statistical tools to analyze the performance of binary classifier systems,
such as medical diagnostic tests, and to classify elements of a population into two
groups, namely “diseased” and “healthy”. In this dissertation, the theoretical construct
of the ROC curve is studied, along with summary measures derived from the ROC
curve, particularly the Area under the Curve (AUC). Different techniques from three
estimation frameworks, namely the non-parametric, parametric and semi-parametric
frameworks, are discussed, and their performance is compared using simulation studies.
The best estimation techniques, according to the simulation studies, are then applied
to two real medical datasets, obtained from Mater Dei hospital. Methodology on how
an optimal threshold value is derived from the ROC curve is discussed, and is then used
to determine the best threshold for both applications.
Description: B.SC.(HONS)STATS.&OP.RESEARCH2017-01-01T00:00:00ZTesting efficiency of football betting markets using adaptive drift models
https://www.um.edu.mt/library/oar/handle/123456789/72975
Title: Testing efficiency of football betting markets using adaptive drift models
Abstract: Over the years, the efficiency of financial markets has been studied extensively in
literature, and the interest for investigating notions of efficiency also in the context
of sports betting markets has been growing considerably. In its semi-strong form,
the efficient market hypothesis holds the concept that a market is efficient if it fully
reflects all publicly available information and has the ability to efficiently adapt to new
information. Under efficiency, betting strategies based on this information should not
be able to generate significant profits and consistent winning patterns. In this study,
betting strategies informed by goal difference forecasts obtained from adaptive drift
models are used to investigate the efficiency of Asian handicap betting markets for
German football games. Findings based on predictions for the 2015/16 and 2016/17
Bundesliga seasons for FC Bayern Munich games suggest that efficiency and the efficient
market hypothesis are supported. However, applying similar methodologies for 1. FSV
Mainz 05 yields substantial winnings and indicates that inefficiency may be detected
among various bookmakers.
Description: B.SC.(HONS)STATS.&OP.RESEARCH2017-01-01T00:00:00Z