Browsing by Author "Blignaut, Rénette"

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    Developing a model of school climate unique to secondary schools in South Africa: A multilevel analysis approach
    (University of the Western Cape, 2018) Winnaar, Lolita Desiree; Blignaut, Rénette; Zuze, Linda
    The educational landscape in South Africa is unique and has also seen many changes since the dawn of democracy more than 20 years ago. The apartheid education system was marred by severe inequalities between schools and, for this reason, the democratic government post 1994 established a number of policies and interventions in an attempt to improve access, equity and quality between schools. The country has made significant advances in improving access to education. This is reflected in the Millennium Development Goals progress indicators showing that, as of 2013, almost all learners between the ages of 7 and 15 were enrolled in schools. While great strides have also been made with regard to equity, evidence shows that many schools in South Africa are still largely inequitable. Education quality, however, is an area that is still of grave concern and the matter requires much attention from educational stakeholders. International studies, such as the Trends in International Mathematics and Science Study (TIMSS) and the Progress in International Reading Literacy Study (PIRLS), use learner performance to measure the quality of the system. Such studies consistently report that South Africa is performing poorly and that large inequalities still exist between schools in the country. Improved quality is associated with effective schools and, in South Africa, only 20% of schools have been found to be functional or effective. Much of research focussed on school effectiveness, both nationally and internationally, however has been explained by factors in the school, including the appropriateness of curriculum content, infrastructure, resources in the school and teacher content knowledge. These factors have been found to be strongly correlated with effective schools.
  • Thumbnail Image
    Item
    Handling heteroskedasticity in the linear regression model
    (University of the Western Cape, 2022) Farrar, Thomas; Blignaut, Rénette
    This research project delves into the problem of heteroskedasticity in the linear regression model. Having defined the problem and its consequences for estimation and inference, a comprehensive literature review of existing methods for diagnosing and correcting for heteroskedasticity is undertaken, with special emphasis on heteroskedasticity tests. New theory on the statistical properties of the Ordinary Least Squares residuals is developed, leading to new models for estimating linear regression error variances. The most important of these models is the Auxiliary Linear Variance Model, which is further classified into sub-types (e.g., clustering, linear, penalised polynomial, spline). Model fitting techniques are discussed, which reduce to quadratic programming problems. An Auxiliary Nonlinear Variance Model is also developed, which can be fitted using a maximum quasi-likelihood method. Techniques for tuning of model hyperparameters and feature selection are discussed. Bootstrap methods of obtaining interval estimates for error variances are also proposed. A new heteroskedasticity test is constructed based on the auxiliary linear variance model. To make existing and new methods of handling heteroskedasticity more accessible to the practitioner, a new package called skedastic has been developed for R statistical software. Its functionality is described in detail.
  • Thumbnail Image
    Item
    The statistical analysis of complex sampling data
    (University of the Western Cape, 2018) Paulse, Bradley; Luus, Retha; Blignaut, Rénette
    Most standard statistical techniques illustrated in text books assume that the data are collected from a simple random sample (SRS) and hence are independently and identically distributed (i.i.d.). In reality, data are often sourced through complex sampling (CS) designs, with a combination of stratification and clustering at different levels of the design. Consequently, the CS data are not i.i.d. and sampling weights that are developed over different stages, are calculated and included in the analysis of this data to account for the sampling design. Logistic regression is often employed in the modelling of survey data since the response under investigation typically has a dichotomous outcome. Furthermore, since the logistic regression model has no homogeneity or normality assumptions, it is appealing when modelling a dichotomous response from survey data. This research considers the comparison of the estimates of the logistic regression model parameters when the CS design is accounted for, i.e. weighting is present, to when the data are modelled using an SRS design, i.e. no weighting. In addition, the standard errors of the estimators will be obtained using three different variance techniques, viz. Taylor series linearization, the jackknife and the bootstrap. The different estimated standard errors will be used in the calculation of the standard (asymptotic) interval which will be compared to the bootstrap percentile interval in terms of the interval coverage probability. A further level of comparison is obtained when using only design weights to those obtained using calibrated and integrated sampling weights. This simulation study is based on the Income and Expenditure Survey (IES) of 2005/2006. The results showed that generally when weighting was used the estimators performed better as opposed to when the design was ignored, i.e. under the assumption of SRS, with the results for the Taylor series linearization being more stable.
  • Thumbnail Image
    Item
    A weighted bootstrap approach to logistic regression modelling in identifying risk behaviours associated with sexual activity
    (Taylor and Francis Group, 2019) Brydon, Humphrey; Blignaut, Rénette; Jacobs, Joachim
    The latest population estimates released by Statistics South Africa indicate that 25.03% of alldeaths in 2017 in South Africa were AIDS-related. Along with these results, it is also reportedthat 7.06% of the population were living with HIV, with the HIV-prevalence among youth(aged 15–24) at 4.64% for 2017 (STATSSA. (2018). Retrieved from Statistics South Africa:http://www.statssa.gov.za/publications/P0302/P03022017.pdf). The data used in the studycontained information related to the risk-taking behaviours associated with the sexualactivity of enteringfirst-year students at the University of the Western Cape. In this study, alogistic regression modelling procedure was carried out on those students that weredetermined to be sexually active, therefore, in the modelling procedure significant riskbehaviours of sexually activefirst-year students could be identified. Of the 14 variablesincluded in the modelling procedure, six were found to be significantly associated withsexually active students.