A Test for Comparing the Location of Two Quadratic Growth Curves

• Activity Number: 231
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Wanchunzi Yu*+ and Mark Reiser
• Companies: Arizona State University and Arizona State University
• Keywords: Random Effect ; Mixed Model ; Quadratic Growth Curve ; Vertex ; Confidence Region ; Power Function

Abstract

The difference in the location for two quadratic growth curves is compared in this paper. For a 2nd degree polynomial, the vertex gives the location of the curve in the XY plain. We present an approximate confidence region for the difference of vertices of two quadratic growth curves using both the gradient and delta methods. To test directly on the vertices, we derive a quadratic-form statistic under the null hypothesis that there is no shift in the location of the vertices in two mixed linear models. The statistic has an approximate chi-squared distribution. We compare the test statistic with an F statistic, which is derived for indirect test on the difference in the location of the vertices based on the intercept and slope parameters. We also present results for a simulation study conducted to assess the influence of sample size, measurement time points and nature of the random effects. Simulation results show that the test statistic performs well in terms of Type I error rate and power. The test statistic is applied to the Tell Efficacy Longitudinal Study, in which sound identification scores for children are modeled as quadratic growth curves for two independent groups.