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A Test and Confidence Set for Comparing the Location of Quadratic Growth Curves


Abstract Quadratic growth curves of 2nd degree polynomial are widely used in longitudinal studies. For a 2nd degree polynomial, the vertex represents the location of the curve in the XY plane. For a quadratic growth curve, we propose an approximate confidence region as well as the confidence interval for x and y-coordinates of the vertex using two methods, the gradient method and the delta method. Under some models, an indirect test on the location of the curve can be based on the intercept and slope parameters, but in other models, a direct test on the vertex is required. We present a quadratic-form statistic for a test of the null hypothesis that there is no shift in the location of the vertex in a linear mixed model. The statistic has an asympto... (more)
Created Date 2015
Contributor Yu, Wanchunzi (Author) / Reiser, Mark (Advisor) / Barber, Jarrett (Committee member) / Kao, Ming-Hung (Committee member) / St Louis, Robert D (Committee member) / Wilson, Jeffrey (Committee member) / Arizona State University (Publisher)
Subject Statistics / Confidence Set / Mixed Models / Power Analysis / Quadratic Growth Curves / Random Effects / Vertex
Type Doctoral Dissertation
Extent 165 pages
Language English
Copyright
Reuse Permissions All Rights Reserved
Note Doctoral Dissertation Statistics 2015
Collaborating Institutions Graduate College / ASU Library
Additional Formats MODS / OAI Dublin Core / RIS


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Description Dissertation/Thesis