Browsing by Author "North, Delia Elizabeth."

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Appraising South African residential property and measuring price developments.
(2022) Bax, Dane Gregory.; Zewotir, Temesgen Tenaw.; North, Delia Elizabeth.
Housing wealth is well established as one of the most important sources of wealth for households and investors. However, owning a home is a fundamental human need, making monitoring residential property prices a social endeavour as well as an economic one, especially under times of economic uncertainty. Residential property prices also have a direct effect on the macroeconomy because of how they influence wealth effects where increased consumption by households is experienced through gains in households balance sheets due to increased equity. Collecting correct and adequate data is vitally important in analysing property market movements and developments, particularly given globalization, and the interlinked nature of financial markets. Although measuring residential property price developments is an important economic and social activity, matching properties over time is extremely difficult because the sale of homes is typically infrequent, characteristics vary, and homes are uniquely located in space. This thesis focuses on appraising several residential property types located throughout South Africa from January 2013 to August 2017, investigating different modelling approaches with the aim of developing a residential property price index. Various methods exist to create residential property price indices, however, hedonic models have proven useful as a quality adjusted approach where pure price changes are measured and not simply changes in the composition of samples over time. Before fitting any models to appraise homes, an autoencoder was built to detect anomalous data, due to human error at the data entry stage. The autoencoder identified improbable data resulting in a final data set of 415 200 records, once duplicate records were identified and removed. This study first investigated generalised linear models as a candidate approach to appraise homes in South Africa which showed possible alternatives to the ubiquitous log linear model. Relaxing functional form assumptions and considering the nested locational structure of homes, hierarchical generalised linear models were considered as the next candidate method. Partitioning around the mediods was applied to find additional spatial groupings which were treated as random effects along with the suburb. The findings showed that the marginal utility of structural attributes was non-linear and smooth functions of covariates were an appropriate treatment. Furthermore, the use of random effects helped account for the spatial heterogeneity of homes through partial pooling. Finally, machine learning algorithms were investigated because of minimal assumptions about the data generating process and the possibility of complex non-linear and interaction effects. Random forests, gradient boosted machines and neural networks were adopted to fit these appraisal functions. The gradient boosted machines had the best goodness of fit, showing non-linear relationships between the structural characteristics of homes and listing prices. Partial dependence plots were able to quantify the marginal utility over the distributions of different structural characteristics. The results show that larger sized homes do not necessarily yield a premium and a diminished return is evident, similar to the results of the hierarchical generalised additive models. The variable importance plots showed that location was the most important predictor followed by the number of bathrooms and the size of a home. The gradient boosted machines achieved the lowest out of sample error and were used to develop the residential property price index. A chained, dual imputation Fisher index was applied to the gradient boosted machines showing nominal and real price developments at a country and provincial level. The chained, dual imputation Fisher index provided less noisy estimates than a simple median mix adjusted index. Although listing prices were used and not transacted prices, the trend was similar to the ABSA Global Property Guide. In order to make this research useful to property market participants, a web application was developed to show how the proposed methodology can be democratised by property portals and real estate agencies. The Listing Price Index Calculator was created to easily communicate the results through a front-end interface, showing how property portals and real estate agencies can leverage their data to aid sellers in determining listing prices to go to market with, help buyers obtain an average estimate of the home they wish to purchase and guide property market participants on price developments.
An assessment of modified systematic sampling designs in the presence of linear trend.
(2017) Naidoo, Llewellyn Reeve.; North, Delia Elizabeth.; Zewotir, Temesgen Tenaw.; Arnab, Raghunath.
