Beyond Standard Assumptions - Semiparametric Models, A Dyadic Item Response Theory Model, and Cluster-Endogenous Random Intercept Models

In most statistical analyses, quantitative education researchers often make simplifying assumptions regarding the manner in which their data was generated in order to answer some of these questions. These assumptions can help to reduce the complexity of the problem, and allow the researcher to describe their data using a simpler, and often times more interpretable, statistical model. However, making some of these assumptions when they are not true can lead to biased estimates and misleading answers. While the standard sets of assumptions associated with commonly-used statistical models are usually sufficient in a wide range of contexts, it will always be beneficial for education researchers to understand what they are, when they are reasonable, and how to modify them if necessary. This dissertation focuses on three of the most common models used in quantitative education research (viz. parametric models like Linear Models (LMs), Item Response Theory (IRT) models, and Random-Intercept Models (RIMs)), discusses the standard sets of assumptions that accompany these models, and then describes related models with less stringent sets of assumptions. In each of the following three chapters, we either explicitly unpack existing models that are useful but are currently still uncommon in the field of education research, or propose novel models and/or estimation strategies for these models. We begin in Chapter 1 with a common parametric model known as the Gaussian LM, and use it as a scaffold to better understand semiparametric models and their estimation. We begin by reviewing how the coefficients of the Gaussian LM are usually estimated using Maximum Likelihood (ML) or Least-Squares (LS). We then introduce the notion of an $m$-estimator as well as that of a Regular Asymptotically Linear estimator, and show how they relate to the ML estimator. In particular, we introduce the notion of influence functions/curves and discuss their geometry together with concepts such as Hilbert spaces and tangent spaces. We then demonstrate, concretely, how to derive the so-called efficient influence function under the Gaussian LM, and show that it is precisely the influence function of the ML and (Ordinary) LS estimators. This shows that the ML estimator (at least under the Gaussian LM) is efficient. Using the foundation built, we move on from the Gaussian LM by relaxing both the assumption that the residuals are normally distributed, as well as the assumption that they have a constant variance, and define this as the Heteroskedastic Linear Model. Unlike the Gaussian LM, this is a semiparametric model. Where possible, we make use of intuition and analogous results from the parametric setting to help describe the workflow for obtaining an efficient estimator for the coefficients of the Heteroskedastic Linear Model. In particular, we derive the nuisance tangent space for this semiparametric model, and use it to obtain the efficient influence function for our model. We then show how to use the efficient influence function to obtain an efficient estimator (which happens to be the Weighted LS estimator) from the (Ordinary) LS estimator via a one-step approach as well as an estimating equations approach. We then conclude by directing readers to more advanced material, including references on more modern approaches to estimating more general semiparametric models such as Targeted Maximum Likelihood Estimation. In Chapter 2, we focus on a class of measurement models known as Item Response Theory models which are useful for measuring latent traits of a subject based on the subject's response to items. We relax the condition that the responses are only a result of the individual's latent trait (and possibly an external rater), and propose a dyadic Item Response Theory (dIRT) model for measuring interactions of pairs of individuals when the responses to items represent the actions (or behaviors, perceptions, etc.) of each individual (actor) made within the context of a dyad formed with another individual (partner). Examples of its use in education include the assessment of collaborative problem solving among students, or the evaluation of intra-departmental dynamics among teachers. The dIRT model generalizes both Item Response Theory models for measurement and the Social Relations Model for dyadic data. Here, the responses of an actor when paired with a partner are modeled as a function of not only the actor's inclination to act and the partner's tendency to elicit that action, but also the unique relationship of the pair, represented by two directional, possibly correlated, interaction latent variables. We discuss generalizations such as accommodating triads or larger groups, but focus on demonstrating the key idea in the dyadic case. We show that estimation may be performed using Markov-chain Monte Carlo implemented in \texttt{Stan}, making it straightforward to extend the dIRT model in various ways. Specifically, we show how the basic dIRT model can be extended to accommodate latent regressions, random effects, distal outcomes. We perform a simulation study that demonstrates that our estimation approach performs well. In the absence of educational data of this form, we demonstrate the usefulness of our proposed approach using speed-dating data instead, and find new evidence of pairwise interactions between participants, describing a mutual attraction that is inadequately characterized by individual properties alone.Finally, in Chapter 3, we consider the often implicit assumption made when estimating the coefficients of structural Random Intercept Models (RIMs) that covariates at all levels do not co-vary with the random intercepts. A violation of this assumption (called cluster-level endogeneity) leads to inconsistent estimates when using standard estimation procedures. For two-level RIMs with such endogeneity, Hausman and Taylor (HT) devised a consistent multi-step instrumental variable estimator using only internal instruments. We, instead, approach this problem by explicitly modeling the endogeneity using a Structural Equation Model (SEM). In this chapter, we compare, through simulation, the HT and SEM estimators, and evaluate their asymptotic and finite sample properties. We show that the SEM approach is also flexible enough to deal with different exchangeability assumptions for the covariates (e.g., whether the correlations between pairs of all units in a cluster are the same) and investigate how these exchangeability assumptions affect finite sample properties of the HT estimator. For the simulations, we propose a new procedure for generating cluster- and unit-level covariates and random intercepts with a fully flexible covariance structure. We also compare our approach to another common approach known as Multilevel Matching using data from the High School and Beyond survey

