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.

Influence of gender and life stressors on longitudinal depression treatment outcomes among older primary care patients

Purpose: Depression in older females is a significant and growing problem. Females who experience life stressors across the life span are at higher risk for developing problems with depression than their male counterparts. The primary aim of this study was (a) to examine gender-specific differences in the correlates of depression in older primary care patients based on baseline and longitudinal analyses; and (b) to examine the longitudinal effect of biopsychosocial risk factors on depression treatment outcomes in different models of behavioral healthcare (i.e., integrated care and enhanced referral). Method: This study used a quantitative secondary data analysis with longitudinal data from the Primary Care Research in Substance Abuse and Mental Health for Elderly (PRISM-E) study. A linear mixed model approach to hierarchical linear modeling was used for analysis using baseline assessment, and follow-up from three-month and six-month. Results: For participants diagnosed with major depressive disorder female gender was associated with increased depression severity at six-month compared to males at six-month. Further, the interaction between gender and life stressors found that females who reported loss of family and friends, family issues, money issues, medical illness was related to higher depression severity compared to males whereas lack of activities was related to lower depression severity among females compared to males. Conclusion: These findings suggest that gender moderated the relationship between specific life stressors and depression severity similar to how a protective factor can impact a person's response to a problem and reduce the negative impact of a risk factor on a problem outcome. Therefore, life stressors may be a reliable predictor of depression for both females and males in either behavioral health treatment model. This study concluded that life stressors influence males basic comfort, stability, and survival whereas life stressors influence females' development, personal growth, and happiness; therefore, life stressors may be a useful component to include in gender-based screening and assessment tools for depression. ^

The order selection and lot sizing problem in the make-to-order environment

This research is motivated by the need for considering lot sizing while accepting customer orders in a make-to-order (MTO) environment, in which each customer order must be delivered by its due date. Job shop is the typical operation model used in an MTO operation, where the production planner must make three concurrent decisions; they are order selection, lot size, and job schedule. These decisions are usually treated separately in the literature and are mostly led to heuristic solutions. The first phase of the study is focused on a formal definition of the problem. Mathematical programming techniques are applied to modeling this problem in terms of its objective, decision variables, and constraints. A commercial solver, CPLEX is applied to solve the resulting mixed-integer linear programming model with small instances to validate the mathematical formulation. The computational result shows it is not practical for solving problems of industrial size, using a commercial solver. The second phase of this study is focused on development of an effective solution approach to this problem of large scale. The proposed solution approach is an iterative process involving three sequential decision steps of order selection, lot sizing, and lot scheduling. A range of simple sequencing rules are identified for each of the three subproblems. Using computer simulation as the tool, an experiment is designed to evaluate their performance against a set of system parameters. For order selection, the proposed weighted most profit rule performs the best. The shifting bottleneck and the earliest operation finish time both are the best scheduling rules. For lot sizing, the proposed minimum cost increase heuristic, based on the Dixon-Silver method performs the best, when the demand-to-capacity ratio at the bottleneck machine is high. The proposed minimum cost heuristic, based on the Wagner-Whitin algorithm is the best lot-sizing heuristic for shops of a low demand-to-capacity ratio. The proposed heuristic is applied to an industrial case to further evaluate its performance. The result shows it can improve an average of total profit by 16.62%. This research contributes to the production planning research community with a complete mathematical definition of the problem and an effective solution approach to solving the problem of industry scale.

