UWCScholar :: Browsing by Author "Kotze, Danelle"

Browsing by Author "Kotze, Danelle"

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Analysis and estimation of customer survival Time in subscription-based businesses
(University of the Western Cape, 2008) Mohammed, Zakariya Mohammed Salih; Kotze, Danelle; Maritz, Johannes Stefan; Dept. of Statistics; Faculty of Science
Subscription-based industries have seen a massive expansion in recent decades. In this type of industry the customer has to subscribe to be able to enjoy the service; there-fore, well-de ned start and end points of the customer relationship with the service provider are known. The length of this relationship, that is the time from subscription to service cancellation, is de ned as customer survival time. Unlike transaction-based businesses, where the emphasis is on the quality of a product and customer acquisition, subscription-based businesses focus on the customer and customer retention. A customer focus requires a new approach: managing according to customer equity (the value of a rm's customers) rather than brand equity (the value of a rm's brands). The concept of customer equity is attractive and straightforward, but the implementation and management of the customer equity approach do present some challenges. Amongst these challenges is that customer asset metric - customer lifetime value (the present value of all future pro ts generated from a customer) - depends upon assumptions about the expected survival time of the customer (Bell et al., 2002; Gupta and Lehmann, 2003). In addition, managing and valuing customers as an asset require extensive data and complex modelling. The aim of this study is to illustrate, adapt and develop methods of survival analysis in analysing and estimating customer survival time in subscription-based businesses. Two particular objectives are studied. The fi rst objective is to rede ne the existing survival analysis techniques in business terms and to discuss their uses in order to understand various issues related to the customer-fi rm relationship. The lesson to be learnt here is the ability of survival analysis techniques to extract important information on customers with regard to their loyalties, risk of cancellation of the service, and lifetime value. The ultimate outcome of this process of studying customer survival time will be to understand the dynamics and behaviour of customers with respect to their risk of cancellation, survival probability and lifetime value. The results of the estimates of customer mean survival time obtained from different nonparametric and parametric approaches; namely, the Kaplan-Meier method as well as exponential, Weibull and gamma regression models were found to vary greatly showing the importance of the assumption imposed on the distribution of the survival time. The second objective is to extrapolate the customer survival curve beyond the empirical distribution. The practical motivation for extrapolating the survival curve beyond the empirical distribution originates from two issues; that of calculating survival probabilities (retention rate) beyond the empirical data and of calculating the conditional survival probability and conditional mean survival time at a speci c point in time and for a speci c time window in the future. The survival probabilties are the main components needed to calculate customer lifetime value and thereafter customer equity. In this regard, we propose a survivor function that can be used to extrapolate the survival probabilities beyond the last observed failure time; the estimation of parameters of the newly proposed extrapolation function is based completely on the Kaplan-Meier estimate of the survival probabilities. The proposed function has shown a good mathematical accuracy. Furthermore, the standard error of the estimate of the extrapolation survival function has been derived. The function is ready to be used by business managers where the objective is to enhance customer retention and to emphasise a customer-centric approach. The extrapolation function can be applied and used beyond the customer survival time data to cover clinical trial applications. In general the survival analysis techniques were found to be valuable in understanding and managing a customer- rm relationship; yet, much still needs to be done in this area of research to make these techniques that are traditionally used in medical studies more useful and applicable in business settings.
Causes and patterns of morbidity and mortality in Afghanistan: Joint estimation of multiple causes in the neonatal period
(Springer, 2014) Adegboye, Oyelola A.; Kotze, Danelle
This paper focuses on investigating the leading cause(s) of death and preventable factors in Afghanistan, using data from verbal autopsies of infant deaths. We are of the view that the presence of a disease in a person may increase the risk of another disease that may contribute to the death process. The influence of individual- and community-level variables on infant morbidity and mortality in Afghanistan is examined. The results of this study suggest the existence of multiple causes of death in the Afghanistan Mortality Survey (AMS). In Afghanistan, complications of pregnancy are clearly a problem and must be adequately improved.
