VTechWorks Repository :: Browsing by Author "Anderson-Cook, Christine M."

Browsing by Author "Anderson-Cook, Christine M."

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Adaptive Fourier Analysis For Unequally-Spaced Time Series Data
Liang, Hong (Virginia Tech, 2002-04-16)
Fourier analysis, Walsh-Fourier analysis, and wavelet analysis have often been used in time series analysis. Fourier analysis can be used to detect periodic components that have sinusoidal shape; however, it might be misleading when the periodic components are not sinusoidal. Walsh-Fourier analysis is suitable for revealing the rectangular trends of time series. The flaw of the Walsh-Fourier analysis is that Walsh functions are not periodic. The resulting Walsh-Fourier analysis is more difficult to interpret than classical Fourier analysis. Wavelet analysis is very useful in analyzing and describing time series with gradual frequency changes. Wavelet analysis also has a shortcoming by giving no exact meaning to the concept of frequency because wavelets are not periodic functions. In addition, all three analysis methods above require equally-spaced time series observations. In this dissertation, by using a sequence of periodic step functions, a new analysis method, adaptive Fourier analysis, and its theory are developed. These can be applied to time series data where patterns may take general periodic shapes that include sinusoids as special cases. Most importantly, the resulting adaptive Fourier analysis does not require equally-spaced time series observations.
An Alternative Estimate of Preferred Direction for Circular Data
Otieno, Bennett Sango (Virginia Tech, 2002-07-25)
Circular or Angular data occur in many fields of applied statistics. A common problem of interest in circular data is estimating a preferred direction and its corresponding distribution. This problem is complicated by the so-called wrap-around effect, which exists because there is no minimum or maximum on the circle. The usual statistics employed for linear data are inappropriate for directional data, as they do not account for the circular nature of directional data. Common choices for summarizing the preferred direction are the sample circular mean, and sample circular median. A newly proposed circular analog of the Hodges-Lehmann estimator is proposed, as an alternative estimate of preferred direction. The new measure of preferred direction is a robust compromise between circular mean and circular median. Theoretical results show that the new measure of preferred direction is asymptotically more efficient than the circular median and that its asymptotic efficiency relative to the circular mean is quite comparable. Descriptions of how to use the methods for constructing confidence intervals and testing hypotheses are provided. Simulation results demonstrate the relative strengths and weaknesses of the new approach for a variety of distributions.
Analysis Methods to Control Performance Variability and Costs in Turbine Engine Manufacturing
Sheldon, Karl Edward (Virginia Tech, 2001-05-04)
Few aircraft engine manufacturers are able to consistently achieve high levels of performance reliability in newly manufactured engines. Much of the variation in performance reliability is due to the combined effect of tolerances of key engine components, including tip clearances of rotating components and flow areas in turbine nozzles. This research presents system analysis methods for determining the maximum possible tolerances of these key components that will allow a turbine engine to pass a number of specified performance constraints at a selected level of reliability. Through the combined use of a state-of-the-art engine performance code, component clearance loss models, and stochastic simulations, regions of feasible design space can be explored that allow for a pre-determined level of engine reliability. As expected, constraints such as spool speed and fuel consumption that are highly sensitive to certain component tolerances can significantly limit the feasible design space of the component in question. Discussed are methods for determining the bounds of any components feasible design space and for selecting the most economical combinations of component tolerances. Unique to this research is the method that determines the tolerances of engine components as a system while maintaining the geometric constraints of individual components. The methods presented in this work allow for any number of component tolerances to be varied or held fixed while providing solutions that satisfy all performance criteria. The algorithms presented in this research also allow for an individual specification of reliability on any number of performance parameters and geometric constraints. This work also serves as a foundation for an even larger algorithm that can include stochastic simulations and reliability prediction of an engine over its entire life cycle. By incorporating information such as time dependent performance data, known mission profiles, and the influence of maintenance into the component models, it would be possible to predict the reliability of an engine over time. Ultimately, a time-variant simulation such as this could help predict the timing and levels of maintenance that will maximize the life of an engine for a minimum cost.