Sampling is used to estimate population parameters, as it is usually impossible to study a whole population, due to time and budget restrictions. There are various sampling designs to address this issue and this thesis is related with a particular probability sampling design, known as systematic sampling. Systematic sampling is operationally convenient and efficient and hence is used extensively in most practical situations. The shortcomings associated with systematic sampling include: (i) it is impossible to obtain an unbiased estimate of the sampling variance when conducting systematic sampling with a single random start; (iii) if the population size is not a multiple of the sample size, then conducting conventional systematic sampling, also known as linear systematic sampling, may result in variable sample sizes. In this thesis, I would like to provide some contribution to the current body of knowledge, by proposing modifications to the systematic sampling design, so as to address these shortcomings. Firstly, a discussion on the measures used to compare the various probability sampling designs is provided, before reviewing the general theory of systematic sampling. The per- formance of systematic sampling is dependent on the population structure. Hence, this thesis concentrates on a specific and common population structure, namely, linear trend. A discussion on the performance of linear systematic sampling and all relative modifica- tions, including a new proposed modification, is then presented under the assumption of linear trend among the population units. For each of the above-mentioned problems, a brief review of all the associated sampling designs from existing literature, along with my proposed modified design, will then be explored. Thereafter, I will introduce a modified sampling design that addresses the above-mentioned problems in tandem, before providing a comprehensive report on the thesis. The aim of this thesis is to provide solutions to the above-mentioned disadvantages, by proposing modified systematic sampling designs and/or estimators that are favourable over its existing literature counterparts. Keywords: systematic sampling; super-population model; Horvitz-Thompson estimator; Yates' end corrections method; balanced modified systematic sampling; multiple-start balanced modified systematic sampling; remainder modified systematic sampling; balanced centered random sampling.
Count data modelling application.
(2019) Ibeji, Jecinta Ugochukwu.; North, Delia Elizabeth.; Zewotir, Temesgen Tenaw.
The rapid increase of total children ever born without a proportionate growth in the Nigerian economy has been a concern and making prediction with count data requires applying appropriate regression model.. As count data assumes discrete, non-negative values, a Poisson distribution is the ideal distribution to describe this data, but it is deficient due to equality of variance and mean. This deficiency results in under/over-dispersion and the estimation of the standard errors will be biased rendering the test statistics incorrect. This study aimed to model count data with the application of total children ever born using a Negative Binomial and Generalized Poisson regression The Nigeria Demographic and Health Survey 2013 data of women within the age of 15-49 years were used and three models applied to investigate the factors affecting the number of children ever born. A predictive count modelling was also carried out based on the performance evaluation metrics (root mean square error, mean absolute error, R-squared and mean square error). In the inferential modeling, Generalized Poisson Model was found to be superior with age of household head (𝑃<.0001), age of respondent at the time of first birth (𝑃<.0001), urban-rural status (𝑃<.0001), and religion (𝑃<.0001) being significantly associated with total children ever born. In the predictive modeling, all the three models showed almost identical performance evaluation metrics but Poisson regression was chosen as the best because it is the simplest model. In conclusion, early marriage, religious belief and unawareness of women who dwell in rural areas should be checked to control total children ever born in Nigeria.
Determinants of optimal adherence over time to antiretroviral therapy amongst HIV positive adults in South Africa : a longitudinal study.
(Springer Verlag., 2011) Maqutu, Dikokole.; Zewotir, Temesgen Tenaw.; North, Delia Elizabeth.; Grobler, Anna Christina.
Highly active antiretroviral therapy (HAART) requires strict adherence to achieve optimal clinical and survival benefits. A study was done to explore the factors affecting HAART adherence among HIV positive adults by reviewing routinely collected patient information in the Centre for the AIDS Programme of Research in South Africa’s (CAPRISA) AIDS Treatment Programme. Records of 688 patients enrolled between 2004 and 2006 were analysed. Patients were considered adherent if they had taken at least 95% of their prescribed drugs. Generalized estimating equations were used to analyse the data. The results showed that HAART adherence increased over time, however, the rate of increase differed by some of the socio-demographic and behavioural characteristics of the patients. For instance, HAART adherence increased in both urban and rural treatment sites over time, but the rate of increase was higher in the rural site. This helped identify sub-populations, such as the urban population, that required ongoing adherence counseling.
Exploring teachers’ instructional practices, confidence and beliefs in teaching mathematics and statistics.
(2018) Umugiraneza, Odette.; Bansilal, Sarah.; North, Delia Elizabeth.
