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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Item Handling of Missing Data with Growth Mixture Models(2019) Lee, Daniel Yangsup; Harring, Jeffrey R; Measurement, Statistics and Evaluation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The recent growth of applications of growth mixture models for inference with longitudinal data has introduced a wide range of research dedicated to testing the different aspects of the model. One area of research that has not drawn much attention, however, is the performance of growth mixture models with missing data and when using the various methods for dealing with them. Missing data are usually an inconvenience that must be addressed in any data analysis scenario, and the use of growth mixture models is no less an exception to this. While the literature on various other aspects of growth mixture models has grown, not much research has been conducted on the consequences of mishandling missing data. Although the literature on missing data has generally accepted the use of modern missing data handling techniques, these techniques are not free of problems nor have they been comprehensively tested in the context of growth mixture models. The purpose of this dissertation is to incorporate the various missing data handling techniques on growth mixture models and, by using Monte Carlo simulation techniques, to provide guidance on specific conditions in which certain missing data handling methods will produce accurate and precise parameter estimates typically compromised when using simple, ad hoc, missing data handling approaches, or incorrect techniques.Item DIFFERENT APPROACHES TO COVARIATE INCLUSION IN THE MIXTURE RASCH MODEL(2014) Li, Tongyun; Jiao, Hong; Measurement, Statistics and Evaluation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The present dissertation project investigates different approaches to adding covariates and the impact in fitting mixture item response theory (IRT) models. Mixture IRT models serve as an important methodology for tackling several important psychometric issues in test development, including detecting latent differential item functioning (DIF). A Monte Carlo simulation study is conducted in which data generated according to a two-class mixture Rasch model (MRM) with both dichotomous and continuous covariates are fitted to several MRMs with misspecified covariates to examine the effects of covariate inclusion on model parameter estimation. In addition, both complete response data and incomplete response data with different types of missingness are considered in the present study in order to simulate practical assessment settings. Parameter estimation is carried out within a Bayesian framework vis-à-vis Markov chain Monte Carlo (MCMC) algorithms. Two empirical examples using the Programme for International Student Assessment (PISA) 2009 U.S. reading assessment data are presented to demonstrate the impact of different specifications of covariate effects for an MRM in real applications.Item Estimating Common Odds Ratio with Missing Data(2005-07-26) Chen, Te-Ching; Smith, Paul J.; Mathematical Statistics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)We derive estimates of expected cell counts for $I\times J\times K$ contingency tables where the stratum variable $C$ is always observed but the column variable $B$ and row variable $A$ might be missing. In particular, we investigate cases where only row variable $A$ might be missing, either randomly or informatively. For $2\times 2\times K$ tables, we use Taylor expansion to study the biases and variances of the Mantel-Haenszel estimator and modified Mantel-Haenszel estimators of the common odds ratio using one pair of pseudotables for data without missing values and for data with missing values, based either on the completely observed subsample or on estimated cell means when both stratum and column variables are always observed. We examine both large table and sparse table asymptotics. \\ Analytic studies and simulation results show that the Mantel-Haenszel estimators overestimate the common odds ratio but adding one pair of pseudotables reduces bias and variance. Mantel-Haenszel estimators with jackknifing also reduces the biases and variances. Estimates using only the complete subsample seem to have larger bias than those based on full data, but when the total number of observations gets large, the bias is reduced. Estimators based on estimated cell means seem to have larger biases and variances than those based only on complete subsample with randomly missing data. With informative missingness, estimators based on the estimated cell means do not converge to the correct common odds ratio under sparse asymptotics, and converge slowly for the large table asymptotics. The Mantel-Haenszel estimators based on incorrectly estimated cell means when the variable $A$ is informatively missing behave similarly to those based on the only complete subsamples. The asymptotic variance formula of the ratio estimators had smaller biases and variances than those based on jackknifing or bootstrapping. Bootstrapping may produce zero divisors and unstable estimates, but adding one pair of pseudotables eliminates these problems and reduces the variability.