Epidemiological analysis of spatially misaligned data: a case of highly pathogenic avian influenza virus outbreak in Nigeria
(Cambridge University Press, 2013) Adegboye, Oyelola A.; Kotze, Danelle
This research is focused on the epidemiological analysis of the transmission of the highly pathogenic avian influenza (HPAI) H5N1 virus outbreak in Nigeria. The data included 145 outbreaks together with the locations of the infected farms and the date of confirmation of infection. In order to investigate the environmental conditions that favoured the transmission and spread of the virus, weather stations were realigned with the locations of the infected farms. The spatial Kolmogorov–Smirnov test for complete spatial randomness rejects the null hypothesis of constant intensity (P < 0·0001). Preliminary exploratory analysis showed an increase in the incidence of H5N1 virus at farms located at high altitude. Results from the Poisson log-linear conditional intensity function identified temperature (−0·9601) and wind speed (0·6239) as the ecological factors that influence the intensity of transmission of the H5N1 virus. The model also includes distance from the first outbreak (−0·9175) with an Akaike’s Information Criterion of −103·87. Our analysis using a point process model showed that geographical heterogeneity, seasonal effects, temperature, wind as well as proximity to the first outbreak are very important components of spread and transmission of HPAI H5N1.
Examining long-run relationships of the BRICS stock market indices to identify opportunities for implementation of statistical arbitrage strategies
(University of the Western Cape, 2012) Meki, Brian; Kotze, Danelle
Purpose:This research investigates the existence of long-term equilibrium relationships among the stock market indices of Brazil, Russia, India, China and South Africa (BRICS). It further investigates cointegrated stock pairs for possible implementation of statistical arbitrage trading techniques.Design:We utilize standard multivariate time series analysis procedures to inspect unit roots to assess stationarity of the series. Thereafter, cointegration is tested by the Johansen and Juselius (1990) procedure and the variables are interpreted by a Vector Error Correction Model (VECM). Statistical arbitrage is investigated through the pairs trading technique.Findings:The five stock indices are found to be cointegrated. Analysis shows that the cointegration rank among the variables is significantly influenced by structural breaks. Two pairs of stock variables are also found to be cointegrated. This guaranteed the mean reversion property necessary for the successful execution of the pairs trading technique. Determining the optimal spread threshold also proved to be highly significant with respect to the success of this trading technique.Value:This research seeks to expand on the literature covering long-run co-movements of the volatile emerging market indices. Based on the cointegration relation shared by the BRICS, the research also seeks to encourage risk taking when investing. We achieve this by showing the potential rewards that can be realized through employing appropriate statistical arbitrage trading techniques in these markets.
An exploratory look at associated factors of poverty on educational attainment in Africa and in-depth multilevel modelling for Namibia.
(BER, 2013) Adegboye, Oyelola A.; Kotze, Danelle
This study examines several indicator variables related to education and poverty in Africa from the Demographic and Health Surveys (DHS). Many have described income and education as one of the fundamental determinants of health and as one of the indicators for socio-economic status. Firstly, data from thirty-six African countries were explored, geographical heterogeneity of the countries were discussed. Secondly, we carried out in-depth multi-level analyses using generating estimating equations on data for 72,230 respondents and from 5,436 households in the Namibia DHS (1992-2006). Results from statistical analyses indicate that age of household head, socioeconomic status of household, parent's level of education, family size and position of a child in the family play a significant role in the educational attainment of household members. We found that these household level characteristics are important predictors of educational attainment. Thus, government policy aimed at reducing household level poverty should be implemented to alleviate the economic power at household level thereby increasing educational attainment
A framework for evaluating an introductory statistics programme at the University of the Western Cape
(University of the Western Cape, 2009) Makapela, Nomawabo; Kotze, Danelle; Dept. of Statistics; Faculty of Science
There have been calls both from the government and private sector for Higher Education institutions to introduce programmes that produce employable graduates whilst at the same time contributing to the growing economy of the country by addressing the skills shortage. Transformation and intervention committees have since been introduced to follow the extent to which the challenges are being addressed (DOE, 1996; 1997; Luescher and Symes, 2003; Forbes, 2007). Amongst the list of issues that needed urgent address were the skills shortage and underperformance of students particularly university entering students (Daniels, 2007; De Klerk, 2006; Cooper, 2001). Research particularly in the South African context, has revealed that contributing to the underperformance of university entering students and shortage of skills are: the legacy of apartheid (forcing certain racial groups to focus on selected areas such as teaching and nursing), the schooling system (resulting in university entering students to struggle), the home language and academic language. Barrell (1998), places stress on language as a contributing factor towards the performance of students. Although not much research has been done on skills shortage, most of the areas with skills shortage require Mathematics, either on a minimum or comprehensive scale. Students who have a strong Mathematics background have proved to perform better compared to students who have a limited or no Mathematics background at all in Grade 12 (Hahn, 1988; Conners, McCown & Roskos-Ewoldsen, 1998; Nolan, 2002).The department of Statistics offers an Introductory Statistics (IS) course at first year level. Resources available to enhance student learning include: a problem-solving component with web-based tutorials and students attending lectures three hours per week. The course material and all the necessary information regarding the course including teach yourself problems, useful web-sites and links students can make use of, are all stored under the Knowledge- Environment for Web-based learning (KEWL). Despite all the available information, the students were not performing well and they were not interested in the course. The department regards statistical numeracy as a life skill. The desire of the department is to break down the fear of Statistics and to bring about a perspective change in students' mindsets. The study was part of a contribution to ensuring that the department has the best first year students in Statistics in the Western Cape achieving a success rate comparable to the national norm.
