Evaluating the Power of Latent Growth Curve Models to Detect Individual

摘要

A major goal of longitudinal research is the direct identification of interindividualndifferences in intraindividual change (Baltes & Nesselroade, 1979; Hertzog &nNesselroade, 2003; Wohlwill, 1991). Latent growth curve models (LGCMs)nexpand on traditional repeated-measures analysis of variance by allowing onento simultaneously model change in the means (fixed effects) and in the variancenand covariance of initial level and change (random effects; Bryk & Raudenbush,n2001; Duncan, Duncan, Strycker, Li, & Alpert, 1999; Laird & Ware, 1982;nMcArdle & Epstein, 1987; Raykov, 1993; Rogosa & Willett, 1985; J. D. Singern& Willett, 2003). Individual differences in rates of change are manifested asnreliable random effects in LGCM slopes.nThere have been relatively few studies of the properties of LGCM significancentests to detect individual differences in change, and the available evidence isnlimited in scope (e.g., Pinheiro & Bates, 2000). Simulation studies of LGCMsnhave typically focused on other questions, such as detecting mean slope differencesnin multiple groups (Fan, 2003; Kim, 2005; Muthén & Curran, 1997).nAware of the lack of criteria describing the limitations of LGCMs in assessingnrandom effects, we (Hertzog, Lindenberger, Ghisletta, & Oertzen, 2006) recentlynevaluated the statistical power of bivariate LGCM to detect correlations of slopesnbetween two variables. Our simulation, which used the Satorra and Saris (1985)napproximation method, indicated that the power to detect slope covariances wasnrelatively low under a number of conditions, especially when the growth curvenreliability (GCR) was less than .90.nThe present Monte Carlo simulation evaluates different methods of testingnfor reliable slope variance in univariate LGCMs. We explicitly evaluate twonlikelihood ratio tests, a 1 df specific variance test and a 2 df generalized variancentest. We also evaluate the behavior of the standard Wald test (the estimated slopenvariance divided by its standard error of the estimate).