A generalized design-comparable effect size modeling and estimation for multiple baseline designs across individuals has been proposed and evaluated by Restricted Maximum Likelihood method in a hierarchical linear model using R. This report evaluates the exact approach of the modeling and estimation by SAS. Three models (MB3, MB4 and MB5) with same fixed effects and different random effects are estimated by PROC MIXED procedure with REML method. The unadjusted size and adjusted effect size are then calculated by matrix operation package PROC IML. The estimations for the fixed effects of the three models are similar to each other and to that of R. The variance components estimated by the two software packages are fairly close for MB3 and MB4, but the results are different for MB5 which exhibits boundary conditions for variance-covariance matrix. This result suggests that the nlme library in R works differently than the PROC MIXEDREML method in SAS under extreme conditions. / text

The class of models which is studied in this paper, multi-unit longitudinal models, combines both the cross-sectional and the longitudinal aspects of observations. Many empirical investigations involve the analysis of data structures that are both cross-sectional (observations are taken on several units at a specific time period or at a specific location) and longitudinal (observations on the same unit are taken over time or space). Multi-unit longitudinal data structures arise in economics and business where panels of subjects are studied over time, biostatistics where groups of patients on different treatments are observed over time, and in situations where data are taken over time and space. Modelling issues in multi-unit longitudinal models with random coefficients and patterned correlation structure are illustrated in the context of two data sets. The first data set deals with short time series data on annual death rates and alcohol consumption for twenty-five European countries. The second data set deals with glaceologic time series data on snow temperature at 14 different locations within a small glacier in the Austrian Alps. A practical model building approach, consisting of model specification, estimation, and diagnostic checking, is outlined. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

The flood of 2000 caused extensive changes within the riparian landscape of the Sabie River, Kruger National Park (KNP). Changes within the riparian landscape and the removal of vegetation resulted in considerable changes in riparian vegetation characteristics. Open patches created by the flood served as a template for the establishment of new species and the regeneration of existing species, which consequently resulted in a patch mosaic. This memorable event encouraged an investigation into the response of the Sabie River ecosystem to the memorable Large Infrequent Disturbance (LID). Riparian ecosystems are driven by varying combinations of environmental factors, such as water availability, disturbance, herbivory, fire and river morphology. This complexity depicts unique vegetation structure and assemblages of associated plant species. The lack of sufficient knowledge on the role of riparian vegetation in the health assessment of surrounding ecosystems along semi-arid rivers prompted the establishment of the Kruger Rivers Post Flood Research Program (KRPFRP). Research conducted through this monitoring program four years after the 2000 flood, revealed no significant changes in the species composition, although the location and density of many common riparian species have been changed. There was a decrease in species density across the macro channel floor (MCF) and an increase in species density across the macro channel bank (MCB). Furthermore, it was reported that the flood altered the distribution of height classes across the macro channel. In general the riparian vegetation was shorter and bushier four years post-flood. These studies furthermore illustrated that the tree to shrub ratio did not change drastically from pre-flood conditions, although a decrease in the number of shrub individuals was reported. The research presented in this dissertation was designed to further explore changes in woody species composition and structure along the Sabie River, KNP at a post flood temporal interval, i.e. between the last survey in 2004 (by the KRPFRP) and 2010. For data compatibility, the sampling and analytical approach of this study conforms to the approach followed by the KRPFRP. Data were sampled within four preselected belt-transects that form part of the larger KRPFRP. All established woody individuals were counted and measured within each contiguous 10 m x 30 m plot within each of the four belt-transects. Log transformed species composition data were analysed through the application of the Bray Curtis dissimilarity index in combination with Ward’s method of clustering. Statistical significant differences between clusters were tested through the application of the Fisher’s exact relationship test. The MIXED Procedure or PROC MIXED model was used to investigate change within the vegetation structural data. Results obtained through the various analytical methods broadly support the findings of the KRPFRP. No significant change in woody species composition could be detected between 2004 and 2010. However, a change in the density (increase and decrease) of certain species across the MCB and MCF was revealed. Species richness and density increased significantly on the MCF oppose to small changes on the MCB. A significant increase in the total number of shrubs on the MCF contributed to an overall increase in woody density for the entire study area between 2004 and 2010. Shrubs therefore remained the most dominant growth form in both sampling years. Trees decreased across the MCB although the total number of established trees remained unchanged between 2004 and 2010. Riparian vegetation structure is directly linked to species assemblages, hence the continued dominance of shrub species along the Sabie River in the KNP The Sabie River riparian landscape is therefore still characterised by short and multi-stemmed woody individuals ten years after the LID. / Thesis (MSc (Environmental Sciences))--North-West University, Potchefstroom Campus, 2013

The flood of 2000 caused extensive changes within the riparian landscape of the Sabie River, Kruger National Park (KNP). Changes within the riparian landscape and the removal of vegetation resulted in considerable changes in riparian vegetation characteristics. Open patches created by the flood served as a template for the establishment of new species and the regeneration of existing species, which consequently resulted in a patch mosaic. This memorable event encouraged an investigation into the response of the Sabie River ecosystem to the memorable Large Infrequent Disturbance (LID). Riparian ecosystems are driven by varying combinations of environmental factors, such as water availability, disturbance, herbivory, fire and river morphology. This complexity depicts unique vegetation structure and assemblages of associated plant species. The lack of sufficient knowledge on the role of riparian vegetation in the health assessment of surrounding ecosystems along semi-arid rivers prompted the establishment of the Kruger Rivers Post Flood Research Program (KRPFRP). Research conducted through this monitoring program four years after the 2000 flood, revealed no significant changes in the species composition, although the location and density of many common riparian species have been changed. There was a decrease in species density across the macro channel floor (MCF) and an increase in species density across the macro channel bank (MCB). Furthermore, it was reported that the flood altered the distribution of height classes across the macro channel. In general the riparian vegetation was shorter and bushier four years post-flood. These studies furthermore illustrated that the tree to shrub ratio did not change drastically from pre-flood conditions, although a decrease in the number of shrub individuals was reported. The research presented in this dissertation was designed to further explore changes in woody species composition and structure along the Sabie River, KNP at a post flood temporal interval, i.e. between the last survey in 2004 (by the KRPFRP) and 2010. For data compatibility, the sampling and analytical approach of this study conforms to the approach followed by the KRPFRP. Data were sampled within four preselected belt-transects that form part of the larger KRPFRP. All established woody individuals were counted and measured within each contiguous 10 m x 30 m plot within each of the four belt-transects. Log transformed species composition data were analysed through the application of the Bray Curtis dissimilarity index in combination with Ward’s method of clustering. Statistical significant differences between clusters were tested through the application of the Fisher’s exact relationship test. The MIXED Procedure or PROC MIXED model was used to investigate change within the vegetation structural data. Results obtained through the various analytical methods broadly support the findings of the KRPFRP. No significant change in woody species composition could be detected between 2004 and 2010. However, a change in the density (increase and decrease) of certain species across the MCB and MCF was revealed. Species richness and density increased significantly on the MCF oppose to small changes on the MCB. A significant increase in the total number of shrubs on the MCF contributed to an overall increase in woody density for the entire study area between 2004 and 2010. Shrubs therefore remained the most dominant growth form in both sampling years. Trees decreased across the MCB although the total number of established trees remained unchanged between 2004 and 2010. Riparian vegetation structure is directly linked to species assemblages, hence the continued dominance of shrub species along the Sabie River in the KNP The Sabie River riparian landscape is therefore still characterised by short and multi-stemmed woody individuals ten years after the LID. / Thesis (MSc (Environmental Sciences))--North-West University, Potchefstroom Campus, 2013