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

Published on Apr 17, 2018in Frontiers in Psychology2.13
· DOI :10.3389/fpsyg.2018.00294
Andreas M. Brandmaier12
Estimated H-index: 12
(MPG: Max Planck Society),
Timo von Oertzen19
Estimated H-index: 19
(MPG: Max Planck Society)
+ 2 AuthorsChristopher Hertzog57
Estimated H-index: 57
(MPG: Max Planck Society)
Abstract
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, which 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.
  • References (42)
  • Citations (3)
References42
Newest
#1Wei Wu (KU: University of Kansas)H-Index: 11
#2Fan Jia (KU: University of Kansas)H-Index: 4
Last.Todd D. Little (TTU: Texas Tech University)H-Index: 67
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#1Andreas M. Brandmaier (MPG: Max Planck Society)H-Index: 12
#2Timo von Oertzen (MPG: Max Planck Society)H-Index: 19
Last.Ulman Lindenberger (UCL: University College London)H-Index: 77
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#1Matthew Joseph Gribbin (MedImmune)H-Index: 7
#2Yueh-Yun Chi (UF: University of Florida)H-Index: 18
Last.Keith E. Muller (UF: University of Florida)H-Index: 41
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#1Ken Kelley (Mendoza College of Business)H-Index: 25
#2Kristopher J. Preacher (Vandy: Vanderbilt University)H-Index: 21
Cited By3
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#1Julian David Karch (LEI: Leiden University)H-Index: 2
#2Julian D. Karch (LEI: Leiden University)
Last.Andreas M. Brandmaier (MPG: Max Planck Society)H-Index: 12
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#1Jacquelyn K. Mallette (ECU: East Carolina University)H-Index: 1
#2Ted G. Futris (UGA: University of Georgia)H-Index: 8
Last.Geoffrey L. Brown (UGA: University of Georgia)H-Index: 14
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#1Elliot M. Tucker-Drob (University of Texas at Austin)H-Index: 27
#2Andreas M. Brandmaier (MPG: Max Planck Society)H-Index: 12
Last.Ulman Lindenberger (MPG: Max Planck Society)H-Index: 77
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#1Andreas M. Brandmaier (MPG: Max Planck Society)H-Index: 12
#2Elisabeth Wenger (MPG: Max Planck Society)H-Index: 11
Last.Ulman Lindenberger (MPG: Max Planck Society)H-Index: 77
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#1Gizem Hülür (UZH: University of Zurich)H-Index: 9
#2Sherry L. Willis (UW: University of Washington)H-Index: 45
Last.Denis Gerstorf (HSU: Humboldt State University)H-Index: 31
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