Some innovative methods to improve profiles derivation

As the government aimed to provide appropriate education to all children (No Child Left Behind Act), it is important that the education providers can assess the performance of the students correctly so that they can provide the appropriate education for the students. Profile analysis is a very useful tool to interpret test scores and measure students’ performance. However, traditionally, profile analysis studies are done using a univariate approach, which has a number of drawbacks. Therefore, the purpose of this study was to develop some innovative methods to enhance the accuracy of profiles derivation. A multistage cluster analytic technique was developed to derive profiles. Its development was based on the foundation work of McDermott’s Multi-stage Euclidean Grouping (MEG) method. This new method is called Modified Multistage Euclidean Grouping (MMEG), and is implemented in SAS macro language. The code is easy to use and provides evaluation statistics of compactness and cross-validation. The simulation results show that MMEG is a good alternative to the time-consuming hierarchical clustering method and it is stable regardless of the cluster structure. The second study in this dissertation was to develop a new method to handle noisy data in cluster analysis through differential weights. Weights were assigned to the variables based on their reliabilities to handle the effect of measurement error in the cluster solution. The simulation results show that the new method can better recover the cluster structure than when the variables were not weighted, especially when the measurement error was large. This gives promise in using the proposed variable weighting in clustering noisy data. In a word, the encouraging results in the simulation studies show that these two new methods developed in this dissertation can enhance the accuracy profile derivation