published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

In longitudinal settings, modeling the covariance structure of repeated measure data is essential for proper analysis. The first paper in this three-paper dissertation presents a survey of four journals in the fields of Education and Psychology to identify the most commonly used methods for analyzing longitudinal data. It provides literature reviews and statistical details for each identified method. This paper also offers a summary table giving the benefits and drawbacks of all the surveyed methods in order to help researchers choose the optimal model according to the structure of their data. Finally, this paper highlights that even when scholars do use more advanced methods for analyzing repeated measure data, they very rarely report (or explore in their discussions) the covariance structure implemented in their choice of modeling. This suggests that, at least in some cases, researchers may not be taking advantage of the optimal covariance patterns. This paper identifies a gap in the standard statistical practices of the fields of Education and Psychology, namely that researchers are not modeling the covariance structure as an extension of fixed/random effects modeling. The second paper introduces the General Serial Covariance (GSC) approach, an extension of the Linear Mixed Modeling (LMM) or Hierarchical Linear Model (HLM) techniques that models the covariance structure using spatial correlation functions such as Gaussian, Exponential, and other patterns. These spatial correlations model the covariance structure in a continuous manner and therefore can deal with missingness and imbalanced data in a straightforward way. A simulation study in the second paper reveals that when data are consistent with the GSC model, using basic HLMs is not optimal for the estimation and testing of the fixed effects. The third paper is a tutorial that uses a real-world data set from a drug abuse prevention intervention to demonstrate the use of the GSC and basic HLM models in R programming language. This paper utilizes variograms (a visualization tool borrowed from geostatistics) among other exploratory tools to determine the covariance structure of the repeated measure data. This paper aims to introduce the GSC model and variogram plots to Education and Psychology, where, according to the survey in the first paper, they are not in use. This paper can also help scholars seeking guidance for interpreting the fixed effect-parameters.

To investigate the effect of environmental pollution on the health of children in the Durban South Industrial Basin (DSIB) due to its proximity to industrial activities, 233 children from five primary schools were considered. Three of these schools were located in the south of Durban while the other two were in the northern residential areas that were closer to industrial activities. Data collected included the participants' demographic, health, occupational, social and economic characteristics. In addition, environmental information was monitored throughout the study specifically, measurements on the levels of some ambient air pollutants. The objective of this thesis is to investigate which of these factors had an effect on the lung function of the children. In order to achieve this objective, different sample survey data analysis techniques are investigated. This includes the design-based and model-based approaches. The nature of the survey data finally leads to the longitudinal mixed model approach. The multicolinearity between the pollutant variables leads to the fitting of two separate models: one with the peak counts as the independent pollutant measures and the other with the 8-hour maximum moving average as the independent pollutant variables. In the selection of the fixed-effects structure, a scatter-plot smoother known as the loess fit is applied to the response variable individual profile plots. The random effects and the residual effect are assumed to have different covariance structures. The unstructured (UN) covariance structure is used for the random effects, while using the Akaike information criterion (AIC), the compound symmetric (CS) covariance structure is selected to be appropriate for the residual effects. To check the model fit, the profiles of the fitted and observed values of the dependent variables are compared graphically. The data is also characterized by the problem of intermittent missingness. The type of missingness is investigated by applying a modified logistic regression model missing at random (MAR) test. The results indicate that school location, sex and weight are the significant factors for the children's respiratory conditions. More specifically, the children in schools located in the northern residential areas are found to have poor respiratory conditions as compared to those in the Durban-South schools. In addition, poor respiratory conditions are also identified for overweight children. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2006.