An important contributor to the quality of teaching mathematics is the knowledge of mathematics teachers. In this study, I explore mathematics teachers’ instructional practices, their confidence and beliefs about the teaching of mathematics and statistics concepts. The reason for focusing on mathematics as well as statistics teaching is that in several schools’ mathematics teachers also teach statistics (because statistics is a part of mathematics). This inspired me to undertake a study in order to investigate teachers’ instructional practices in teaching both mathematics and statistics among learners from grade 4 and upwards in KwaZulu-Natal (KZN) schools. The use of KZN as a research location provides an advantage of identifying issues of mathematics teachers’ practices in developing countries. The study was conducted with 75 mathematics teachers from KwaZulu-Natal (KZN) in South Africa who agreed to participate in the study while they were enrolled in an in-service course designed to improve their understanding of statistics. The teachers were invited to participate by filling in a detailed questionnaire, which was adopted from the study of Beswick, Callingham and Watson (2012) which was conducted with teachers from Australia. The detailed questionnaire consisted of open ended, Likert scale as well as yes-no responses. The instrument surveyed the teachers about various aspects of their teaching practices such as the formulation of lesson objectives, the use of the different approaches to introduce mathematics and statistics topics, the use of various teaching and assessments strategies to teach different topics as well as their descriptions about learners’ possible understanding or misunderstanding of the topics. The study also elicited from the teachers their reflections about how they would improve mathematics and statistics teaching and learning. In addition, the study examined the teachers’ beliefs about using mathematics and statistics in everyday life as well as in the classroom, and their confidence in relation to teaching the various mathematics and statistics topics. In addition, the study explored how teachers integrate technology in teaching and learning maths/stats topics. Furthermore, their content knowledge was put under the spotlight through the examination of their solutions to mathematical tasks. The findings revealed that 65.3% of the participants managed to set appropriate lesson objectives. Moreover, these teachers reported that they mostly use practical examples, real life approaches and explicit instruction when teaching the topics. It was also reported by most teachers that they tend to focus on a single approach when they introduce a concept in the classroom. Furthermore, less than half the teachers reported that their learners showed an understanding of mathematics and statistics concepts. For the methods and assessments, teachers generally use a single method and more than one type of assessment. I also found that teachers mostly focus on teacher-led instructional methods and formal assessments. Furthermore, the findings revealed that teachers’ demographic factors such as teaching experience, gender and participation in professional development courses are associated with the choice of a variety of teaching and assessments methods (p-value<0.05). For the use of curriculum, the findings revealed that 19% of teachers had no idea about how they would integrate topics across the curriculum in teaching and learning. With respect to the teachers’ reflections about improving teaching and learning mathematics and statistics, teachers said that developing learners’ interest in learning these conceptions, developing grouping and learner-centred approaches for teaching, applying investigation, practical and real life examples would contribute to improvements. Furthermore, the findings suggest that teachers should use the curriculum in the teaching process and upgrade their studies by doing postgraduate courses in education as the factors that would influence them to make a continuous improvement in the teaching process. The findings showed that participating in professional development courses is a factor that motivate teachers to use curriculum (p-value<0.05). For their content knowledge about solving specific tasks, the findings revealed that teachers demonstrated more understanding in finding the correct answer for the problem of using percentage than for fraction and pie chart. However, they struggled to provide justifications for their answers. This indicated a lack of specialised content knowledge, which refers to ability to give the detailed mathematics explanations to teach the given task and weigh up and analyse unconventional solution methods of their students. Teaching experience becomes an important factor to help teachers develop their content knowledge and solve mathematical tasks appropriately (p-value<0.05). In terms of their confidence in teaching various topics, the finding revealed that teachers were confident in teaching fractions, decimals, percentages, histograms and pie charts, patterns and measurements; however their confidence was lower with respect to teaching aspects requiring connections between mathematics and statistics to other learning areas. In relation to their beliefs, teachers reported a positive view towards the need to be mathematically and statistically literate in everyday life, as well in their teaching practices in general. With regards to the use of technology in teaching mathematics and statistics, the findings indicated that almost all the teachers reported that they never use computers in mathematics and statistics discourse. Although the teachers reported that they do not use computers in teaching and learning, about 80% of the participants conveyed a positive view that using technology improves learners’ understanding of mathematics and statistics. The findings further indicate that the teachers’ propensity to use technology in instructional practice is associated with demographic factors of age, experience and gender (p-value<0.05). The study suggests that teachers should attend more professional development programmes which would improve existing teaching strategies.
