abstract: When analyzing longitudinal data it is essential to account both for the correlation inherent from the repeated measures of the responses as well as the correlation realized on account of the feedback created between the responses at a particular time and the predictors at other times. A generalized method of moments (GMM) for estimating the coefficients in longitudinal data is presented. The appropriate and valid estimating equations associated with the time-dependent covariates are identified, thus providing substantial gains in efficiency over generalized estimating equations (GEE) with the independent working correlation. Identifying the estimating equations for computation is of utmost importance. This paper provides a technique for identifying the relevant estimating equations through a general method of moments. I develop an approach that makes use of all the valid estimating equations necessary with each time-dependent and time-independent covariate. Moreover, my approach does not assume that feedback is always present over time, or present at the same degree. I fit the GMM correlated logistic regression model in SAS with PROC IML. I examine two datasets for illustrative purposes. I look at rehospitalization in a Medicare database. I revisit data regarding the relationship between the body mass index and future morbidity among children in the Philippines. These datasets allow us to compare my results with some earlier methods of analyses. / Dissertation/Thesis / Arizona Medicare Data on Rehospitalization / Philippine Data on Children's Morbidity / M.S. Statistics 2012

Ph.D. (Geography) / Skillful management and planning of the earth's natural resources and of agricultural production necessitates a great deal of Information regarding the resources and relevant soclo-economlc factors, as well as better Information on crop yield expectations throughout the year. These Intricate processes can often be simplified Into models. Most of Nature's systems (for example climatic systems) are, however, too complex to allow realistic models to be evaluated numerically and are therefore examined by means of simulation models through which the Interaction with time between physical processes Is established. The purpose Is to understand these processes In order to forecast the results of these changes and Interactions. The aim of this study Is to construct a composite climate model that (1) computes missing climate values, and (2) extrapolates climate values until the expected date of harvesting, by simulation using the random sampling of values from reference ("look-up") tables, In order that (3) the climate files, with simulated climate values, could be used with the parameter files as Input files for the CERES-Maize model. The CERES-Maize model uses dally values to simulate the growth, development and yield of the maize plant. The respective crop forecasting results obtained for actual and simulated climate values are then to be evaluated. Climate files, with four variables, were obtained on magnetic computer tape from the South African Weather Bureau for the study area In the Eastern Transvaal. The preliminary processing was done by the use of SA5-programmes and these files were then exported from the mainframe computer to a personal computer and stored on floppy disks. Climate reference flies were compiled from the original climate flies by sorting the climate data according to the Julian date. The missing values In the climate reference flies and the original climate files were restored from the files of neighbouring weather stations, as calculated orestimated values by.means of a suitable method of computation. Some of the methods used, were derived after comparing the graphs of the time-series of a number of climate files. Aclimate simulation model was compiled In which climatic elements were simulated by sampling values a set number of times randomly from the climate reference files. The mean of these sampled values were adjusted by multiplying It with a factor representing the climatic change over time. A climate file, also containing simulated values, and a theoretical parameter Input file were then used as the Input flies for a revised edition of the CERES-Maize model. A comparison of the results obtained for the 1986/87 growing season when the climate files, with actual and simulated values respectively, were used as Inputs for the CERES-Maize model, Indicated very promising results. The values predicted for two climate flies (1962-1987) differed by about 18%, whereas a difference of only about 8% between those predicted for two smaller climate files (actual and simulated values respectively), representing only the 1986/87 season, was recorded. The difference between values predicted for the climate file, mentioned last, and consisting only of simulated climate values, and those forecasted for the original and complete climate data file, was only 5%. As Indicated by the arithmetic mean, there is again a tendency towards the mean values.

The purpose of this study was to investigate analytical approaches for estimating the optimum (profit maximizing) rate of initial overstory kill for increasing seasonal forage availability on a specific ranch. The models were developed using the big sagebrush (Artemisia tridentata) - crested wheatgrass (Agropyron cristatum, A. desertorum) vegetation type on a Utah cow-calf-yearling operation as an example. The models should be applicable on any ranching situation where understory forage production is constrained by the establishment and growth of undesirable overstory vegetation. Three model forms were developed and compared for their applicability to on-the-ground investment decision making. Single treatment period (STP) static and dynamic models and a multiple treatment period (MTP) dyne.mic model were theoretically developed. Ee.ch model we.s formulated using e. biological production function relating under story production to ini tie.l kill percentage, e. cost of overstory kill function fore. specific overstory reduction method, and a derived demand function for seasonal forage availability. The production function was estimated in both static and dynamic forms for use in the different models. The remaining functions were used in the same form for a11 model applications. Results indicated that the STP static optimization model holds the most promise for an on-the-ground decision making tool at the present time. Data to estimate dynamic production functions over a variety of vegetation types and grazing management situations essentially do not exist. This deficiency makes the use of long-term dynamic models less feasible for current decisions. It does not, however, alleviate the need to recognize long-term biological and economic relationships in making such decisions. The STP static model indicated that for the example Utah ranch a target big sagebrush kill rate between 89 and 100 percent would be optimal depending on the derived demand and cost of kill functions used. Target kill rates other than the optimum would represent potentially significant opportunity costs to this particular operation. The optimal solution obtained by this method is expected to change depending on the situation being analyzed. The model must be applied on a specific ranch basis and was not designed to make general recommendations.

