Relating the classical covariance adjustment techniques of multivariate growth curve models to modern univariate mixed effects models

Biometrics
Susan K MikulichT J Crowley

Abstract

The relationship between the modern univariate mixed model for analyzing longitudinal data, popularized by Laird and Ware (1982, Biometrics 38, 963-974), and its predecessor, the classical multivariate growth curve model, summarized by Grizzle and Allen (1969, Biometrics 25, 357-381), has never been clearly established. Here, the link between the two methodologies is derived, and balanced polynomial and cosinor examples cited in the literature are analyzed with both approaches. Relating the two models demonstrates that classical covariance adjustment for higher-order terms is analogous to including them as random effects in the mixed model. The polynomial example clearly illustrates the relationship between the methodologies and shows their equivalence when all matrices are properly defined. The cosinor example demonstrates how results from each method may differ when the total variance-covariance matrix is positive definite, but that the between-subjects component of that matrix is not so constrained by the growth curve approach. Additionally, advocates of each approach tend to consider different covariance structures. Modern mixed model analysts consider only those terms in a model's expectation (or linear combinations), and ...Continue Reading

Citations

Jun 26, 2007·Journal of Gastrointestinal Surgery : Official Journal of the Society for Surgery of the Alimentary Tract·Richard A PeruginiJohn J Kelly
Nov 26, 2013·Journal of Statistical Computation and Simulation·Guangxiang Zhang, John J Chen
Mar 14, 2002·Biometrics·M Pourahmadi, M J Daniels
Oct 1, 2003·Statistics in Medicine·Susan K MikulichThomas J Crowley
Jan 3, 2013·Statistics in Medicine·Andrea FontanaFabio Pellegrini
Jan 31, 2018·Statistics in Medicine·J M MaddenA P Fitzgerald

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