Marketing practices and their effectiveness in Taiwan's colleges of technology

The main purpose of this study was to investigate marketing practices in Taiwan's institutions of higher education and their relationship with students' college choice behaviors and attitudes. The study was conducted in 11 Taiwan's colleges of technology. It employed a multistrand conversion mixed model design, consisting of a qualitative and a quantitative strand. Funnel-sequenced interviews were conducted with 19 college administrators and the results were content analyzed using a constant-comparative method. The administrator interview data were also quantitized and used in cluster analysis of the institutions. Questionnaire data were collected from 1474 freshmen students, and analyzed using several univariate and multivariate statistical techniques including factor analysis, MANOVA, and correspondence analysis. ^ Analyses indicated that a weak relationship existed between institutions' marketing intensity and students' college choice. Students did not consider institutions' recruitment activities useful in their college searching process. They also reported little knowledge of their current school when they were deciding to enroll. Data analysis also revealed that students were practically oriented in their college selection. Academic resources, employability after graduation, and tuition were the most important attributes in students' college selection. Parents and students' social network such as friends and high school teachers were significant personal sources in enrollment decisions while institutions' representatives (i.e., recruiters) were considered the least influential. ^ Using cluster analysis, institutions were divided into three groups based on intensity of marketing efforts. Multivariate analysis of variance did not reveal significant differences between the college choice behaviors and attitudes of students who entered these three types of institutions. ^ Content analysis of the administrators' interviews indicated that the majority of them practiced passive marketing. This was primarily as a result of resistance to active marketing, lack of leadership commitment, insufficient financial and human resources, little faculty involvement, and inexperience in marketing. In comparison to public institutions, private institutions showed a more favorable attitude towards marketing concepts. They were well advanced in their recruitment activities while public schools were relatively hesitant to use marketing. Curriculum issues were not well represented in marketing activities and did not seem to be impacted by marketing needs. Based on the analysis of qualitative and quantitative data, it can be concluded that in these colleges, curriculum was more driven by commercial and industrial interest than by students' demands. ^ Theoretical, policy, and methodological implementation of the results were discussed. ^

Reading comprehension and mathematical concept acquisition through the use of math stories with bilingual children

Math storybooks are picture books in which the understanding of mathematical concepts is central to the comprehension of the story. Math stories have provided useful opportunities for children to expand their skills in the language arts area and to talk about mathematical factors that are related to their real lives. The purpose of this study was to examine bilingual children's reading and math comprehension of the math storybooks. ^ The participants were randomly selected from two Korean schools and two public elementary schools in Miami, Florida. The sample consisted of 63 Hispanic American and 43 Korean American children from ages five to seven. A 2 x 3 x (2) mixed-model design with two between- and one within-subjects variable was used to conduct this study. The two between-subjects variables were ethnicity and age, and the within-subjects variable was the subject area of comprehension. Subjects were read the three math stories individually, and then they were asked questions related to reading and math comprehension. ^ The overall ANOVA using multivariate tests was conducted to evaluate the factor of subject area for age and ethnicity. As follow-up tests for a significant main effect and a significant interaction effect, pairwise comparisons and simple main effect tests were conducted, respectively. ^ The results showed that there were significant ethnicity and age differences in total comprehension scores. There were also age differences in reading and math comprehension, but no significant differences were found in reading and math by ethnicity. Korean American children had higher scores in total comprehension than those of Hispanic American children, and they showed greater changes in their comprehension skills at the younger ages, from five to six, whereas Hispanic American children showed greater changes at the older ages, from six to seven. Children at ages five and six showed higher scores in reading than in math, but no significant differences between math and reading comprehension scores were found at age seven. ^ Through schooling with integrated instruction, young bilingual children can move into higher levels of abstraction and concepts. This study highlighted bilingual children's general nature of thinking and showed how they developed reading and mathematics comprehension in an integrated process. ^

Trichloroethylene fate and transport studies and biodegradation kinetics in the saturated zone

Permeable reactive barriers (PRB) are constructed from soil solid amendments to support the growth of bacteria that are capable of degrading organic contaminants. The objective of this study was to identify low-cost soil solid amendments that could retard the movement of trichloroethylene (TCE) while serving as long-lived carbon sources to foster its biodegradation in shallow groundwater through the use of a PRB. The natural amendments high in organic carbon content such as eucalyptus mulch, compost, wetland peat, organic humus were compared based on their geophysical characteristics, such as pHw, porosity and total organic carbon (TOC), and as well as TCE sorption potentials. The pHw values were within neutral range except for pine bark mulch and wetland peat. All other geophysical characteristics of the amendments showed suitability for use in a PRB. While the Freundlich model showed better fit for compost and pine bark mulch, the linear sorption model was adequate for eucalyptus mulch, wetland peat and Everglades muck within the concentration range studied (0.2-0.8 mg/L TCE). According to these results, two composts and eucalyptus mulch were selected for laboratory column experiments to evaluate their effectiveness at creating and maintaining conditions suitable for TCE anaerobic dechlorination. The columns were monitored for pH, ORP, TCE degradation, longevity of nutrients and soluble TOC to support TCE dechlorination. Native bacteria in the columns had the ability to convert TCE to DCEs; however, the inoculation with the TCE-degrading culture greatly increased the rate of biodegradation. This caused a significant increase in by-product concentration, mostly in the form of DCEs and VC followed by a slow degradation to ethylene. Of the tested amendments eucalyptus mulch was the most effective at supporting the TCE dechlorination. The experimental results of TCE sequential dechlorination took place in eucalyptus mulch and commercial compost from Savannah River Site columns were then simulated using the Hydrus-1D model. The simulations showed good fit with the experimental data. The results suggested that sorption and degradation were the dominant fate and transport mechanisms for TCE and DCEs in the column, supporting the use of these amendments in a permeable reactive barrier to remediate the TCE.