Factors affecting first-month adherence to antiretroviral therapy among HIV-positive adults in South Africa.
(Taylor & Francis co-published with NISC., 2010) Maqutu, Dikokole.; Zewotir, Temesgen Tenaw.; North, Delia Elizabeth.; Naidoo, Kogieleum.; Grobler, Anna Christina.
This study explores the influence of baseline factors on first-month adherence to highly active antiretroviral therapy (HAART) among adults. The study design involved a review of routinely collected patient information in the CAPRISA AIDS Treatment (CAT) programme, at a rural and an urban clinic in KwaZulu-Natal Province, South Africa. The records of 688 patients enrolled in the CAT programme between June 2004 and September 2006 were analysed. Adherence was calculated from pharmacy records (pill counts) and patients were considered adherent if they had taken at least 95% of their prescribed drugs. Logistic regression was used to analyse the data and account for confounding factors. During the first month of therapy, 79% of the patients were adherent to HAART. HAART adherence was negatively associated with a higher baseline CD4 count. Women had better adherence if they attended voluntarily testing and counselling or if they had taken an HIV test because they were unwell, while men had higher adherence if they were tested due to perceived risk of HIV infection. HAART adherence was positively associated with higher age among patients who possessed cell phones and among patients who provided a source of income in the urban setting, but not in the rural setting. Though long-term data from this cohort is required to fully evaluate the impact of non-adherence in the first month of treatment, this study identifies specific groups of patients at higher risk for whom adherence counselling should be targeted and tailored. For example, first-month HAART adherence can be improved by targeting patients initiated on treatment with a high CD4 count.
Imputation for nonresponse using the Annual Financial Statistics Survey.
(2011) Singh, Smeeta.; North, Delia Elizabeth.; Zewotir, Temesgen Tenaw.
In this dissertation, we focus on the Annual Financial Statistics (AFS) survey. This is a survey conducted by Statistics South Africa, the national statistics office of South Africa. The main purpose of this survey is to provide information for compiling of the GDP estimates, value-added and its components, which are used to monitor and develop government policies. The AFS covers a sample of private enterprises operating the formal non-agricultural business sector of the South African economy, excluding financial, insurance and government institutions. Quality is a key area of importance in this organisation and therefore methodology and standards need to be monitored, evaluated and reviewed on a regular basis. This would assist in ensuring that Statistics South Africa is following international best practices for collection and estimation of official statistics. We focus on nonresponse for the Annual Financial Statistics survey, and investigate an alternative method for adjusting for nonresponse and in particular focus on improving the method of dealing with nonresponse thereby improving the estimates from the AFS survey.
Inference from finite population sampling : a unified approach.
(2007) Hargovan, Kashmira Ansuyah.; Arnab, Raghunath.; North, Delia Elizabeth.
In this thesis, we have considered the inference aspects of sampling from a finite population. There are significant differences between traditional statistical inference and finite population sampling inference. In the case of finite population sampling, the statistician is free to choose his own sampling design and is not confined to independent and identically distributed observations as is often the case with traditional statistical inference. We look at the correspondence between the sampling design and the sampling scheme. We also look at methods used for drawing samples. The non – existence theorems (Godambe (1955), Hanurav and Basu (1971)) are also discussed. Since the minimum variance unbiased estimator does not exist for infinite populations, a number of estimators need to be considered for estimating the same parameter. We discuss the admissible properties of estimators and the use of sufficient statistics and the Rao-Blackwell Theorem for the improvement of inefficient inadmissible estimators. Sampling strategies using auxiliary information, relating to the population, need to be used as no sampling strategy can provide an efficient estimator of the population parameter in all situations. Finally few well known sampling strategies are studied and compared under a super population model.
Longitudinal clinical covariates influence on CD4+ cell count after seroconversion.
(2019) Tinarwo, Partson.; Zewotir, Temesgen Tenaw.; North, Delia Elizabeth.