Asymptotic Results for Model Robust Regression
Starnes, Brett Alden (Virginia Tech, 1999-12-14)
Since the mid 1980's many statisticians have studied methods for combining parametric and nonparametric esimates to improve the quality of fits in a regression problem. Notably in 1987, Einsporn and Birch proposed the Model Robust Regression estimate (MRR1) in which estimates of the parametric function, ƒ, and the nonparametric function, 𝑔, were combined in a straightforward fashion via the use of a mixing parameter, λ. This technique was studied extensively at small samples and was shown to be quite effective at modeling various unusual functions. In 1995, Mays and Birch developed the MRR2 estimate as an alternative to MRR1. This model involved first forming the parametric fit to the data, and then adding in an estimate of 𝑔 according to the lack of fit demonstrated by the error terms. Using small samples, they illustrated the superiority of MRR2 to MRR1 in most situations. In this dissertation we have developed asymptotic convergence rates for both MRR1 and MRR2 in OLS and GLS (maximum likelihood) settings. In many of these settings, it is demonstrated that the user of MRR1 or MRR2 achieves the best convergence rates available regardless of whether or not the model is properly specified. This is the "Golden Result of Model Robust Regression". It turns out that the selection of the mixing parameter is paramount in determining whether or not this result is attained.
Asymptotic Worst-Case Analyses for the Open Bin Packing Problem
Ongkunaruk, Pornthipa (Virginia Tech, 2005-10-07)
The open bin packing problem (OBPP) is a new variant of the well-known bin packing problem. In the OBPP, items are packed into bins so that the total content before the last item in each bin is strictly less than the bin capacity. The objective is to minimize the number of bins used. The applications of the OBPP can be found in the subway station systems in Hong Kong and Taipei and the scheduling in manufacturing industries. We show that the OBPP is NP-hard and propose two heuristic algorithms instead of solving the problem to optimality. We propose two offline algorithms in which the information of the items is known in advance. First, we consider the First Fit Decreasing (FFD) which is a good approximation algorithm for the bin packing problem. We prove that its asymptotic worst-case performance ratio is no more than 3/2. We observe that its performance for the OBPP is worse than that of the BPP. Consequently, we modify it by adding the algorithm that the set of largest items is the set of last items in each bin. Then, we propose the Modified First Fit Decreasing (MFFD) as an alternative and prove that its asymptotic worst-case performance ratio is no more than 91/80. We conduct empirical tests to show their average-case performance. The results show that in general, the FFD and MFFD algorithms use no more than 33% and 1% of the number of bins than that of optimal packing, respectively. In addition, the MFFD is asymptotically optimal when the sizes of items are (0,1) uniformly distributed.
Bayesian Methodology for Missing Data, Model Selection and Hierarchical Spatial Models with Application to Ecological Data
Boone, Edward L. (Virginia Tech, 2003-01-31)
Ecological data is often fraught with many problems such as Missing Data and Spatial Correlation. In this dissertation we use a data set collected by the Ohio EPA as motivation for studying techniques to address these problems. The data set is concerned with the benthic health of Ohio's waterways. A new method for incorporating covariate structure and missing data mechanisms into missing data analysis is considered. This method allows us to detect relationships other popular methods do not allow. We then further extend this method into model selection. In the special case where the unobserved covariates are assumed normally distributed we use the Bayesian Model Averaging method to average the models, select the highest probability model and do variable assessment. Accuracy in calculating the posterior model probabilities using the Laplace approximation and an approximation based on the Bayesian Information Criterion (BIC) are explored. It is shown that the Laplace approximation is superior to the BIC based approximation using simulation. Finally, Hierarchical Spatial Linear Models are considered for the data and we show how to combine analysis which have spatial correlation within and between clusters.