Imputation techniques for non-ordered categorical missing data
(University of the Western Cape, 2016) Karangwa, Innocent; Kotze, Danelle; Blignaut, Renette
Missing data are common in survey data sets. Enrolled subjects do not often have data recorded for all variables of interest. The inappropriate handling of missing data may lead to bias in the estimates and incorrect inferences. Therefore, special attention is needed when analysing incomplete data. The multivariate normal imputation (MVNI) and the multiple imputation by chained equations (MICE) have emerged as the best techniques to impute or fills in missing data. The former assumes a normal distribution of the variables in the imputation model, but can also handle missing data whose distributions are not normal. The latter fills in missing values taking into account the distributional form of the variables to be imputed. The aim of this study was to determine the performance of these methods when data are missing at random (MAR) or completely at random (MCAR) on unordered or nominal categorical variables treated as predictors or response variables in the regression models. Both dichotomous and polytomous variables were considered in the analysis. The baseline data used was the 2007 Demographic and Health Survey (DHS) from the Democratic Republic of Congo. The analysis model of interest was the logistic regression model of the woman’s contraceptive method use status on her marital status, controlling or not for other covariates (continuous, nominal and ordinal). Based on the data set with missing values, data sets with missing at random and missing completely at random observations on either the covariates or response variables measured on nominal scale were first simulated, and then used for imputation purposes. Under MVNI method, unordered categorical variables were first dichotomised, and then K − 1 (where K is the number of levels of the categorical variable of interest) dichotomised variables were included in the imputation model, leaving the other category as a reference. These variables were imputed as continuous variables using a linear regression model. Imputation with MICE considered the distributional form of each variable to be imputed. That is, imputations were drawn using binary and multinomial logistic regressions for dichotomous and polytomous variables respectively. The performance of these methods was evaluated in terms of bias and standard errors in regression coefficients that were estimated to determine the association between the woman’s contraceptive methods use status and her marital status, controlling or not for other types of variables. The analysis was done assuming that the sample was not weighted fi then the sample weight was taken into account to assess whether the sample design would affect the performance of the multiple imputation methods of interest, namely MVNI and MICE. As expected, the results showed that for all the models, MVNI and MICE produced less biased smaller standard errors than the case deletion (CD) method, which discards items with missing values from the analysis. Moreover, it was found that when data were missing (MCAR or MAR) on the nominal variables that were treated as predictors in the regression model, MVNI reduced bias in the regression coefficients and standard errors compared to MICE, for both unweighted and weighted data sets. On the other hand, the results indicated that MICE outperforms MVNI when data were missing on the response variables, either the binary or polytomous. Furthermore, it was noted that the sample design (sample weights), the rates of missingness and the missing data mechanisms (MCAR or MAR) did not affect the behaviour of the multiple imputation methods that were considered in this study. Thus, based on these results, it can be concluded that when missing values are present on the outcome variables measured on a nominal scale in regression models, the distributional form of the variable with missing values should be taken into account. When these variables are used as predictors (with missing observations), the parametric imputation approach (MVNI) would be a better option than MICE.
An investigation into the methodologies of value-at -risk and a simulation process of a portfolio of financial instruments.
