Browsing by Author "Shieh, GW"

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General multivariate linear models for longitudinal studies
(2000)
Shieh, GW
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管理科學系
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Department of Management Science
Longitudinal studies occur frequently in many different disciplines. To fully utilize the potential value of the information contained in a longitudinal data, various multivariate linear models have been proposed. The methodology and analysis are somewhat unique in their own ways and their relationships are not well understood and presented. This article describes a general multivariate linear model for longitudinal data and attempts to provide a constructive formulation of the components in the mean response profile. The objective is to point out the extension and connections of some well-known models that have been obscured by different areas of application. More importantly, the model is expressed in a unified regression form from the subject matter considerations. Such an approach is simpler and more intuitive than other ways to modeling and parameter estimation. As a consequence the analyses of the general class of models for longitudinal data can be easily implemented with standard software.
The inequality between the coefficient of determination and the sum of squared simple correlation coefficients
(2001-05-01)
Shieh, GW
;
管理科學系
;
Department of Management Science
The inequality between the coefficient of determination and the sum of two squared simple correlation coefficients in a two-variable regression model is reexamined through two relative measures. They are the relative coefficient of determination and the relative simple correlation, which are the ratio of the coefficient of determination to the sum of squares of the two simple correlations and the ratio of two simple correlations, respectively. This approach not only permits new insights into their relationship hut also allows clear and informative visual representations of various aspects of the counterintuitive condition. We consider the occurrence and corresponding magnitude? probability and expected magnitude of the enhancement-synergism situation. Numerical examples are presented to illustrate these phenomena.