Precision, Reliability, and Effect Size of Slope Variance in Latent Growth Curve Models: Implications for Statistical Power Analysis

Frontiers in Psychology

卷:9

Timo von Oertzen²  Ulman Lindenberger³  Andreas M. Brandmaier⁷  Christopher Hertzog⁸  Paolo Ghisletta⁹ 

[1] Center for Lifespan Psychology, Max Planck Institute for Human Development, Berlin, Germany;

[2] Department für Psychologie, Universität der Bundeswehr München, Neubiberg, Germany;

[3] Department of Political and Social Sciences, European University Institute, Fiesole, Italy;

[4] Department of Psychology, University of Virginia, Charlottesville, VA, United States;

[5] Faculty of Psychology (French), Swiss Distance Learning University, Brig, Switzerland;

[6] Faculty of Psychology and Educational Sciences, University of Geneva, Geneva, Switzerland;

[7] Max Planck UCL Centre for Computational Psychiatry and Ageing Research, Berlin, Germany;

[8] School of Psychology, Georgia Institute of Technology, Atlanta, GA, United States;

[9] Swiss National Center of Competences in Research LIVES-Overcoming Vulnerability: Life Course Perspectives - University of Geneva, Geneva, Switzerland;

关键词: linear latent growth curve model;    statistical power;    effect size;    effective error;    structural equation modeling;    reliability;   

DOI  :  10.3389/fpsyg.2018.00294

来源: DOAJ

【 摘 要 】

Latent Growth Curve Models (LGCM) have become a standard technique to model change over time. Prediction and explanation of inter-individual differences in change are major goals in lifespan research. The major determinants of statistical power to detect individual differences in change are the magnitude of true inter-individual differences in linear change (LGCM slope variance), design precision, alpha level, and sample size. Here, we show that design precision can be expressed as the inverse of effective error. Effective error is determined by instrument reliability and the temporal arrangement of measurement occasions. However, it also depends on another central LGCM component, the variance of the latent intercept and its covariance with the latent slope. We derive a new reliability index for LGCM slope variance—effective curve reliability (ECR)—by scaling slope variance against effective error. ECR is interpretable as a standardized effect size index. We demonstrate how effective error, ECR, and statistical power for a likelihood ratio test of zero slope variance formally relate to each other and how they function as indices of statistical power. We also provide a computational approach to derive ECR for arbitrary intercept-slope covariance. With practical use cases, we argue for the complementary utility of the proposed indices of a study's sensitivity to detect slope variance when making a priori longitudinal design decisions or communicating study designs.

【 授权许可】

Unknown