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.

More information is available at Theses and Dissertations at University of Maryland Libraries.

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Subject: search.filters.subject.Factor Analysis

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    IRT vs. Factor Analysis Approaches in Analyzing Multigroup Multidimensional Binary Data: The Effect of Structural Orthogonality, and the Equivalence in Test Structure, Item Difficulty, & Examinee Groups
    (2008-05-30) Lin, Peng; Lissitz, Robert W; Measurement, Statistics and Evaluation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    The purpose of this study was to investigate the performance of different approaches in analyzing multigroup multidimensional binary data under different conditions. Two multidimensional Item Response Theory (MIRT) methods (concurrent MIRT calibration and separate MIRT calibration with linking) and one factor analysis method (concurrent factor analysis calibration) were examined. The performance of the unidimensional IRT method compared to its multidimensional counterparts was also investigated. The study was based on simulated data. Common-item nonequivalent groups design was employed with the manipulation of four factors: the structural orthogonality, the equivalence of test structure, the equivalence of item difficulty, and the equivalence of examinee groups. The performance of the methods was evaluated based on the recovery of the item parameters and the estimation of the true score of the examinees. The results indicated that, in general, the concurrent factor analysis method performed as well as, sometimes even better than, the two MIRT methods in recovering the item parameters. However, in estimating the true score of examinees, the concurrent MIRT method usually performed better than the concurrent factor analysis method. The results also indicated that the unidimensional IRT method was quite robust to the violation of unidimensionality assumption.
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    Factor Analysis of Cross-Classified Data
    (2005-08-04) Tsou, Hsiao-Hui Sophie; Slud, Eric V; Mathematical Statistics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    This thesis introduces a model hierarchy related to Principal Component Analysis and Factor Analysis, in which vector measurements are linearly decomposed into a relatively small set of hypothetical principal directions, for purposes of dimension reduction. The mathematical specification of unknown parameters in the models is unified. Identifiability of the suitably defined models is proved. The EM algorithm and the Newton-Raphson algorithm based on likelihoods and profile likelihoods are implemented to get computationally effective (maximum likelihood) estimators for the unknown parameters. A restricted model (with some error variances $0$) and a sufficient condition for a local maximum likelihood estimate are established. Score tests are constructed to check whether error variances are $0$, which is shown to be associated with non-identifiability of models. Statistical tests of goodness of fit of the models to data are established in a likelihood ratio testing framework, so that the most parsimoniously parameterized model consistent with the data can be chosen for purposes of description and classification of the experimental settings. The results are applied on a real data set involving coronal cross-sectional ultrasound pictures of the human tongue surface during speech. The likelihood ratio test is used to test the fit of the PARAFAC model on the real coronal tongue data, leading to a finding of inadequacy of the PARAFAC model.