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.

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.

Hydrological dynamics between a coastal aquifer and the adjacent estuarine system, Biscayne Bay, South Florida

Geochemical and geophysical approaches have been used to investigate the freshwater and saltwater dynamics in the coastal Biscayne Aquifer and Biscayne Bay. Stable isotopes of oxygen and hydrogen, and concentrations of Sr2+ and Ca2+ were combined in two geochemical mixing models to provide estimates of the various freshwater inputs (precipitation, canal water, and groundwater) to Biscayne Bay and the coastal canal system in South Florida. Shallow geophysical electromagnetic and direct current resistivity surveys were used to image the geometry and stratification of the saltwater mixing zone in the near coastal (less than 1km inland) Biscayne Aquifer. The combined stable isotope and trace metal models suggest a ratio of canal input-precipitation-groundwater of 38%–52%–10% in the wet season and 37%–58%–5% in the dry season with an error of 25%, where most (20%) of the error was attributed to the isotope regression model, while the remaining 5% error was attributed to the Sr2+/Ca2+ mixing model. These models suggest rainfall is the dominate source of freshwater to Biscayne Bay. For a bay-wide water budget that includes saltwater and freshwater mixing, fresh groundwater accounts for less than 2% of the total input. A similar Sr 2+/Ca2+ tracer model indicates precipitation is the dominate source in 9 out of 10 canals that discharge into Biscayne Bay. The two-component mixing model converged for 100% of the freshwater canal samples in this study with 63% of the water contributed to the canals coming from precipitation and 37% from groundwater inputs ±4%. There was a seasonal shift from 63% precipitation input in the dry season to 55% precipitation input in the wet season. The three end-member mixing model converged for only 60% of the saline canal samples possibly due to non-conservative behavior of Sr2+ and Ca2+ in saline groundwater discharging into the canal system. Electromagnetic and Direct Current resistivity surveys were successful at locating and estimating the geometry and depth of the freshwater/saltwater interface in the Biscayne Aquifer at two near coastal sites. A saltwater interface that deepened as the survey moved inland was detected with a maximum interpreted depth to the interface of 15 meters, approximately 0.33 km inland from the shoreline. ^

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.

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.

Seagrass sediments as a global carbon sink: Isotopic constraints

Seagrass meadows are highly productive habitats found along many of the world's coastline, providing important services that support the overall functioning of the coastal zone. The organic carbon that accumulates in seagrass meadows is derived not only from seagrass production but from the trapping of other particles, as the seagrass canopies facilitate sedimentation and reduce resuspension. Here we provide a comprehensive synthesis of the available data to obtain a better understanding of the relative contribution of seagrass and other possible sources of organic matter that accumulate in the sediments of seagrass meadows. The data set includes 219 paired analyses of the carbon isotopic composition of seagrass leaves and sediments from 207 seagrass sites at 88 locations worldwide. Using a three source mixing model and literature values for putative sources, we calculate that the average proportional contribution of seagrass to the surface sediment organic carbon pool is ∼50%. When using the best available estimates of carbon burial rates in seagrass meadows, our data indicate that between 41 and 66 gC m−2 yr−1 originates from seagrass production. Using our global average for allochthonous carbon trapped in seagrass sediments together with a recent estimate of global average net community production, we estimate that carbon burial in seagrass meadows is between 48 and 112 Tg yr−1, showing that seagrass meadows are natural hot spots for carbon sequestration.

Applying stable isotopes to examine food-web structure: an overview of analytical tools

Stable isotope analysis has emerged as one of the primary means for examining the structure and dynamics of food webs, and numerous analytical approaches are now commonly used in the field. Techniques range from simple, qualitative inferences based on the isotopic niche, to Bayesian mixing models that can be used to characterize food-web structure at multiple hierarchical levels. We provide a comprehensive review of these techniques, and thus a single reference source to help identify the most useful approaches to apply to a given data set. We structure the review around four general questions: (1) what is the trophic position of an organism in a food web?; (2) which resource pools support consumers?; (3) what additional information does relative position of consumers in isotopic space reveal about food-web structure?; and (4) what is the degree of trophic variability at the intrapopulation level? For each general question, we detail different approaches that have been applied, discussing the strengths and weaknesses of each. We conclude with a set of suggestions that transcend individual analytical approaches, and provide guidance for future applications in the field.

