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This study used statistical simulation to calculate differential statistical power in dynamic structural equation models with groups (as in McArdle & Prindle, 2008). Patterns of between-group differences were simulated to provide insight into how model parameters influence power approximations. Chi-square and root mean square error of approximation (RMSEA) power approximation procedures were used to compare the effects of parameter manipulations and how researchers should interpret findings. The chi-square power of perfect fit calls for at least 270 individuals to detect moderate differences, whereas the RMSEA procedure of close fit seems to require as many as 1,450 participants. It is shown that parameters that provide input into the change score that the transfer leads to affect power versus indirect pathways. A discussion of differences in approximation values and future research directions follows. (Contains 3 tables and 4 figures.)

In recent years the use of the latent curve model (LCM) among researchers in social sciences has increased noticeably, probably thanks to contemporary software developments and the availability of specialized literature. Extensions of the LCM, like the the latent change score model (LCSM), have also increased in popularity. At the same time, the R statistical language and environment, which is open source and runs on several operating systems, is becoming a leading software for applied statistics. We show how to estimate both the LCM and LCSM with the sem, lavaan, and OpenMx packages of the R software. We also illustrate how to read in, summarize, and plot data prior to analyses. Examples are provided on data previously illustrated by Ferrer, Hamagami, and McArdle (2004). The data and all scripts used here are available on the first author's Web site. (Contains 5 figures.)

Latent difference score models (e.g., McArdle & Hamagami, 2001) are extended to include effects from prior changes to subsequent changes. This extension of latent difference scores allows for testing hypotheses where recent changes, as opposed to recent levels, are a primary predictor of subsequent changes. These models are applied to bivariate longitudinal data collected as part of the Baltimore Longitudinal Study of Aging on memory performance, measured by the California Verbal Learning Test, and lateral ventricle size, measured by structural MRIs. Results indicate that recent increases in the lateral ventricle size were a leading indicator of subsequent declines in memory performance from age 60 to 90. (Contains 4 tables, 2 footnotes, and 8 figures.)

Bayesian methods are becoming very popular despite some practical difficulties in implementation. To assist in the practical application of Bayesian methods, we show how to implement Bayesian analysis with WinBUGS as part of a standard set of SAS routines. This implementation procedure is first illustrated by fitting a multiple regression model and then a linear growth curve model. A third example is also provided to demonstrate how to iteratively run WinBUGS inside SAS for Monte Carlo simulation studies. The SAS codes used in this study are easily extended to accommodate many other models with only slight modification. This interface can be of practical benefit in many aspects of Bayesian methods because it allows the SAS users to benefit from the implementation of Bayesian estimation and it also allows the WinBUGS user to benefit from the data processing routines available in SAS. (Contains 3 figures and 3 tables.)

The main purpose of this research is to evaluate the performance of a Bayesian approach for estimating unknown change points using Monte Carlo simulations. The univariate and bivariate unknown change point mixed models were presented and the basic idea of the Bayesian approach for estimating the models was discussed. The performance of Bayesian estimation was evaluated using simulation studies of longitudinal data with different sample sizes, varying change point values, different levels of Level-1 variances, and univariate versus bivariate outcomes. The numerical results compared the performance of the Bayesian methods with the first-order Taylor expansion method and the adaptive Gaussian quadrature method implemented in SAS PROC NLMIXED. These simulation results showed that the first-order Taylor expansion method and the adaptive Gaussian quadrature method were sensitive to the initial values, making the results somewhat unreliable. In contrast, these simulation results showed that Bayesian estimation was not sensitive to the initial values and the fixed-effects and Level-1 variance parameters can be accurately estimated in all of the conditions. One concern was that the estimates of the Level-2 covariance parameters were found to be biased when the Level-1 variance was large in the bivariate model. However, and in general, the new Bayesian approach to the estimation of turning points in longitudinal data proved to be quite robust and practically useful. (Contains 7 tables, 2 figures, and 2 notes.)