A Test for Comparing the Location of Quadratic Growth Curves

• Activity Number: 614
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Wanchunzi Yu*+ and Mark Reiser
• Companies: and Arizona State University
• Keywords: Vertex ; Mixed Model ; Quadratic Growth Curve ; Confidence Region

Abstract

Quadratic growth curves of 2nd degree polynomial are widely used in longitudinal studies. For a 2nd degree polynomial, the vertex gives the location of the curve in the XY plane. We present an approximate confidence region for the vertex using two methods, a gradient method and the delta method. 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 vertices 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 mixed linear model. The statistic has an approximate chi-squared distribution. We also present results for a simulation study conducted to assess the influence of sample size and nature of the random effects. Simulation results show that the test statistic performs well in terms of Type I error rate and power. We also present interpretations of shift in the location of the vertex.