The filter paper method for measuring soil water potential was evaluated. The method was calibrated using salt solutions (-1.4 bars to -22.4 bars), sample chamber psychrometer (-1 to -50 bars), pressure plate (-0.1 to - 15 bars) and soil column at equilibrium (0 to -0.2 bars). It was found that the absolute temperature had little effect on the predicted soil water potential, but a temperature variation had a large effect. It was found that the temperature fluctuation must be small. The predicted water potential was influenced by the type of contact of the soil with the filter paper. It is suggested that one filter paper be placed beneath the soil (good contact for liquid or vapour flow) and one filter paper be placed above the soil not in physical contact (allowing vapour flow only). The equilibrium between the filter paper and soil mass was essential completed by the end of two days and certainly by the end of five days.

An important management practice within the 60-80 million acres of Pinyon-Juniper woodlands is to convert these woodlands to open rangelands. The success or failure of seedling adapted grasses in place of trees is contingent upon the revegetation techniques employed and upon fortuitous weather patterns. In order to formulate policy for Pinyon-Juniper control decisions, persons responsible for such policies need to know the risks of introducing range grasses into given areas. This thesis is essentially a hypothesis concerning the magnitude of such risks. Pinyon-Juniper control has been practiced widely in the five state areas of Arizona, Colorado, Nevada, New Mexico, and Utah. Justification for control and conversion of the woodlands to open grazing areas rests on the assumption that the trees have little apparent utility and, therefore they should be replaced by a grass resource which has relatively greater value. In its extreme form the assumption involves the notion that the trees are actually detrimental to the productivity of the land. they become a hindrance to the growth of various forms of plant life considered desirable. Considerable investment, primarily at the expense of society, has been incurred in the transformation process. Until recent years control projects have been limited to the most accessible sites and areas "invaded" by Pinyon-Juniper trees. At present the conversion place has slackened due to the limited number of remaining accessible sites in some areas, but more importantly to the fact that the projects have had a history of mixed success. While certain rules of thumb have been put forth to explain the nature of the factors influencing seedling emergence and increased forage production, these are so volatile that an apprehension of failure exists among land managers. The intensity of investment can only be balanced against risk levels if there is basic understanding of the roles played by the variables influencing seedling establishment and forage increase. Both policy and nonpolicy (not subject to human manipulation) variables must be identified and their influences upon success measured. The analysis that follows begins by setting forth the objectives to be achieved in evaluating the tree conversion process and its associated risk. Next a theory of range grass seedling establishment is presented. The appropriate variables are identified and an "establishment" model is applied to the empirical data. A third section specifically treats weather as a major influence upon seedling emergence and forage production. A model expressed in probabilistic terms, employing the Markov property is applied to available data to evaluate weather index movements. Finally having dealt with emergence, a theory is developed to explain expected forage production in the period following emergence. The parameters of the associated model are obtained from empirical data.

Land surface actual evapotranspiration (ET) is an important process in terrestrial water balance and reliable estimates of ET are necessary to improve water resources management. In this regard, there is a growing body of literature that recognizes the importance of an accurate ET model. Among them, the complementary relationship between ET and potential ET (ETP) has been the subject of many studies because it uses only meteorological data as inputs. However, there is an increasing concern that some complementary relationship models perform poorly under dry conditions. To overcome this limitation, this dissertation was designed to extend the latest complementary relationship model, Modified GG, using both meteorological data and vegetation information, NDVI, which is readily available from remote sensing data. The proposed model, Adjusted GG-NDVI, was validated by comparing to other ET models and measured ET data. With Adjusted GG-NDVI, this dissertation addressed the applicability of using ET as a proxy for drought monitoring. As a result, the drought patterns from the proposed drought index, EWDI, were consistent with commonly used USDM in the United States. More importantly, this study described drought conditions by comprehensively considering both precipitation and vegetation conditions. Taken together, these findings have significant implications for the understanding of how ET can assist in water resources management.