A preliminary analysis of the correlation of food-web characteristics with hydrology and nutrient gradients in the southern Everglades

We estimated trophic position and carbon source for three consumers (Florida gar, Lepisosteus platyrhincus; eastern mosquitofish, Gambusia holbrooki; and riverine grass shrimp, Palaemonetes paludosus) from 20 sites representing gradients of productivity and hydrological disturbance in the southern Florida Everglades, U.S.A. We characterized gross primary productivity at each site using light/dark bottle incubation and stem density of emergent vascular plants. We also documented nutrient availability as total phosphorus (TP) in floc and periphyton, and the density of small fishes. Hydrological disturbance was characterized as the time since a site was last dried and the average number of days per year the sites were inundated for the previous 10 years. Food-web attributes were estimated in both the wet and dry seasons by analysis of δ15N (trophic position) and δ13C (food-web carbon source) from 702 samples of aquatic consumers. An index of carbon source was derived from a two-member mixing model with Seminole ramshorn snails (Planorbella duryi) as a basal grazing consumer and scuds (amphipods Hyallela azteca) as a basal detritivore. Snails yielded carbon isotopic values similar to green algae and diatoms, while carbon values of scuds were similar to bulk periphyton and floc; carbon isotopic values of cyanobacteria were enriched in C13compared to all consumers examined. A carbon source similar to scuds dominated at all but one study site, and though the relative contribution of scud-like and snail-like carbon sources was variable, there was no evidence that these contributions were a function of abiotic factors or season. Gar consistently displayed the highest estimated trophic position of the consumers studied, with mosquitofish feeding at a slightly lower level, and grass shrimp feeding at the lowest level. Trophic position was not correlated with any nutrient or productivity parameter, but did increase for grass shrimp and mosquitofish as the time following droughts increased. Trophic position of Florida gar was positively correlated with emergent plant stem density.

Ecohydrology, evapotranspiration and hydrogeochemistry of carbonate mangrove wetlands

Coastal environments can be highly susceptible to environmental changes caused by anthropogenic pressures and natural events. Both anthropogenic and natural perturbations may directly affect the amount and the quality of water flowing through the ecosystem, both in the surface and subsurface and can subsequently, alter ecological communities and functions. The Florida Everglades and the Sian Ka'an Biosphere Reserve (Mexico) are two large ecosystems with an extensive coastal mangrove ecotone that represent a historically altered and pristine environment, respectively. Rising sea levels, climate change, increased water demand, and salt water intrusion are growing concerns in these regions and underlies the need for a better understanding of the present conditions. The goal of my research was to better understand various ecohydrological, environmental, and hydrogeochemical interactions and relationships in carbonate mangrove wetlands. A combination of aqueous geochemical analyses and visible and near-infrared reflectance data were employed to explore relationships between surface and subsurface water chemistry and spectral biophysical stress in mangroves. Optical satellite imagery and field collected meteorological data were used to estimate surface energy and evapotranspiration and measure variability associated with hurricanes and restoration efforts. Furthermore, major ionic and nutrient concentrations, and stable isotopes of hydrogen and oxygen were used to distinguish water sources and infer coastal groundwater discharge by applying the data to a combined principal component analysis-end member mixing model. Spectral reflectance measured at the field and satellite scales were successfully used to estimate surface and subsurface water chemistry and model chloride concentrations along the southern Everglades. Satellite imagery indicated that mangrove sites that have less tidal flushing and hydrogeomorphic heterogeneity tend to have more variable evapotranspiration and soil heat flux in response to storms and restoration. Lastly, water chemistry and multivariate analyses indicated two distinct fresh groundwater sources that discharge to the phosphorus-limited estuaries and bays of the Sian Ka'an Biopshere Reserve; and that coastal groundwater discharge was an important source for phosphorus. The results of the study give us a better understanding of the ecohydrological and hydrogeological processes in carbonate mangrove environments that can be then be extrapolated to similar coastal ecosystems in the Caribbean.

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. ^

A non-linear discrete stochastic optimization model for Advanced Access patient appointment scheduling

Access to healthcare is a major problem in which patients are deprived of receiving timely admission to healthcare. Poor access has resulted in significant but avoidable healthcare cost, poor quality of healthcare, and deterioration in the general public health. Advanced Access is a simple and direct approach to appointment scheduling in which the majority of a clinic's appointments slots are kept open in order to provide access for immediate or same day healthcare needs and therefore, alleviate the problem of poor access the healthcare. This research formulates a non-linear discrete stochastic mathematical model of the Advanced Access appointment scheduling policy. The model objective is to maximize the expected profit of the clinic subject to constraints on minimum access to healthcare provided. Patient behavior is characterized with probabilities for no-show, balking, and related patient choices. Structural properties of the model are analyzed to determine whether Advanced Access patient scheduling is feasible. To solve the complex combinatorial optimization problem, a heuristic that combines greedy construction algorithm and neighborhood improvement search was developed. The model and the heuristic were used to evaluate the Advanced Access patient appointment policy compared to existing policies. Trade-off between profit and access to healthcare are established, and parameter analysis of input parameters was performed. The trade-off curve is a characteristic curve and was observed to be concave. This implies that there exists an access level at which at which the clinic can be operated at optimal profit that can be realized. The results also show that, in many scenarios by switching from existing scheduling policy to Advanced Access policy clinics can improve access without any decrease in profit. Further, the success of Advanced Access policy in providing improved access and/or profit depends on the expected value of demand, variation in demand, and the ratio of demand for same day and advanced appointments. The contributions of the dissertation are a model of Advanced Access patient scheduling, a heuristic to solve the model, and the use of the model to understand the scheduling policy trade-offs which healthcare clinic managers must make. ^