The Acquired Immunodeficiency Syndrome (AIDS) pandemic is a global challenge. The human immunodeficiency virus (HIV) is notoriously known for weakening the immune system and opening channels for opportunistic infections. The Cluster of Difference 4 (CD4+) cells are mainly killed by the HIV and hence used as a health indicator for HIV infected patients. In the past, the CD4+ count diagnostics were very expensive and therefore beyond the reach of many in resource-limited settings. Accordingly, the CD4+ count’s clinical covariates were the potential diagnostic tools. From a different angle, it is essential to examine a trail of the clinical covariates effecting the CD4+ cell response. That is, inasmuch as the immune system regulates the CD4+ count fluctuations in reaction to the viral invasion, the body’s other complex functional systems are bound to adjust too. However, little is known about the corresponding adaptive behavioural patterns of the clinical covariates influence on the CD4+ cell count. The investigation in this study was carried out on data obtained from the Centre for the Programme of AIDS research in South Africa (CAPRISA), where initially, HIV negative patients were enrolled into different cohorts, for different objectives. These HIV negative patients were then followed up in their respective cohort studies. As soon as a patient seroconverted in any of the cohort studies, the patient was then enrolled again, into a new cohort of HIV positive patients only. The follow-up on the seroconvertants involved a simultaneous recording of repeated measurements of the CD4+ count and 46 clinical covariates. An extensive exploratory analysis was consequently performed with three variable reduction methods for high-dimensional longitudinal data to identify the strongest clinical covariates. The sparse partial least squares approach proved to be the most appropriate and a robust technique to adopt. It identified 18 strongest clinical covariates which were subsequently used to fit other sophisticated statistical models including the longitudinal multilevel models for assessing inter-individual variation in the CD4+ count due to each clinical covariate. Generalised additive mixed models were then used to gain insight into the CD4+ count trends and possible adaptive optimal set-points of the clinical covariates. To single out break-points in the change of linear relationships between the CD4+ count and the covariates, segmented regression models were employed. In getting to grips with the understanding of the highly complex and intertwined relationships between the CD4+ count, clinical covariates and the time lagged effects during the HIV disease progression, a Structural Equation Model (SEM) was constructed and fitted. The results showed that sodium consistently changed its effects at 132mEq/L and 140 mEq/L across all the post HIV infection phases. Generally, the covariate influence on the CD4+ count varied with infection phase and widely between individuals during the anti-retroviral therapy (ART). We conlude that there is evidence of covariate set-point adaptive behaviour to positively influence the CD4+ cell count during the HIV disease progression.
The management of missing categorical data : comparison of multiple imputation and subset correspondence analysis.
(2015) Hendry, Gillian Margaret.; Zewotir, Temesgen Tenaw.; Naidoo, Rajen.; North, Delia Elizabeth.
Missing data is a common problem in research and the manner in which this ‘missingness’ is managed, is crucial to the validity of analysis outcomes. This study illustrates the use of two diverse methods to handle, in particular, missing categorical data. These methods are applied to a set of data which intended to identify relationships between asthma severity in children and environmental, behavioural, genetic and socio-economic factors. This dataset suffered from substantial missingness. The first method involved the application of two approaches to multiple imputation, each adopting different distributional specifications. A practical challenge, previously undocumented, was encountered in the application of multiple imputation when interactions, to be identified and included in the analysis model, were needed for the imputation model. This study found that by imputing a single set of complete data using the expectation maximization (EM) algorithm for covariance matrices, it was possible to identify relevant interactions for inclusion in the imputation model. The second method illustrated the application of correspondence analysis to a subset of the data that includes only the measured data categories. The application of subset correspondence analysis (s-CA) with incomplete data, as well as its sensitivity to the type of missingness, has not been well documented, if at all. There is also no evidence of research in which interactions have been added to an analysis with s-CA. In this study its use, both with and without interactions, was illustrated and the results, when compared to those from the multiple imputation approach, were found to be similar and favourably complementary. A simulation study found that s-CA performed well with any type of missingness, provided the amount of missingness is less than 30% on any variable with incomplete data. Across all analyses, relationships found between asthma severity and factors were consistent with known relationships, thus providing confirmation of the reliability of the methods.
Modelling residential electricity usage within the eThekwini Municipal Area.
(2014) Reade, Samantha.; Zewotir, Temesgen Tenaw.; North, Delia Elizabeth.