Cluster-Based Bounded Influence Regression
Lawrence, David E. (Virginia Tech, 2003-07-17)
In the field of linear regression analysis, a single outlier can dramatically influence ordinary least squares estimation while low-breakdown procedures such as M regression and bounded influence regression may be unable to combat a small percentage of outliers. A high-breakdown procedure such as least trimmed squares (LTS) regression can accommodate up to 50% of the data (in the limit) being outlying with respect to the general trend. Two available one-step improvement procedures based on LTS are Mallows 1-step (M1S) regression and Schweppe 1-step (S1S) regression (the current state-of-the-art method). Issues with these methods include (1) computational approximations and sub-sampling variability, (2) dramatic coefficient sensitivity with respect to very slight differences in initial values, (3) internal instability when determining the general trend and (4) performance in low-breakdown scenarios. A new high-breakdown regression procedure is introduced that addresses these issues, plus offers an insightful summary regarding the presence and structure of multivariate outliers. This proposed method blends a cluster analysis phase with a controlled bounded influence regression phase, thereby referred to as cluster-based bounded influence regression, or CBI. Representing the data space via a special set of anchor points, a collection of point-addition OLS regression estimators forms the basis of a metric used in defining the similarity between any two observations. Cluster analysis then yields a main cluster "halfset" of observations, with the remaining observations becoming one or more minor clusters. An initial regression estimator arises from the main cluster, with a multiple point addition DFFITS argument used to carefully activate the minor clusters through a bounded influence regression framework. CBI achieves a 50% breakdown point, is regression equivariant, scale equivariant and affine equivariant and distributionally is asymptotically normal. Case studies and Monte Carlo studies demonstrate the performance advantage of CBI over S1S and the other high breakdown methods regarding coefficient stability, scale estimation and standard errors. A dendrogram of the clustering process is one graphical display available for multivariate outlier detection. Overall, the proposed methodology represents advancement in the field of robust regression, offering a distinct philosophical viewpoint towards data analysis and the marriage of estimation with diagnostic summary.
Construction and Analysis of Linear Trend-Free Factorial Designs Under a General Cost Structure
Kim, Kiho (Virginia Tech, 1997-07-28)
When experimental units exhibit a smooth trend over time or in space, random allocation of treatments may no longer be appropriate. Instead, systematic run orders may have to be used to reduce or eliminate the effects of such a trend. The resulting designs are referred to as trend-free designs. We consider here, in particular, linear trend-free designs for factorial treatment structures such that estimates of main effects and two-factor interactions are trend-free. In addition to trend-freeness we incorporate a general cost structure and propose methods of constructing optimal or near-optimal full or fractional factorial designs. Building upon the generalized foldover scheme (GFS) introduced by Coster and Cheng (1988) we develop a procedure of selection of foldover vectors (SFV) which is a construction method for an appropriate generator matrix. The final optimal or near-optimal design can then be developed from this generator matrix. To achieve a reduction in the amount of work, i.e., a reduction of the large number of possible generator matrices, and to make this whole process easier to use by a practitioner, we introduce the systematic selection of foldover vectors (SSFV). This method does not always produce optimal designs but in all cases practical compromise designs. The cost structure for factorial designs can be modeled according to the number of level changes for the various factors. In general, if cost needs to be kept to a minimum, factor level changes will have to be kept at a minimum. This introduces a covariance structure for the observations from such an experiment. We consider the consequences of this covariance structure with respect to the analysis of trend-free factorial designs. We formulate an appropriate underlying mixed linear model and propose an AIC-based method using simulation studies, which leads to a useful practical linear model as compared to the theoretical model, because the theoretical model is not always feasible. Overall, we show that estimation of main effects and two-factor interactions, trend-freeness, and minimum cost cannot always be achieved simultaneously. As a consequence, compromise designs have to be considered, which satisfy requirements as much as possible and are practical at the same time. The proposed methods achieve this aim.
