University of Maryland DRUM  
University of Maryland Digital Repository at the University of Maryland

Digital Repository at the University of Maryland (DRUM) >
Theses and Dissertations from UMD >
UMD Theses and Dissertations >

Please use this identifier to cite or link to this item:

Authors: Choi, Jaehwa
Advisors: Hancock, Gregory R
Department/Program: Measurement, Statistics and Evaluation
Type: Dissertation
Sponsors: Digital Repository at the University of Maryland
University of Maryland (College Park, Md.)
Subjects: Psychology, Psychometrics
Education, Tests and Measurements
Keywords: SEM
Ordinal Variables
Categorical Data
Issue Date: 28-Jul-2006
Abstract: Due to the superiority of latent means models (LMM) over the modeling of means on a single measured variable (ANOVA) or on a composite (MANOVA) in terms of power and effect size estimation, LMM is starting to be recognized as a powerful modeling technique. Conducting a group difference (e.g., a treatment effect) testing at the latent level, LMM enables us to analyze the consequence of the measurement error on measured level variable(s). And, this LMM has been developed for both interval indicators (IILMM; Jöreskog & Goldberger, 1975, Muthén, 1989, Sörbom, 1974) and ordinal indicators (OILMM; Jöreskog, 2002). Recently, effect size estimates, post hoc power estimates, and a priori sample size determination for LMM have been developed for interval indicators (Hancock, 2001). Considering the frequent analysis of ordinal data in the social and behavior sciences, it seems most appropriate that these measures and methods be extended to LMM involving such data, OILMM. However, unlike IILMM, the OILMM power analysis involves various additional issues regarding the ordinal indicators. This research starts with illustrating various aspects of the OILMM: options for handling ordinal variables' metric level, options of estimating OILMM, and the nature of ordinal data (e.g., number of categories, categorization rules). Also, this research proposes a test statistic of the OILMM power analysis parallel to the IILMM results by Hancock (2001). The main purpose of this research is to examine the effect of categorization (mostly focused on the options handling ordinal indicators, and number of ordinal categories) on Type I error and power in OILMM based on the proposed measures and OILMM test statistic. A simulation study is conducted particularly for the two-populations between-subjects design case. Also, a numerical study is provided using potentially useful statistics and indices to help understanding the consequence of the categorization especially when one treats ordinal data as if they had metric properties.
Appears in Collections:UMD Theses and Dissertations
Human Development & Quantitative Methodology Theses and Dissertations

Files in This Item:

File Description SizeFormatNo. of Downloads
umi-umd-3673.pdf2.26 MBAdobe PDF905View/Open

All items in DRUM are protected by copyright, with all rights reserved.


DRUM is brought to you by the University of Maryland Libraries
University of Maryland, College Park, MD 20742-7011 (301)314-1328.
Please send us your comments