In this study we use linear mixed models to model residential electricity consumption within the eThekwini municipal area. Utilities around South Africa are required to estimate monthly electricity consumptions for each household within their jurisdiction however, little work has been done to find models that may be used to do so. As part of the modelling process we investigate seasonal trends in consumption as well as temporal and spatial variations. Data for the study were obtained from eThekwini Electricity, a subsidiary of eThekwini Municipality. Key findings of the research include confirming the presence of a seasonal pattern in monthly electricity consumption and proving that variations in consumption of different households are not related to the physical distance between them. Models developed in this study also have applications in prediction and may be used to predict future electricity consumption for individual households. Predictions made using the models from this study were found to be closer to the actual value, than that of the customary eThekwini Electricity predicted values.
Partial exchangeability and related topics.
(1991) North, Delia Elizabeth.; Dale, Andrew Ian.
Partial exchangeability is the fundamental building block in the subjective approach to the probability of multi-type sequences which replaces the independence concept of the objective theory. The aim of this thesis is to present some theory for partially exchangeable sequences of random variables based on well-known results for exchangeable sequences. The reader is introduced to the concepts of partially exchangeable events, partially exchangeable sequences of random variables and partially exchangeable o-fields, followed by some properties of partially exchangeable sequences of random variables. Extending de Finetti's representation theorem for exchangeable random variables to hold for multi-type sequences, we obtain the following result to be used throughout the thesis: There exists a o-field, conditional upon which, an infinite partially exchangeable sequence of random variables behaves like an independent sequence of random variables, identically distributed within types. Posing (i) a stronger requirement (spherical symmetry) and (ii) a weaker requirement (the selection property) than partial exchangeability on the infinite multi-type sequence of random variables, we obtain results related to de Finetti's representation theorem for partially exchangeable sequences of random variables. Regarding partially exchangeable sequences as mixtures of independent and identically distributed (within types) sequences, we (i) give three possible expressions for the directed random measures of the partially exchangeable sequence and (ii) look at three possible expressions for the o-field mentioned in de Finetti's representation theorem. By manipulating random measures and using de Finetti's representation theorem, we point out some concrete ways of constructing partially exchangeable sequences. The main result of this thesis follows by extending de Finetti's represen. tation theorem in conjunction with the Chatterji principle to obtain the following result: Given any a.s. limit theorem for multi-type sequences of independent random variables, identically distributed within types, there exists an analogous theorem satisfied by all partially exchangeable sequences and by all sub-subsequences of some subsequence of an arbitrary dependent infinite multi-type sequence of random variables, tightly distributed within types. We finally give some limit theorems for partially exchangeable sequences of random variables, some of which follow from the above mentioned result.
Special topics in probabilistic exchangeability and its applications.
(2017) Huang, Chun-Kai.; North, Delia Elizabeth.; Zewotir, Temesgen Tenaw.
This thesis evolves around a probabilistic concept called exchangeability and its generalised forms. It is aimed at exploring connections between exchangeability and other sub-areas in mathematical statistics. These connections include theoretical implications, generalisation of existing methodologies and applications to real-world data. There are three topics of particular interest. The rst topic is related to the linkage between de Finetti's representation theorem (for exchangeable sequences) and existence conditions for Hausdor moment problems over k-dimensional simplexes. The equivalence of these two results are proved over the most general case in nite spaces. This is a generalisation of existing theory and uses an alternative approach to previous work in the literature. This connection, while theoretically interesting in its own right, may also lead to further cross- eld applications, such as distribution re-construction from nite moments or in the approximations to nite exchangeable sequences and nite moment problems. Secondly, we explore a currently popular topic, namely extreme value theory (EVT), which has been widely applied to areas such as hydrology, earth sciences and nance. Classical results from EVT assume that the data sequence is independent and identically distributed (IID). We generalise this assumption to exchangeable random sequences. This caters for more general approaches to EVT that allows for data dependency. Resampling techniques are utilised for estimating the parameters' prior distributions. We utilise these new methods for Value-at-Risk (VaR) estimation in nancial stock returns. This is done for both cases with and without GARCH lters. These new VaR models are also compared to existing models in the literature and shows promising improvements. For the nal topic, exchangeability is applied to two-phase sampling with an auxiliary variable. In particular, our focus is on a two-phase strati ed sampling design, under the assumption that readings for the study variable are exchangeable within stratum. This will again provide a generalisation from the usual IID assumption in applications of multiple-phase sampling. It is amalgamated with stationary bootstrapping at various levels of sampling to estimate within stratum and cross strata covariances. We show that our approach provides a more conservative estimate for the sampling variance of the two-phase estimator for the mean (i.e., the ratio estimator), as compared to the conventional IID method by Rao (1973)
Statistical analysis of the attitudes towards blood donation and transfusion in Mali.