Contributions to Profile Monitoring and Multivariate Statistical Process Control
Williams, James Dickson (Virginia Tech, 2004-12-01)
The content of this dissertation is divided into two main topics: 1) nonlinear profile monitoring and 2) an improved approximate distribution for the T² statistic based on the successive differences covariance matrix estimator. Part 1: Nonlinear Profile Monitoring In an increasing number of cases the quality of a product or process cannot adequately be represented by the distribution of a univariate quality variable or the multivariate distribution of a vector of quality variables. Rather, a series of measurements are taken across some continuum, such as time or space, to create a profile. The profile determines the product quality at that sampling period. We propose Phase I methods to analyze profiles in a baseline dataset where the profiles can be modeled through either a parametric nonlinear regression function or a nonparametric regression function. We illustrate our methods using data from Walker and Wright (2002) and from dose-response data from DuPont Crop Protection. Part 2: Approximate Distribution of T² Although the T² statistic based on the successive differences estimator has been shown to be effective in detecting a shift in the mean vector (Sullivan and Woodall (1996) and Vargas (2003)), the exact distribution of this statistic is unknown. An accurate upper control limit (UCL) for the T² chart based on this statistic depends on knowing its distribution. Two approximate distributions have been proposed in the literature. We demonstrate the inadequacy of these two approximations and derive useful properties of this statistic. We give an improved approximate distribution and recommendations for its use.
Correlation of corrosion measurements and bridge conditions with NBIS deck rating
Ramniceanu, Andrei (Virginia Tech, 2004-10-11)
Since the use of epoxy coated steel has become mandatory starting in the 1980s, recent studies have shown that epoxy coating does not prevent corrosion, but instead will debond from the steel reinforcement in as little as 4 years (Weyers RE et al, 1998) allowing instead a much more insidious form of corrosion to take place known as crevice corrosion. Therefore, it is important to determine if the nondestructive corrosion activity detection methods are applicable to ECR as well as institute guidelines for interpreting the results. Since the corrosion of reinforcing steel is directly responsible for damage to concrete structures, it is surprising that nondestructive corrosion assessment methods are not part of regular bridge inspection programs such as PONTIS and NBIS. Instead, the inspection and bridge rating guidelines of federally mandated programs such as NBIS are so vague as to allow for a relatively subjective application by the field inspectors. Clear cover depths, resistance, corrosion potentials, linear polarization data, as well as environmental exposure and structural data were collected from a sample of 38 bridge decks in the Commonwealth of Virginia. These structures were further divided in three subsets: bridge decks with a specified w/c ratio of 0.47, bridge decks with a specified w/c ratio of 0.45 and bridge decks with a specified w/cm ratio of 0.45. This data was then correlated to determine which parameters are the most influential in the assignment of NBIS condition rating. Relationships between the non-destructive test parameters were also examined to determine if corrosion potentials and linear polarization are applicable to epoxy coated steel. Based on comparisons of measurements distributions, there is an indication that corrosion potential tests may be applicable to structures reinforced with epoxy coated steel. Furthermore, these conclusions are supported by statistical correlations between resistivity, half cell potentials and linear polarization measurements. Unfortunately, although apparently applicable, as of now there are no guidelines to interpret the results. Based on the linear corrosion current density data collected, no conclusion can be drawn regarding the applicability of the linear polarization test. As far as the NBIS deck rating is concerned, since the inspection guidelines are so vague, age becomes a very easy and attractive factor to the field personnel to rely on. However, this conclusion is far from definitive since the very large majority of structures used in this particular study had only two rating values out of theoretically ten and realistically five possible rating values.
