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EFFECT OF CATEGORIZATION ON TYPE I ERROR AND POWER IN ORDINAL INDICATOR LATENT MEANS MODELS FOR BETWEEN-SUBJECTS DESIGNS
Hancock, Gregory R
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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.