(University of the Western Cape, 2004) Ballam, Gamal Abdel Hussein; Kotze, Danelle
Financial companies such as investment and commercial banks as well as insurance companies, mutual and pension funds hold assets in the form of financial instruments in portfolios. Nowadays, financial instruments have proliferated so much that there are so many forms of them namely: derivatives, common stock, corporate and government bonds, foreign exchange and contracts. With so many financial instruments, companies can have very large and diversified portfolios for which they must quantify the risk. With high profile calamities that have rocked the financial world lately, the need for better risk management has never been so in demand as before. Value-at-Risk (VaR) is the latest addition in the investor's toolkit as far as measurements of risk is concerned. This new measure of risk complements well the existing risk measures that exist.Unfortunately, VaR is not unanimous and it has attracted a lot of critics over the years. This research thesis is threefold: to introduce the reader to the VaR concept; to discuss the different methods that exist to calculate VaR; and, finally, to simulate the VaR of a portfolio of government bonds. The first part of this research is to introduce the reader to the general idea of risk forms and its management, the role that the existing risk measures have played so far and the coming up of the new technique, which is VaR. The pros and cons that accompany a new technique are discussed as well as the history of VaR. The second part is about the different methods that exist to compute the VaR of a portfolio. Usually, VaR methodologies fall into three categories namely: Parametric; Historical; and Monte Carlo. In this research, the advantages and disadvantages of these three methods are discussed together with a step-wise method on how to proceed to calculate the VaR of a portfolio using any of the three methods. The practical side of this thesis deals about the VaR simulation of a portfolio of financial instruments. The chosen financial instruments are four South African government bonds with different characteristics. VaR for this particular portfolio will then be simulated by the three main methods. Eleven different simulations are run and they are compared against a Control Simulation (Benchmark Portfolio) to see how factors influencing VaR measure cope under different conditions. The main idea here was to check how VaR measures can change under different portfolio characteristics and to interpret these changes. Moreover, the VaR estimates under the three different methods will be compared
Market segmentation and factors affecting stock returns on the JSE
(2008) Chimanga, Artwell S.; Kotze, Danelle
This study examines the relationship between stock returns and market segmentation. Monthly returns of stocks listed on the JSE from 1997-2007 are analysed using mostly the analytic factor and cluster analysis techniques. Evidence supporting the use of multi-index models in explaining the return generating process on the JSE is found. The results provide additional support for Van Rensburg (1997)'s hypothesis on market segmentation on the JSE.
Maths4Stats: Opleiding vir onderwysers
(AOSIS, 2013) Blignaut, Renette; Luus, Retha; Lombard, Ronell; Latief, Abduraghiem; Kotze, Danelle
Maths4Stats: Educating teachers. The inadequate nature of the education infrastructure in South Africa has led to poor academic performance at public schools. Problems within schools such as under-qualified teachers and poor teacher performance arise due to the poorly constructed education system in our country. The implementation in 2012 of the Curriculum and Assessment Policy Statement (CAPS) at public schools in South Africa saw the further crippling of some teachers, as they were unfamiliar with parts of the CAPS subject content. The Statistics and Population Studies department at the University of the Western Cape was asked to join the Maths4Stats project in 2012. This project was launched by Statistics South Africa in an effort to assist in training the teachers in statistical content within the CAPS Mathematics curricula. The University of the Western Cape's team would like to share their experience of being part of the Maths4Stats training in the Western Cape. This article focuses on how the training sessions were planned and what the outcomes were. With the knowledge gained from our first Maths4Stats experience, it is recommended that future interventions are still needed to ensure that mathematics teachers become well-informed and confident to teach topics such as data handling, probability and regression analysis.
Multi-year trend analysis of childhood immunization uptake and coverage in Nigeria
(Cambridge University Press, 2013) Adegboye, Oyelola A.; Kotze, Danelle; Adegboye, Olasunkanmi A.
As a leading indicator of child health, under-ﬁve mortality was incorporated in the United Nations Millennium Development Goals with the aim of reducing the rate by two-thirds between 1990 and 2015. Under-ﬁve mortality in Nigeria is alarmingly high, and many of the diseases that result in mortality are vaccine preventable. This study evaluates the uptake of childhood immunization in Nigeria from 1990 to 2008. A multi-year trend analysis was carried out using Alternating Logistic Regression on 46,130 children nested within 17,380 mothers in 1938 communities from the Nigerian Demographic and Health Surveys from 1990 to 2008. The ﬁndings reveal that mother-level and community-level variability are signiﬁcantly associated with immunization uptake in Nigeria. The model also indicates that children delivered at private hospitals have a higher chance of being immunized than children who are delivered at home. Children from the poorest families (who are more likely to be delivered at home) have a lower chance of being immunized than those from the richest families (OR = 0.712; 95% CI, 0.641–0.792). Similarly, the chance of children with a mother with no education being immunized is decreased by 17% compared with children whose mother has at least a primary education. In the same way, children of mothers who are gainfully employed and those of older mothers have statistically signiﬁcantly higher odds of being immunized. Children of households with a female head are less likely to be immunized than those from male-headed households. The statistical signiﬁcance of the community–survey year interaction term suggests an increase in the odds of a child being immunized over the years and spread over communities. Evidence-based policy should lay more emphasis on mother- and community- level risk factors in order to increase immunization coverage among Nigerian children.
