Longitudinal Multivariate Psychology by Ferrer Emilio Boker Steven M. Grimm Kevin J

Author:Ferrer, Emilio,Boker, Steven M.,Grimm, Kevin J.
Language: eng
Format: epub
Publisher: Taylor & Francis (CAM)
Published: 2019-12-23T16:00:00+00:00

General Discussion

As Baltes and Nesselroade (1979) and McArdle and Nesselroade (2014) emphasized, it is important to identify and study interindividual differences in intraindividual changes. For the covariance structure specification of growth curve modeling, there are various recommendations. For example, Gurka et al. (2011) recommended “backwards selection” with starting with an unstructured pattern. Verbeke & Molenberghs (2009) also suggested that one can start with a “saturated” model and then perform “model deduction” to investigate whether some random effects can be removed. We generally agree with their recommendation, given that there is sufficient accuracy and power in variance testing and model selection. Thus, it is important to use a valid and more powerful variance testing approach. In the discussion of the first issue, we have generally recommended the generalized variance tests coupled with the mixture distribution approach under constrained estimation, because they yielded well controlled Type I error rates and higher statistical power. We do not recommend the Wald specific test, because the results are too conservative, although it may be the easiest for one to obtain the WS test result. In practice, variance testing can be underpowered (e.g., Hertzog et al., 2008; Ke & Wang, 2015) and model selection criteria such as AIC and BIC may lead to inaccurate decisions, especially when the sample size is small (e.g., Liu, Rovine, & Molenaar, 2012). Thus, the backwards selection approach may lead to over-simplified covariance structures.

For appropriately specifying the covariance structure for a growth curve analysis, in addition to the use of variance tests and model selection criteria, we recommend conducting sensitivity analysis by: (1) fitting various covariance structures with and without using robust standard error estimators to the data; and (2) comparing the inference results on the latent factor means or fixed effects from the various models/methods. If the results from a model with a simplified covariance structure are different from those from a model with a more complex covariance structure, it may indicate that the simplified covariance structure is over-simplified and thus mis-specified. If the inference results from a model with a simplified covariance structure are similar to those from a model with a more complex covariance structure, we are more confident with the inferences.

In this chapter, we used linear growth curve modeling as an example to discuss the two related issues about interindividual differences in intraindividual changes. In psychological and behavioral research, the latent true change trajectories can be nonlinear (e.g., Grimm et al., 2011; McArdle, Ferrer-Caja, Hamagami, & Woodcock, 2002; McArdle, Grimm, Hamagami, Bowles, & Meredith, 2009; McArdle & Wang, 2008; Wang & McArdle, 2008). For nonlinear growth curve modeling, the performance of different variance testing approaches for detecting interindividual differences in nonlinear changes and the consequences of misspecifying covariance structures on inferences about the nonlinear mean structures should be investigated in future research.

In summary, we hope this chapter can help researchers understand the features of various variance testing approaches for detecting interindividual differences in intraindividual changes and thus use an appropriate one under their research context. We also

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