Fast and Efficient Compressive Sensing using Structurally Random Matrices

This paper introduces a new framework of fast and efficient sensing matrices for practical compressive sensing, called Structurally Random Matrix (SRM). In the proposed framework, we pre-randomize a sensing signal by scrambling its samples or flipping its sample signs and then fast-transform the randomized samples and finally, subsample the transform coefficients as the final sensing measurements. SRM is highly relevant for large-scale, real-time compressive sensing applications as it has fast computation and supports block-based processing. In addition, we can show that SRM has theoretical sensing performance comparable with that of completely random sensing matrices. Numerical simulation results verify the validity of the theory as well as illustrate the promising potentials of the proposed sensing framework

Reducing Uncertainties in Conservation Decision-Making for American Alligators

Effective conservation decision-making necessitates monitoring programs that are designed to collect unbiased and precise measurements of relevant attributes deemed to reduce structural uncertainty of the managed resource state. American alligators (Alligator mississippiensis; hereafter alligator) are a keystone species within the southeastern United States that have cascading effects on ecosystem structure and function, and are managed under consumptive use management programs throughout their range. Management of alligator populations in South Carolina is challenging due to pervasive uncertainties regarding the size class distribution, which is only partially observable using the primary monitoring tool (nightlight surveys), a lack of demographic parameter estimates, and identification of measurable attributes that could pose conservation threats (e.g., drought, contaminants). My objective was to develop analytical tools to reduce partial observability in alligator monitoring and identify potential drivers of alligator population dynamics to reduce structural uncertainty. I developed a Bayesian integrated population model (IPM) that produced among the first demographic parameter estimates for alligators in South Carolina and determined that survival probabilities increased greatly among immature size classes, but are relatively similar among adults (\u3e0.90); a pattern that has been previously reported for American crocodiles (Crocodylus acutus). The IPM produced size-class specific abundance estimates for alligators from count data with prolific state uncertainty (\u3e60% unknown size observations). In general, alligator abundance trends were uncertain and appeared to vary spatially, though the mean population growth (λ) estimates for all sites, IPM versions, and the Lefkovtich matrix were \u3c1, indicating a population decline. However, the 95% Bayesian credible intervals for λ at one survey site included 1, indicating some uncertainty. I then used the demographic parameter estimates to simulate virtual alligator populations under varying gradations of initial population density, harvest rate to determine an optimal level of spatiotemporal replication for a monitoring programs. To evaluate the need to obtain size class-specific abundance estimates, the simulated count data from the underlying virtual population was total individuals (of all size classes). Based on fundamental objectives to maximize financial effectiveness and minimize management and ecological uncertainty, all of the harvest and density scenarios (except low density and maximum harvest) selected a monitoring program with six temporal replicates (the maximum) and 320 spatial replicates (1 spatial replicate = 0.5 km river segment). In general, data reliability (precision and accuracy) was more sensitive to increasing temporal, compared to spatial, replication, which has been previously reported in other simulation based studies in which detection probabilities are low (p\u3c 0.10). Moreover, all scenarios and monitoring programs induced changes in alligator size class structure, though the effects were minimized with reduced harvest rate, increase survey effort and population density. In synthesis, the demographic parameter estimates produced by the IPM can and are being used to improve monitoring methodology for alligators in South Carolina, and provide a mechanism to increase the demographic resolution of monitoring data, inform optimal monitoring decisions, and explore further uncertainties associate with harvest decisions. Finally, to better elucidate potential drivers of alligator population status, I evaluated total mercury (THg) concentrations in adult alligator whole blood from a longitudinal mark-recapture study. I determined that THg in whole blood was best described by an interactive effect of sex and predicted age, as calculated by predicted age at first capture using a recently developed growth model for alligators in South Carolina. THg concentrations averaged 0.16 ± 0.05 mg kg-1 ww and were slightly higher in males than female, though the overall average is significantly lower than other estimates reported in the Florida Everglades and the Savannah River Site in South Carolina. The quadratic effect of THg with predicted age, in which older individuals had lower levels than younger individuals is novel, and contrasts with previous assumptions that THg bioaccumulates with age (i.e., does not decrease). We posit that determinate (asymptotic) growth, which could accompany age-related changes in foraging patters and metabolism, could potentially explain the lower THg we detected in the oldest individuals. The results from our study could highlight the need for long-term longitudinal monitoring of sentinel species to further evaluate our hypotheses

