The performance of multilevel growth curve models under an autoregressive moving average process

The authors examined the robustness of multilevel linear growth curve modeling to misspecification of an autoregressive moving average process. As previous research has shown (J. Ferron, R. Dailey, & Q. Yi, 2002; O. Kwok, S. G. West, & S. B. Green, 2007; S. Sivo, X. Fan, & L. Witta, 2005), estimates of the fixed effects were unbiased, and Type I error rates for the tests of the fixed effects were generally accurate when the present authors correctly specified or underspecified the model. However, random effects were poorly estimated under many conditions, even under correct model specification. Further, fit criteria performed inconsistently and were especially inaccurate when small sample sizes and short series lengths were combined. With the exception of elevated Type I error rates that occurred under some conditions, the best performance was obtained by use of an unstructured covariance matrix at the first level of the growth curve model.