(2016) Osman, Farzana.; North, Delia Elizabeth.; Zewotir, Temesgen Tenaw.
The demand for blood transfusion in Mali is high, because of the high prevalence of anemia, which is mostly caused by malaria, malnutrition and pregnancy-related complications. In this study a classic KNOWLEDGE, ATTITUDE AND PRACTICE (KAP) SURVEY was conducted on 323 individuals in Mali. Questions asked were aimed at finding what people in the study know about blood donation, how they feel about donating and receiving blood, and how they behave when asked to donate blood. The objective of this study is to develop a theoretical framework to better understand the attitudes toward blood donation and transfusion in Mali, thereby identifying factors that motivate and deter blood donation, and also to identify interventions to improve the supply of blood transfusion. A main effect logistic regression model was carried out to the model the relationship between willingness status of blood donating and thirteen explanatory variables. Multiple correspondence analysis was used to confirm the results obtained. Due to the nonresponse in the survey, techniques used to handle missing data values were also explored. More than 50% of individuals in the study responded as non-donors, however a vast majority of respondents reported their intent to become future donors. Also, the male population responded as majority donors at 58.8%. Results found, indicate that females were less likely to be donors in the Mali population and individuals that had knowledge about the different type of blood groups were more inclined to be donors. Overall results produced from the statistical methods employed in this study were consistent across the methods.
Statistical methods for causal inference in observational studies.
(2020) Amusa, Lateef Babatunde.; Zewotir, Temesgen Tenaw.; North, Delia Elizabeth.
Estimating causal effects is essential in the evaluation of a treatment or intervention. It is particularly straightforward for well-designed experiments. However, when the treatment assignment is complicated by confounders, as in the case of observational studies, such inferences regarding the treatment effects, require more sophisticated adjustments. In this thesis, we investigated different matching techniques in terms of how well they balance the treatment groups on the covariates, as well as their efficiency in estimating treatment effects. We considered the various algorithm variants of these matching techniques, which include propensity score matching, Mahalanobis distance matching, and coarsened exact matching. Secondly, we proposed two new strategies for estimating treatment effects, namely, covariatebalancing rank-based Mahalanobis distance (CBRMD) and an improved version of CBRMD (iCBRMD).We evaluated their performance via simulations and some reallife datasets. Thirdly, we investigated a relatively new optimization-based alternative, known as entropy balancing, which has been used rarely in the applied biomedical literature. We shared our experiences learned from using entropy balancing in non-experimental studies, via Monte Carlo simulations and an empirical application. We further extended the evaluation of entropy balancing to some standard measures of causal treatment effects, namely; difference in means, odds ratios, rate ratios and hazard ratios. We pulled together our evaluations by conducting Monte Carlo simulations, evaluating both well-established methods and the more recently proposed methods. These adjustment techniques were evaluated under different scenarios that align with the practical reality. Finally, we utilized a dataset from a recently conducted HIV Incidence Provincial Surveillance System (HIPSS) study, to apply the considered techniques to a public health issue in South Africa.
Statistical modelling and spatial mapping of crime in South Africa.
(2016) Naidoo, Belisha.; North, Delia Elizabeth.; Zewotir, Temesgen Tenaw.
This research investigates factors related to crime rates for the 2013/2014 South African Crime Survey. The survey provides personal information and crime related experiences for all members of the 25 605 households that was part of the study. Using the generalized linear model analysis we show that the crime outcomes significantly differed between provinces. A further data set, containing aggregated crime statistics from 1 140 police stations, had the GPS co-ordinates included which allowed for spatial mapping of crime incidence. Results may be used to predict crime hot spots in the country, thereby having the potential to inform crime reduction initiatives, which could be deployed strategically in order to minimize overall crime by focusing on the potential crime hot spots. In a country where resources are limited and that careful planning is essential, this study potentially has a lot to offer.