Cost Penalized Estimation and Prediction Evaluation for Split-Plot Designs
Liang, Li; Anderson-Cook, Christine M.; Robinson, Timothy J. (Virginia Tech, 2005-02-02)
The use of response surface methods generally begins with a process or system involving a response y that depends on a set of k controllable input variables (factors) x₁, x₂,…,xk. To assess the effects of these factors on the response, an experiment is conducted in which the levels of the factors are varied and changes in the response are noted. The size of the experimental design (number of distinct level combinations of the factors as well as number of runs) depends on the complexity of the model the user wishes to fit. Limited resources due to time and/or cost constraints are inherent to most experiments, and hence, the user typically approaches experimentation with a desire to minimize the number of experimental trials while still being able to adequately estimate the underlying model.
Effect of Environmental Conditions and Structural Design on Linear Cracking in Virginia Bridge Decks
Keller, Wesley John (Virginia Tech, 2004-04-15)
Chloride-induced corrosion of reinforcing steel is widely accepted as the primary cause of premature deterioration in concrete bridge decks (Brown, M.C., 2002). Since linear cracking in concrete cover can potentially accelerate chloride ingress to the depth of the reinforcing steel, there is reason to believe that severity of deck cracking can significantly influence the time to first repair and/or rehabilitation of the bridge deck. Surface width, orientation, and length of cracks in 38 Virginia bridge decks were investigated in order to characterize the general distribution of deck cracking in the commonwealth of Virginia. Crack data was correlated to structural/material design parameters and environmental exposure conditions in order to determine significant predictor-response relationships. The majority of surveyed bridge decks were divided into four classifications of deck type based on superstructure type and construction era, either 1968-1971 or 1984-1991. Surveyed bridge decks that did not fit into any of the four classifications were used to form more generalized subsets. These larger subsets were used to determine if significant influence factors could be translated to broader classifications of bridge decks. Transverse beam spacing, annual average daily truck traffic (AADTT), resistivity of the deck concrete, chloride exposure, and the percentage of concrete clear cover depths less than or equal to 38mm (1.5 in) were all determined to have a significant correlation with linear deck cracking.
Functional Properties of Restructured Boneless Pork Produced From Pse and Rfn Pork Utilizing Non-Meat Adjuncts
Schilling, Mark Wesley (Virginia Tech, 2002-07-12)
Boneless cured pork was produced from combinations of pale, soft, and exudative (PSE) and red, firm, and non-exudative (RFN) semimembranosus muscle differing in amount of modified food starch (MFS), sodium caseinate (SC), and soy protein concentrate (SPC). Response Surface Methodology was utilized to determine the effects of these adjuncts on water holding capacity, color, and texture. Both RFN pork and PSE pork were selected based on visual color for the following five treatments for processing: 100 % PSE, 75% PSE +25 % RFN, 50 % PSE+ 50 % RFN, 25 % PSE +75 % RFN, and 100 % RFN. Fifteen ingredient combinations for each PSE and RFN treatment combination yielded 75 treatments per replication. Three replications of each treatment were completed. Chemical composition and color of raw materials also were measured and used as covariates to determine their effect on the above-mentioned responses. Utilization of SC decreased (p<0.05) cooking loss, lightness, and cohesiveness. SPC incorporation decreased (p<0.05) cooking loss, cohesiveness, and redness, and MFS inclusion decreased (p<0.05) expressible moisture and cohesiveness. Utilization of SC and MFS increased (p<0.05) redness and SPC incorporation increased (p<0.05) yellowness. Results indicated that combining soy protein concentrate and modified food starch together in formulations demonstrated the greatest potential of these adjuncts to improve water binding, color, and texture in pale, soft, and exudative pork. Utilization of combinations of these adjuncts demonstrates potential to improve protein functionality in PSE as well as RFN pork. This research also demonstrated that diluting RFN pork with no more than 25 % PSE pork allows the formation of a high quality boneless deli ham roll.
A Genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint Approximations
Gantovnik, Vladimir B.; Gürdal, Zafer; Watson, Layne T.; Anderson-Cook, Christine M. (Department of Computer Science, Virginia Polytechnic Institute & State University, 2003)
This paper describes a new approach for reducing the number of the fitness and constraint function evaluations required by a genetic algorithm (GA) for optimization problems with mixed continuous and discrete design variables. The proposed additions to the GA make the search more effective and rapidly improve the fitness value from generation to generation.The additions involve memory as a function of both discrete and continuous design variables, and multivariate approximation of the individual functions' responses in terms of several continuous design variables. The approximation is demonstrated for the minimum weight design of a composite cylindrical shell with grid stiffeners.
A genetic algorithm with memory for mixed discrete-continuous design optimization
Gantovnik, Vladimir B.; Anderson-Cook, Christine M.; Gürdal, Zafer; Watson, Layne T. (Department of Computer Science, Virginia Polytechnic Institute & State University, 2003)
This paper describes a new approach for reducing the number of the fitness function evaluations required by a genetic algorithm (GA) for optimization problems with mixed continuous and discrete design variables. The proposed additions to the GA make the search more effective and rapidly improve the fitness value from generation to generation. The additions involve memory as a function of both discrete and continuous design variables, multivariate approximation of the fitness function in terms of several continuous design variables, and localized search based on the multivariate approximation. The approximation is demonstrated for the minimum weight design of a composite cylindrical shell with grid stiffeners.
Graphical Tools, Incorporating Cost and Optimizing Central Composite Designs for Split-Plot Response Surface Methodology Experiments
Liang, Li (Virginia Tech, 2005-03-28)
In many industrial experiments, completely randomized designs (CRDs) are impractical due to restrictions on randomization, or the existence of one or more hard-to-change factors. Under these situations, split-plot experiments are more realistic. The two separate randomizations in split-plot experiments lead to different error structure from in CRDs, and hence this affects not only response modeling but also the choice of design. In this dissertation, two graphical tools, three-dimensional variance dispersion graphs (3-D VDGs) and fractions of design space (FDS) plots are adapted for split-plot designs (SPDs). They are used for examining and comparing different variations of central composite designs (CCDs) with standard, V- and G-optimal factorial levels. The graphical tools are shown to be informative for evaluating and developing strategies for improving the prediction performance of SPDs. The overall cost of a SPD involves two types of experiment units, and often each individual whole plot is more expensive than individual subplot and measurement. Therefore, considering only the total number of observations is likely not the best way to reflect the cost of split-plot experiments. In this dissertation, cost formulation involving the weighted sum of the number of whole plots and the total number of observations is discussed and the three cost adjusted optimality criteria are proposed. The effects of considering different cost scenarios on the choice of design are shown in two examples. Often in practice it is difficult for the experimenter to select only one aspect to find the optimal design. A realistic strategy is to select a design with good balance for multiple estimation and prediction criteria. Variations of the CCDs with the best cost-adjusted performance for estimation and prediction are studied for the combination of D-, G- and V-optimality criteria and each individual criterion.
Impact of Specification Changes on Chloride Induced Corrosion Service Life of Virginia Bridge Decks
Kirkpatrick, Trevor Joe (Virginia Tech, 2001-07-12)
A model to determine the time to first repair and subsequent rehabilitation of concrete bridge decks exposed to chloride deicer salts that recognizes and incorporates the statistical nature of factors affecting the corrosion process is developed. The model expands on an existing deterministic model using statistical computing techniques, including resampling techniques such as the parametric and simple bootstrap. Emphasis was placed on the diffusion portion of the diffusion-cracking model, but advances can be readily included for the time for corrosion deterioration after corrosion initiation. Data collected from ten bridge decks built in Virginia between 1981 and 1994 was used to model the surface chloride concentration, apparent diffusion coefficient, and clear cover depth. Several ranges of the chloride corrosion initiation concentration, as determined from the available literature, were investigated. The time to first repair and subsequent rehabilitation predicted by the stochastic model is shorter than the time to first repair and subsequent rehabilitation predicted by the deterministic model, but is believed to more accurately reflect the true nature of bridge deck deterioration. The model was validated using historical service life data for 129 bridge decks built in Virginia between 1968 and 1972. The time to rehabilitation predicted for the set of bridge decks built between 1981 and 1994 by the stochastic model was approximately 13 years longer than the normalized time to rehabilitation projected for the bridge decks built between 1968 and 1972 using historical data. The increase in time to rehabilitation for the newer set of bridge decks was attributed to a reduction in the specified maximum water/cement ratio and increase in clear cover depth.