Tropical seagrass-associated macroalgae distributions and trends relative to water quality

Tropical coastal marine ecosystems including mangroves, seagrass beds and coral reef communities are undergoing intense degradation in response to natural and human disturbances, therefore, understanding the causes and mechanisms present challenges for scientist and managers. In order to protect our marine resources, determining the effects of nutrient loads on these coastal systems has become a key management goal. Data from monitoring programs were used to detect trends of macroalgae abundances and develop correlations with nutrient availability, as well as forecast potential responses of the communities monitored. Using eight years of data (1996–2003) from complementary but independent monitoring programs in seagrass beds and water quality of the Florida Keys National Marine Sanctuary (FKNMS), we: (1) described the distribution and abundance of macroalgae groups; (2) analyzed the status and spatiotemporal trends of macroalgae groups; and (3) explored the connection between water quality and the macroalgae distribution in the FKNMS. In the seagrass beds of the FKNMS calcareous green algae were the dominant macroalgae group followed by the red group; brown and calcareous red algae were present but in lower abundance. Spatiotemporal patterns of the macroalgae groups were analyzed with a non-linear regression model of the abundance data. For the period of record, all macroalgae groups increased in abundance (Abi) at most sites, with calcareous green algae increasing the most. Calcareous green algae and red algae exhibited seasonal pattern with peak abundances (Φi) mainly in summer for calcareous green and mainly in winter for red. Macroalgae Abi and long-term trend (mi) were correlated in a distinctive way with water quality parameters. Both the Abi and mi of calcareous green algae had positive correlations with NO3−, NO2−, total nitrogen (TN) and total organic carbon (TOC). Red algae Abi had a positive correlation with NO2−, TN, total phosphorus and TOC, and the mi in red algae was positively correlated with N:P. In contrast brown and calcareous red algae Abi had negative correlations with N:P. These results suggest that calcareous green algae and red algae are responding mainly to increases in N availability, a process that is happening in inshore sites. A combination of spatially variable factors such as local current patterns, nutrient sources, and habitat characteristics result in a complex array of the macroalgae community in the seagrass beds of the FKNMS.

Differential outcomes of two -way and transitional programs on English language learners at different entry levels

This study investigated the effects of two types of bilingual education programs (two-way and transitional) on the academic performance, attitudes, and metacognitive awareness of 5th grade students who entered kindergarten or first grade with different levels of English proficiency. The multi-stage sample consisted of students who had participated in each program for a period of at least five years. A mixed model design allowed for the collection of quantitative and qualitative data that were analyzed accordingly and integrated. ^ The findings indicated no significant differences between the two groups on measures of academic achievement in English. Significant differences were found in the number of semesters required for the students to become proficient English speakers. An important conclusion, based on these findings, was that the students enrolled in the two-way bilingual education (TWBE) programs learned English faster. Moreover, they maintained a high level of proficiency in Spanish, scoring significantly higher than the transitional bilingual education group on measures of Spanish reading ability.^ Questionnaire and interview data indicated that the students in the two-way bilingual education programs tended to use more Spanish for recreational purposes and tended to rate themselves as more proficient Spanish speakers than their peers. Conversely, the students enrolled in the transitional bilingual education programs tended to rate themselves as more proficient in English than their peers. ^ The level of English language proficiency upon entering school (five years later) was found to make a difference in academic achievement, as measured by standardized tests. Five years of schooling did not fully eliminate the gap in academic performance between students with different ESOL entry levels at kindergarten. However, entry level did not have an effect on attitudes towards bilingualism. ^ It is concluded that, although there was no significant difference between the two groups on measures of academic achievement in English, TWBE and transitional programs have differential effects. Students in the TWBE programs acquired oral language at a faster rate, developed literacy skills in their native language, and acquired more positive attitudes towards bilingualism. Theoretical, methodological, and policy implications of the findings are discussed. ^