Multiple imputation of unordered categorical missing data: A comparison of the multivariate normal imputation and multiple imputation by chained equations
(Brazilian Statistical Association, 2016) Karangwa, Innocent; Kotze, Danelle; Blignaut, Renette
. Missing data are common in survey data sets. Enrolled subjects do not often have data recorded for all variables of interest. The inappropriate handling of them may negatively affect the inferences drawn. Therefore, special attention is needed when analysing incomplete data. The multivariate normal imputation (MVNI) and the multiple imputation by chained equations (MICE) have emerged as the best techniques to deal with missing data. The former assumes a normal distribution of the variables in the imputation model and the latter fills in missing values taking into account the distributional form of the variables to be imputed. This study examines the performance of these methods when data are missing at random on unordered categorical variables treated as predictors in the regression models. First, a survey data set with no missing values is used to generate a data set with missing at random observations on unordered categorical variables.
Statistical modelling of clustered and incomplete data with applications in population health studies in developing countries
(University of Western Cape, 2014) Adegboye, Oyelola Abdulwasiu; Kotze, Danelle
The United Nations (UN) Millennium Development Goals (MDGs) drafted eight goals to be achieved by the year 2015, namely: eradicating extreme poverty and hunger, achieving universal primary education, promoting gender equality and women empowerment, reducing child mortality, improving maternal health, combating HIV/AIDS, malaria and other diseases, ensuring environmental sustainability and lastly developing a global partnership for development. Many public health studies often result in complicated and complex data sets, the nature of these data sets could be clustered, multivariate, longitudinal, hierarchical, spatial, temporal or spatio-temporal. This often results in what is called correlated data, because the assumption of independence among observations may not be appropriate. The shared genetic traits in the studies of illness or shared household characteristics among family members in the studies of poverty are examples of correlated data. In cross-sectional studies, individuals may be nested within sub-clusters (e.g., families) that are nested within clusters (e.g., environment), thus causing correlation within clusters. Ignoring the structure of the data may result in asymptotically biased parameter estimates. Clustered data may also be a result of geographical location or time (spatial and temporal). A crucial step in modelling correlated data is the speci cation of the dependency by choosing the covariance/correlation function. However, often the choice for a particular application is unclear and diagnostic tests will have to be carried out, following tting of a model. This study's view of developing countries investigates the prospects of achieving MDGs through the development of flexible predictor statistical models. The first objective of this study is to explore the existing methods for modelling correlated data sets (hierarchical, multilevel and spatial) and then apply the methods in a novel way to several data sets addressing the underlying MDGs. One of the most challenging issue in spatial or spatio-temporal analysis is the choice of a valid and yet exible correlation (covariance) structure. In cases of high dimensionality of the data, where the number of spatial locations or time points that produced the observations is large, the analysis of such data presents great computational challenges. It is debatable whether some of the classical correlation structures adequately reect the dependency in the data. The second objective is to propose a new flexible technique for handling spatial, temporal and spatio-temporal correlations. The goal of this study is to resolve the dependencies problems by proposing a more robust method for modelling spatial correlation. The techniques are used for di erent correlation structures and then combined to form the resulting estimating equations using the platform of the Generalized Method of Moments. The proposed model will therefore be built on a foundation of the Generalized Estimating Equations; this has the advantage of producing consistent regression parameter estimates under mild conditions due to separation of the processes of estimating the regression parameters from the modelling of the correlation. These estimates of the regression parameters are consistent under mild conditions. Thirdly, to account for spatio-temporal correlation in data sets, a method that decouples the two sources of correlations is proposed. Speci cally, the spatial and temporal e ects were modelled separately and then combined optimally. The approach circumvents the need of inverting the full covariance matrix and simpli es the modelling of complex relationships such as anisotropy, which is known to be extremely di cult or Lastly, large public health data sets consist of a high degree of zero counts where it is very di cult to distinguish between "true zeros" and "imputed" zeros. This can be due to the reporting mechanism as a result of insecurity, technical and logistics issues. The focus is therefore on the implementation of a technique that is capable of handling such a problem. The study will make the assumption that "imputed" zeros are a random event and consider the option of discarding the zeros, and then model a conditional Poisson model, conditioning on all cases greater than 0.

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