Power Analysis for the Test on the Location of Quadratic Growth Curves

• Activity Number: 544
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Wanchunzi Yu* and Mark Reiser
• Companies: Arizona State University and Arizona State University
• Keywords: Power Function ; Random Effect ; Mixed Model ; Quadratic Growth Curve ; Vertex

Abstract

Quadratic growth curves of 2nd degree polynomial are widely used in longitudinal studies. For a 2nd degree polynomial, the vertex displays the location of the curve in the XY plane. Under some models, an indirect test on the location of the vertex can be based on the intercept and slope parameters; but in other models, a direct test on the vertex is required. In this project, we derive 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 a large sample chi-square distribution. For 2nd degree polynomials from two independent groups, another chi-square statistic is derived for a test that there is no difference of location between the two curves, and it is compared to an F statistic. Power functions are presented for both the indirect F test and the direct chi-square test. We calculate the theoretical power and propose a simulation study to investigate the power of the tests. An analysis is also presented using the TELL efficacy longitudinal study, in which sound identification scores for children are modeled as quadratic growth curves for two groups, TELL and control curriculum.