Linear Mixed Model Robust Regression
Waterman, Megan Janet Tuttle (Virginia Tech, 2002-05-08)
Mixed models are powerful tools for the analysis of clustered data and many extensions of the classical linear mixed model with normally distributed response have been established. As with all parametric models, correctness of the assumed model is critical for the validity of the ensuing inference. Model robust regression techniques predict mean response as a convex combination of a parametric and a nonparametric model fit to the data. It is a semiparametric method by which incompletely or incorrectly specified parametric models can be improved through adding an appropriate amount of a nonparametric fit. We apply this idea of model robustness in the framework of the linear mixed model. The mixed model robust regression (MMRR) predictions we propose are convex combinations of predictions obtained from a standard normal-theory linear mixed model, which serves as the parametric model component, and a locally weighted maximum likelihood fit which serves as the nonparametric component. An application of this technique with real data is provided.
A Model for the PTX Properties of H2O-NaCl
Atkinson, Allen Bradley Jr. (Virginia Tech, 2002-07-16)
In many geologic environments, fluids have compositions that are approximated by the H₂O-NaCl system. When minerals grow in the presence of such fluids, some of the solution is trapped in the growing mineral as fluid inclusions. The salinity, temperature of homogenization, and pressure of homogenization are required to predict the trapping conditions of the fluid inclusion. In the laboratory the salinity and the temperature of homogenization of the trapped fluid are easily determined however, the pressure of homogenization cannot be determined directly, and must be calculated from an equation of state. A statistical model that relates the vapor pressure of H₂O-NaCl to the fluid temperature and composition has been developed. The model consists of equations that predict the vapor pressure of H₂O-NaCl from the eutectic temperature (-21.2°C) to 1500°C and for all compositions between the pure end-members. The model calculates the vapor pressure based on the composition (wt% NaCl) and the temperature of homogenization, which can be directly obtained from laboratory studies of fluid inclusions. This information in turn can be used to construct the isochore, or line of constant volume, along which the fluid inclusion was trapped. Finally the isochore can be used to determine the temperature and pressure at which the host mineral of the fluid inclusion was trapped.
Model Robust Regression Based on Generalized Estimating Equations
Clark, Seth K. (Virginia Tech, 2002-03-29)
One form of model robust regression (MRR) predicts mean response as a convex combination of a parametric and a nonparametric prediction. MRR is a semiparametric method by which an incompletely or an incorrectly specified parametric model can be improved through adding an appropriate amount of a nonparametric fit. The combined predictor can have less bias than the parametric model estimate alone and less variance than the nonparametric estimate alone. Additionally, as shown in previous work for uncorrelated data with linear mean function, MRR can converge faster than the nonparametric predictor alone. We extend the MRR technique to the problem of predicting mean response for clustered non-normal data. We combine a nonparametric method based on local estimation with a global, parametric generalized estimating equations (GEE) estimate through a mixing parameter on both the mean scale and the linear predictor scale. As a special case, when data are uncorrelated, this amounts to mixing a local likelihood estimate with predictions from a global generalized linear model. Cross-validation bandwidth and optimal mixing parameter selectors are developed. The global fits and the optimal and data-driven local and mixed fits are studied under no/some/substantial model misspecification via simulation. The methods are then illustrated through application to data from a longitudinal study.

Browsing by Author "Anderson-Cook, Christine M."

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