Magister Scientiae - MSc / This thesis looks at the effect that the introduction of various techniques (weighting, bootstrapping and variable selection) has on the accuracy of the modelling process when using logistic regression. The data used in the modelling process is based on the sexual activity of entering first-year students at the University of the Western Cape, therefore, by constructing logistic regression models based on this data, certain predictor variables or factors associated with the sexual activity of these students are identified. The sample weighting technique utilized in this thesis assigned a weight to a student based on gender and racial representations within a sample when compared to the population of the entering first-year. The use of a sample weighting technique is shown to produce a more effective modelling process than a modelling process without weighting. The bootstrapping procedure is shown to produce logistic regression models that are more accurate. Utilizing more than 200 bootstrap samples did not necessarily produce logistic regression models that were more accurate than using a total of 200 bootstrap samples. It is, however, concluded that a weighted bootstrap modelling procedure will result in more accurate models compared to a procedure without this intervention. The forward, backward, stepwise, Newton-Raphson and Fisher variable selection methods are used. The Newton-Raphson and Fisher methods are found not to be effective when used in a logistic modelling process, whereas the forward, backward and stepwise methods are all shown to produce very similar results. Six predictor variables or factors are identified with respect to the sexual activity of the specified students: the age of the student; whether they consume alcohol or not; their racial grouping; whether an HIV test has been taken; the importance of religion in influencing their sexual behaviour; and whether they smoke or not.i i Conclusions are reached with respect to improvements that could be made to the HIV prevention programme at UWC with reference to the sexual activity of entering first-years.

Non-response is an error common to most surveys. In this dissertation, the error of non-response is described in terms of its sources and its contribution to the Mean Square Error of survey estimates. Various response and completion rates are defined. Techniques are examined that can be used to identify the extent of nonresponse bias in surveys. Methods to identify auxiliary variables for use in nonresponse adjustment procedures are described. Strategies for dealing with nonresponse are classified into two types, namely preventive strategies and post hoc adjustments of data. Preventive strategies discussed include the use of call-backs and follow-ups and the selection of a probability sub-sample of non-respondents for intensive follow-ups. Post hoc adjustments discussed include population and sample weighting adjustments and raking ratio estimation to compensate for unit non-response as well as various imputation methods to compensate for item non-response. / Mathematical Sciences / M. Com. (Statistics)

Non-response is an error common to most surveys. In this dissertation, the error of non-response is described in terms of its sources and its contribution to the Mean Square Error of survey estimates. Various response and completion rates are defined. Techniques are examined that can be used to identify the extent of nonresponse bias in surveys. Methods to identify auxiliary variables for use in nonresponse adjustment procedures are described. Strategies for dealing with nonresponse are classified into two types, namely preventive strategies and post hoc adjustments of data. Preventive strategies discussed include the use of call-backs and follow-ups and the selection of a probability sub-sample of non-respondents for intensive follow-ups. Post hoc adjustments discussed include population and sample weighting adjustments and raking ratio estimation to compensate for unit non-response as well as various imputation methods to compensate for item non-response. / Mathematical Sciences / M. Com. (Statistics)