UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.

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Subject: search.filters.subject.Markov Chain Monte Carlo

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    Estimation of a Function of a Large Covariance Matrix Using Classical and Bayesian Methods
    (2018) Law, Judith N.; Lahiri, Partha; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    In this dissertation, we consider the problem of estimating a high dimensional co- variance matrix in the presence of small sample size. The proposed Bayesian solution is general and can be applied to dierent functions of the covariance matrix in a wide range of scientic applications, though we narrowly focus on a specic application of allocation of assets in a portfolio where the function is vector-valued with components which sum to unity. While often there exists a high dimension of time series data, in practice only a shorter length is tenable, to avoid violating the critical assumption of equal covariance matrix of investment returns over the period. Using Monte Carlo simulations and real data analysis, we show that for small sample size, allocation estimates based on the sample covariance matrix can perform poorly in terms of the traditional measures used to evaluate an allocation for portfolio analysis. When the sample size is less than the dimension of the covariance matrix, we encounter diculty computing the allocation estimates because of singularity of the sample covariance matrix. We evaluate a few classical estimators. Among them, the allocation estimator based on the well-known POET estimator is developed using a factor model. While our simulation and data analysis illustrate the good behavior of POET for large sample size (consistent with the asymptotic theory), our study indicates that it does not perform well in small samples when compared to our pro- posed Bayesian estimator. A constrained Bayes estimator of the allocation vector is proposed that is the best in terms of the posterior risk under a given prior among all estimators that satisfy the constraint. In this sense, it is better than all classi- cal plug-in estimators, including POET and the proposed Bayesian estimator. We compare the proposed Bayesian method with the constrained Bayes using the tradi- tional evaluation measures used in portfolio analysis and nd that they show similar behavior. In addition to point estimation, the proposed Bayesian approach yields a straightforward measure of uncertainty of the estimate and allows construction of credible intervals for a wide range of parameters.
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    A MIXED-STRATEGIES RASCH TESTLET MODEL FOR LOW-STAKES TESTLET-BASED ASSESSMENTS
    (2013) Chen, Ying-Fang; Jiao, Hong; Measurement, Statistics and Evaluation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    In low-stakes assessments, a lack of test-taking motivation inevitably occurs because test scores impose inconsequential effects on test takers' academic records. A common occurrence is that some test takers are unmotivated and simply apply random guessing strategy rather than solution strategy in taking a test. Testlet effects also arise because educational assessment items are frequently written in testlet units. A challenge to psychometric measurement is that conventional item response theory models do not sufficiently account for test-taking motivation heterogeneity and testlet effects. These construct-irrelevant variances affect test validity, accuracy of parameter estimates, and targeted inferences. This study proposes a low-stakes assessment measurement model that can simultaneously explain test-taking motivation heterogeneity and testlet effects. The performance and effectiveness of the proposed model are evaluated through a simulation study. Its utility is demonstrated through an application to a real standardized low-stakes assessment dataset. Simulation results show that overlooking test-taking motivation heterogeneity and testlet effects adversely affected model-data fit and model parameter estimates. The proposed model improved model-data fit and classification accuracy and well recovered model parameters under test-taking motivation heterogeneity and testlet effects. For the real data application, the item response dataset, which was originally calibrated with the Rasch model, was fitted better by the proposed model. Both test-taking motivation heterogeneity and testlet effects were identified in the real dataset. Finally, a set of variables selected from the real dataset is used to explore potential factors that characterize the latent classes of test-taking motivation. In the science assessment, science proficiency was associated with test-taking motivation heterogeneity.
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    A MIXTURE RASCH MODEL WITH A COVARIATE:A SIMULATION STUDY VIA BAYESIAN MARKOV CHAIN MONTE CARLO ESTIMATION
    (2009) Dai, Yunyun; Mislevy, Robert J; Measurement, Statistics and Evaluation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    Mixtures of item response theory models have been proposed as a technique to explore response patterns in test data related to cognitive strategies, instructional sensitivity, and differential item functioning (DIF). Estimation proves challenging due to difficulties in identification and questions of effect size needed to recover underlying structures. In particular, the impact of auxiliary variables, or covariates, for examinees in estimation has not been systematically explored. The goal of this dissertation is to carry out a systematically designed simulation study to investigate the performance of mixture Rasch model (MRM) under Bayesian estimation using Markov Chain Monte Carlo (MCMC) method. The dependent variables in this study are (1) the proportion of cases in which the generating mixture structure is recovered, and (2) among those cases in which the structure is recovered, the bias and root mean squared error of parameter estimates. The foci of the study are to use a flexible logistic regression model to parameterize the relation between latent class membership and the examinee covariate, to study MCMC estimation behavior in light of effect size, and to provide insights and suggestions on model application and model estimation.