Comparison of Some Improved Estimators for Linear Regression Model under Different Conditions

Multiple linear regression model plays a key role in statistical inference and it has extensive applications in business, environmental, physical and social sciences. Multicollinearity has been a considerable problem in multiple regression analysis. When the regressor variables are multicollinear, it becomes difficult to make precise statistical inferences about the regression coefficients. There are some statistical methods that can be used, which are discussed in this thesis are ridge regression, Liu, two parameter biased and LASSO estimators. Firstly, an analytical comparison on the basis of risk was made among ridge, Liu and LASSO estimators under orthonormal regression model. I found that LASSO dominates least squares, ridge and Liu estimators over a significant portion of the parameter space for large dimension. Secondly, a simulation study was conducted to compare performance of ridge, Liu and two parameter biased estimator by their mean squared error criterion. I found that two parameter biased estimator performs better than its corresponding ridge regression estimator. Overall, Liu estimator performs better than both ridge and two parameter biased estimator.

Social Network Structure as a Critical Success Condition for Open Source Software Project Communities

In recent years, a surprising new phenomenon has emerged in which globally-distributed online communities collaborate to create useful and sophisticated computer software. These open source software groups are comprised of generally unaffiliated individuals and organizations who work in a seemingly chaotic fashion and who participate on a voluntary basis without direct financial incentive. The purpose of this research is to investigate the relationship between the social network structure of these intriguing groups and their level of output and activity, where social network structure is defined as 1) closure or connectedness within the group, 2) bridging ties which extend outside of the group, and 3) leader centrality within the group. Based on well-tested theories of social capital and centrality in teams, propositions were formulated which suggest that social network structures associated with successful open source software project communities will exhibit high levels of bridging and moderate levels of closure and leader centrality. The research setting was the SourceForge hosting organization and a study population of 143 project communities was identified. Independent variables included measures of closure and leader centrality defined over conversational ties, along with measures of bridging defined over membership ties. Dependent variables included source code commits and software releases for community output, and software downloads and project site page views for community activity. A cross-sectional study design was used and archival data were extracted and aggregated for the two-year period following the first release of project software. The resulting compiled variables were analyzed using multiple linear and quadratic regressions, controlling for group size and conversational volume. Contrary to theory-based expectations, the surprising results showed that successful project groups exhibited low levels of closure and that the levels of bridging and leader centrality were not important factors of success. These findings suggest that the creation and use of open source software may represent a fundamentally new socio-technical development process which disrupts the team paradigm and which triggers the need for building new theories of collaborative development. These new theories could point towards the broader application of open source methods for the creation of knowledge-based products other than software.

Examining the Validity of the GRE General Test Scores and Undergraduate GPA for Predicting Success in Graduate School at a Large Racially and Ethnically Diverse Public University in Southeast Florida

The purpose of the study was to determine the degree of relationships among GRE scores, undergraduate GPA (UGPA), and success in graduate school, as measured by first year graduate GPA (FGPA), cumulative graduate GPA, and degree attainment status. A second aim of the study was to determine whether the relationships between the composite predictor (GRE scores and UGPA) and the three success measures differed by race/ethnicity and sex. A total of 7,367 graduate student records (masters, 5,990; doctoral: 1,377) from 2000 to 2010 were used to evaluate the relationships among GRE scores, UGPA and the three success measures. Pearson’s correlation, multiple linear and logistic regression, and hierarchical multiple linear and logistic regression analyses were performed to answer the research questions. The results of the correlational analyses differed by degree level. For master’s students, the ETS proposed prediction that GRE scores are valid predictors of first year graduate GPA was supported by the findings from the present study; however, for doctoral students, the proposed prediction was only partially supported. Regression and correlational analyses indicated that UGPA was the variable that consistently predicted all three success measures for both degree levels. The hierarchical multiple linear and logistic regression analyses indicated that at master’s degree level, White students with higher GRE Quantitative Reasoning Test scores were more likely to attain a degree than Asian Americans, while International students with higher UGPA were more likely to attain a degree than White students. The relationships between the three predictors and the three success measures were not significantly different between men and women for either degree level. Findings have implications both for practice and research. They will provide graduate school administrators with institution-specific validity data for UGPA and the GRE scores, which can be referenced in making admission decisions, while they will provide empirical and professionally defensible evidence to support the current practice of using UGPA and GRE scores for admission considerations. In addition, new evidence relating to differential predictions will be useful as a resource reference for future GRE validation researchers.