Aspects of Credit Risk Modeling

Imperial Users onl

Catalysts for steam reforming of Ethanol in a catalytic wall reactor

La energía se ha convertido en una necesidad vital para garantizar el desarrollo de las sociedades modernas. Entre las diferentes posibles alternativas para producir energía, el hidrogeno presenta varias características que lo convierten en un atractivo vector energético: primero, se trata de una tecnología más eficiente para transformar la energía química en electricidad -por ejemplo, utilizando pilas de-combustible, las cuales también reducen de manera significativa los niveles de emisión de CO2 -; en segundo lugar, el hidrogeno puede ser producido a partir de una amplia variedad de materias primas, incluyendo recursos renovables y no renovables. Sin embargo, las tecnologías para producir hidrogeno para applicaciones con pilas de combustible aun requieren de un esfuerzo en investigación y desarrollo.El objetivo principal de esta tesis fue de evaluar técnicamente las opciones para preparar y utilizar catalizadores en placas insertados en un reactor de pared catalítica para producir hidrogeno mediante el reformado por vapor de etanol bajo condiciones de alta eficiencia térmica. Para completar el objetivo general y los objetivos específicos, se diseño un plan experimental sistemático, compuesto de tres partes: documentación, experimentación y simulación numérica. La información utilizada se puede clasificar en tres ramas: primero, una revisión detallada de las características generales que presentan las técnicas de reformado, seguido por una revisión descriptiva del reformado por vapor de etanol, enfocado en los principales aspectos de la preparación de catalizadores y la realización de la reacción química. A continuación en segundo lugar, se presenta una descripción acerca de reactores estructurados y los métodos para preparar catalizadores. Por último, en tercer lugar, se expone una explicación centrada en los materiales, equipos y métodos empleados para explorar el rendimiento de los catalizadores. Esta parte incluye la descripción de: algunas de las técnicas analíticas más comunes para caracterizar y evaluar tanto catalizadores como compuestos químicos y la descripción de las herramientas utilizadas en la simulación numérica.El primer bloque de simulación numérica tiene como fin evaluar las posibles restricciones termodinámicas por medio de análisis específicos basados en el equilibrio termodinámico, tanto del reactor como del proceso integrado. Luego, se ejecuta un mapeo del conjunto de condiciones operacionales, compuesto por cuatro variables principales: (temperatura, relación vapor carbón, presión y factor de recobro de hidrogeno en el separador de membrana). Ello con el fin de garantizar una operación auto-térmica del procesador de combustible. Se compara la habilidad y la ventaja entre los diferentes tipos de catalizadores publicados en trabajos previos en base a las condiciones termodinámicas ideales determinadas en el análisis termodinámico.Para los catalizadores en polvo, se realizo experimentos de caracterización y reacción mediante el empleo de un reactor de lecho fijo. Se ha efectuado un estudio sistematico para comparar la actividad y la selectividad de dos tipos de catalizadores, bajo condiciones moderadas de temperatura y relación vapor carbón. Los catalizadores basados en níquel (Ni/La2O3-Al2O3) y cobalto (Co-Fe/ZnO y Co-Mn/ZnO) han sido preparados y probados a las siguientes condiciones: temperatura en el rango de 400-500°C, relación vapor carbono entre 2 y 4, tiempo de contacto desde 4.3 hasta 1100 min·gcat molEtOH-1, cubriendo un rango de conversión de etanol desde 20 hasta 100%. Se ha efectuado un diseño de análisis multifactorial para establecer la influencia de las variables (temperatura, relación vapor carbón, tiempo de contacto y formulación del catalizador) en términos de la conversión de etanol y la selectividad hacia los diferentes productos.Por último, se ha efectuado la caracterización, simulación y experimentación utilizando una configuración de reactor de pared catalítica. Primero, se emplea un modelo en 2D para analizar las características principales del reactor de pared catalítica diseñado y construido para realizar la reacción sobre las placas con catalizador previamente preparadas. En segundo lugar, se expone de manera detallada el método seguido para preparar dos tipos diferentes de placas catalíticas. Estas placas con catalizador son caracterizadas de manera similar al método empleado con los catalizadores en polvo. Luego, se ha realizado un estudio sistemático para comparar la actividad y la selectividad de los dos tipos de placas catalíticas. Por último, mediante un modelo 1D se revelan aspectos fundamentales de la configuración del reactor de pared catalítica utilizando una configuración con dos canales paralelos, en los cuales se ejecutan una reacción endotérmica y otra exotérmica respectivamente.La principal conclusión de este trabajo es que el reformado por vapor de etanol puede ser realizado bajo condiciones de alta eficiencia térmica si se emplea un diseño basado en un reactor de pared catalítica con recobro de calor integrado a una unidad de separación para la