Systematic sampling from finite populations.
(2013) Naidoo, Llewellyn Reeve.; North, Delia Elizabeth.
The impossibility to reach an entire population, owing to time and budget constraints, results in the need for sampling to estimate population parameters. There are various methods of sampling and this thesis deals with a specific method of probability sampling, known as systematic sampling. Problems within the systematic sampling context include: (i) If the size of the population is not a multiple of the size of the sample, then conventional systematic sampling (also known as linear systematic sampling) will either result in variable sample sizes, or constant sample sizes that are greater than required; (ii) Linear systematic sampling is not the most preferred probability sampling design for populations that exhibit linear trend; (iii) An unbiased estimate of the sampling variance cannot be obtained from a single systematic sample. I will attempt to make an original contribution to the current body of knowledge, by introducing three new modified systematic sampling designs to address the problems mentioned in (ii) and (iii) above. We will first discuss the measures to compare the various probability sampling designs, before providing a review of systematic sampling. Thereafter, the methodology of linear systematic sampling will be examined as well as two other methodologies to overcome the problem in (i). We will then obtain e fficiency related formulas for the methodologies, after which we will demonstrate that the e fficiency of systematic sampling depends on the correlation of the population units, which in turn depends on the arrangement and structure of the population. As a result, we will compare linear systematic sampling with other common probability sampling designs, under various population structures. Further designs of linear systematic sampling (including a new proposed design), which are considered to be optimal for populations that exhibit linear trend, will then be examined to resolve the problem mentioned in (ii). Thereafter, we will tackle the problem in (iii) by exploring various strategies, which include two new designs. Finally, we will obtain numerical comparisons for all the designs discussed in this thesis, on various population structures, before providing a comprehensive report on the thesis.
Towards successful mathematical literacy learning - a study of preservice teacher education module.
(2007) Hobden, Sally Diane.; Mitchell, Claudia Arlene.; North, Delia Elizabeth.
The purpose of this study was to extend our knowledge about mathematical literacy learning with the focus on a foundational preservice teacher education module required for prospective teachers. The construct of mathematical proficiency provided a framework for understanding how successful learning depends on a multiplicity of competences, and in particular to highlight the pivotal role of a productive disposition towards mathematics in becoming mathematically literate. The main questions that guided the study were as follows: What is the nature and strength of the productive disposition strand of mathematical proficiency evident in preservice teachers entering a Mathematical Literacy module and how does this productive disposition change over the course of the module? and What pedagogical practices and learning behaviours best enable preservice teachers to achieve mathematical literacy? The study was undertaken as two overlapping case studies, the first describing the preservice teachers at the onset of their studies in the Mathematical Literacy for Educators module, and in the second, a three part story-telling case study of the unfolding of the module over three years from 2003 to 2005. The mathematics autobiographies of 254 preservice teachers and the data obtained from a premodule questionnaire and introductory class activities contributed to the first case study which was summarised in the form of three fictional letters. Written reflections, final module evaluations and the insights of my co-workers contributed to the second case study which documented the successes and struggles of the preservice teachers as the module unfolded each year. Complementary mixed methods techniques were used to analyse the multiple sources of data and to weave strong ropes of evidence to support the findings. Statistical analysis pointed to themes which were supported or tempered by qualitative evidence reported in the voices of the preservice teachers themselves. The analysis revealed that many of the preservice teachers entering the Mathematical Literacy for Educators module had found their school experience of mathematics to be dispiriting and consequently had developed negative dispositions towards the subject. The change in this disposition depended on their success in the module and the empathy shown by the lecturer. Helpful pedagogical practices were found to be those that supported language difficulties in learning mathematics, assisted in organising learning, remediated for poor schooling background in mathematics and took account of the diversity amongst the students. I argue that many of the lessons learned and insights gained from teaching the Mathematical Literacy for Educators module are relevant to the expanding number of mathematics courses required as part of humanities programmes. In addition, they can inform practices at school level and in both in mathematics and mathematical literacy teacher education.