Indiana University-Purdue University Indianapolis (IUPUI) / A significant hurdle for analyzing big data is the lack of effective technology and statistical inference methods. A popular approach for analyzing data with large sample is subsampling. Many subsampling probabilities have been introduced in literature (Ma, \emph{et al.}, 2015) for linear model. In this dissertation, we focus on generalized estimating equations (GEE) with big data and derive the asymptotic normality for the estimator without resampling and estimator with resampling. We also give the asymptotic representation of the bias of estimator without resampling and estimator with resampling. we show that bias becomes significant when the data is of high-dimensional. We also present a novel subsampling method called A-optimal which is derived by minimizing the trace of some dispersion matrices (Peng and Tan, 2018). We derive the asymptotic normality of the estimator based on A-optimal subsampling methods. We conduct extensive simulations on large sample data with high dimension to evaluate the performance of our proposed methods using MSE as a criterion. High dimensional data are further investigated and we show through simulations that minimizing the asymptotic variance does not imply minimizing the MSE as bias not negligible. We apply our proposed subsampling method to analyze a real data set, gas sensor data which has more than four millions data points. In both simulations and real data analysis, our A-optimal method outperform the traditional uniform subsampling method.

In recent years, the United States has seen a high demand for dam rehabilitation projects as most dam infrastructure has started to reach or exceed the expected life span of 50-70 years. Rehabilitation projects can be very expensive, however, and the funding options for dam owners are limited. To raise awareness, organizations such as ASDSO and the Virginia DCR release cost estimates every few years to encourage more investment in dam infrastructure. Unfortunately, many cost estimates have been made with limited data and outdated methodologies. This research collects a new sample of cost data for Virginia dam rehabilitation projects and uses it to assess key factors for cost estimating. Factors such as height, drainage area, hazard classification, and ownership type were used to make regression models that predict the cost of addressing Virginia's non-compliant dams. This study estimates that approximately $300 million is needed to address Virginia's 98 deficient high hazard, local government owned dams and that $122 million of that estimate is need for SWCD dams alone. / Master of Science / Dam rehabilitation refers to the repair, removal, or upgrade of an existing dam structure. Rehabilitation projects are done when dams start to exceed their intended life span (approximately 50-60 years) or when policy makers change the required safety standards. The demand for dam rehabilitation has been increasing for the past several years as more and more dams are being identified as unsafe, but the available funding for rehabilitation projects is limited and competitive to obtain for dam owners. To raise awareness, dam safety agencies release cost estimates every few years to encourage government leaders and the general public to take action. However, these estimates need to be taken with caution as they are often made with limited data availability and outdated methodologies. This research collects a new sample of cost data for Virginia dam rehabilitation projects that have occurred in the last 15 years. Dam characteristics such as height, watershed size, downstream risk potential, and ownership type were used to form equations that predict the cost of addressing Virginia's non-compliant dams. This study estimates that approximately $300 million is needed to address Virginia's 98 deficient high hazard, local government owned dams and that $122 million of that estimate is need for Virginia's Soil and Water Conservation District dams alone.

A computerised cost estimating system, which can be used for making preliminary estimates of fixed capital investment of process plants, has been developed. The contituents of the system are (1) a cost calculating routine, COSMOD, compatible with existing modular executive programs, such as GEMCS, (2) an equipment data base, and (3) an equipment catalogue. The following are the significant characteristics of the cost estimating system.It has flexibility. It can be used as an independent cost estimating system, or as part of a modular executive-aided computer program. As part of an executive aided system, it may be used as a subroutine to a 'module* or 'unit computation', or as a 'module' or 'unit computation' itself. It will estimate the cost of one or more equipment but is capable of accepting costs generated external to itself. It requires relatively little computer space and time. The COSMOD program is concise and efficient. Its common block requirements in executive-aided systems is small. It adds little to the cost or time of running equipment design cases on the computer. It has access to a large quantity of data on equipment costs. Its data base contains cost information on nearly 300 different types of equipment, ensuring satisfactory fulfilment of its varying and often complex data requirements. The data are organised in a multiple record, random access file. This allows direct access to the equipment data of interest. It also allows easy addition, deletion or change to the data on file. An equipment catalogue is provided for the user. It provides information about the equipment whose cost data are available in COSMOD*s data file, and serves as a guide for the user in selecting and in providing data required by COSMOD. In conclusion, this work makes available, complete with cost estimating data and equipment catalogue, a preliminary capital cost estimating system, the absence of which has discouraged or impeded economic evaluations in plant design studies on the computer. / Thesis / Master of Engineering (ME)

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