purificación del hidrogeno. Las placas catalíticas han demostrado ser un elemento fundamental en este tipo de reactor porque incrementan de manera significativa el transporte de calor que se requiere para sostener las reacciones endotérmicas.Energy has become a fundamental necessity to guarantee modern society development. Among different alternatives possible to produce energy, hydrogen presents several characteristics which make it an attractive energy vector: first, more efficient processes to transform chemical energy into electricity -such as Fuel Cells that, in addition, will help to reduce significantly CO2 emission levels-; and second, hydrogen can be produced from a large variety of feed stocks, including fossil and renewable resources. However, as hydrogen production technologies for Fuel Cell applications are not available commercially yet, it still requires additional R&D efforts.The principal objective of this thesis was to evaluate technical feasibility for preparing and using catalytic plates in a Catalytic Wall Reactor configuration to produce hydrogen by Steam Reforming of Ethanol under conditions of high thermal efficiency. To fulfill the overall and specific objectives, a systematic experimental plan was designed and executed. It was composed of three main parts: documentation, experimentation and numerical simulation. Background information is divided into three branches, first a detailed overview of technical features for reforming technology, followed by a descriptive review of Steam Reforming of Ethanol key aspects for catalysts preparation and reaction performance. Third is presented a comprehensive examination on structured reactor and catalyst preparation methods. In this part is exposed a detailed explanation of materials, equipments, and methods employed for screening catalyst and evaluating catalytic reactor performance. Also, is presented employed techniques for catalyst characterization and fluid analysis. Finally are described tools for numerical simulation.First component of numerical simulations evaluates possible thermodynamic constrains through specific analyses based on thermodynamic equilibrium of reactor and integrated fuel processor. Then, is performed a mapping for the set of four operational variables (temperature, steam to carbon ratio, pressure, and hydrogen recovery in the membrane separator), that allow an auto-thermal operation of the fuel processor. The suitability and advantages of the different catalysts preparations that are known from recent publications are discussed on the basis of the operation conditions determined on the thermodynamic analysis.Experimental work is performed for powder catalyst characterization and catalytic experimentation using a Packed Bed Reactor (PBR). It has conducted a systematic study to compare the activity and selectivity of two types of catalyst at moderate temperature and steam to carbon (SC) ratios. Nickel-based catalysts (Ni/La2O3-Al2O3) and novel Co-based catalysts (Co-Fe/ZnO and Co-Mn/ZnO) have been prepared and tested at temperatures of 400 and 500 °C, Steam to Carbon (SC) molar ratios of 2 and 4, and contact times from 4.3 to 1100 min·gcat molEtOH-1, covering a range of ethanol conversion from 20 to 100%. A multifactorial design analysis has been conducted to establish the significance of temperature, SC ratio, contact time and catalyst formulation on ethanol conversion and selectivity towards the different reaction products.At last, it is carried out the catalytic plate characterization, simulation and experimentation using a Catalytic Wall Reactor configuration. First, is used a 2D modeling to analyze main characteristics of the Catalytic Wall Reactor designed and constructed to perform reactions on the prepared catalytic plates. Prepared catalytic plates are characterize in a similar way to that employed for the powder catalysts. After that, it was conducted a systematic study to compare the activity and selectivity of two types of catalytic plates. 1D model reveals main aspects on thermal performance for a theoretical Catalytic Wall Reactor using two co-current channels with endothermic and exothermic reactions respectively.Main conclusion from this work is that Steam Reforming of Ethanol can be performed at high thermal efficiency if the design of the fuel processor is based on structured catalytic wall reactors with integrated heat recovery coupled to a separation unit for hydrogen purification. Catalytic plates have proven to be a key component on CWR because improves significantly the heat transfer which is required to sustain endothermic reactions

FY 1988 scientific and technical reports, articles, papers and presentations

This document presents formal NASA technical reports, papers published in technical journals, and presentations by MSFC personnel in FY 88. It also includes papers of MSFC contractors. After being announced in STAR, all of the NASA series reports may be obtained from the NationaL Technical Information Service, 5285 Port Royal Road, Springfield, VA 22161. The information in this report may be of value to the scientific and engineering community in determining what information has been published and what is available