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This article offers different examples of how to fit latent growth curve (LGC) models to longitudinal data using a variety of different software programs (i.e., LISREL, Mx, Mplus, AMOS, SAS). The article shows how the same model can be fitted using both structural equation modeling and multilevel software, with nearly identical results, even in the case of models of latent growth fitted to incomplete data. The general purpose of this article is to provide a demonstration that integrates programming features from different software. The most immediate goal is to help researchers implement these LGC models as a useful way to test hypotheses of growth.

Describes some applications of latent growth curve models in the context of structural equation modeling using data from P. Trickett and F. Putnam (1993) on the physical height of abused (n=77) and nonabused (n=75) adolescent girls. Presents power calculations for the ability of the different models to discern the growth of the abuse sample from the control sample. (SLD)

Although finite mixture models have received considerable attention, particularly in the social and behavioral sciences, an alternative method for creating homogeneous groups, structural equation model trees (Brandmaier, von Oertzen, McArdle, & Lindenberger, 2013), is a recent development that has received much less application and consideration. It is our aim to compare and contrast these methods for uncovering sample heterogeneity. We illustrate the use of these methods with longitudinal reading achievement data collected as part of the Early Childhood Longitudinal Study–Kindergarten Cohort. We present the use of structural equation model trees as an alternative framework that does not assume the classes are latent and uses observed covariates to derive their structure. We consider these methods as complementary and discuss their respective strengths and limitations for creating homogeneous groups. [ABSTRACT FROM PUBLISHER]

Change over time often takes on a nonlinear form. Furthermore, change patterns can be characterized by heterogeneity due to unobserved subpopulations. Nonlinear mixed-effects mixture models provide one way of addressing both of these issues. This study attempts to extend these models to accommodate time-unstructured data. We develop methods to fit these models in both the structural equation modeling framework as well as the Bayesian framework and evaluate their performance. Simulations show that the success of these methods is driven by the separation between latent classes. When classes are well separated, a sample of 200 is sufficient. Otherwise, a sample of 1,000 or more is required before parameters can be accurately recovered. Ignoring individually varying measurement occasions can also lead to substantial bias, particularly in the random-effects parameters. Finally, we demonstrate the application of these techniques to a data set involving the development of reading ability in children. [ABSTRACT FROM PUBLISHER]

A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM’s utility. [ABSTRACT FROM PUBLISHER]

This research focuses on the problem of model selection between the latent change score (LCS) model and the autoregressive cross-lagged (ARCL) model when the goal is to infer the longitudinal relationship between variables. We conducted a large-scale simulation study to (a) investigate the conditions under which these models return statistically (and substantively) different results concerning the presence of bivariate longitudinal relationships, and (b) ascertain the relative performance of an array of model selection procedures when such different results arise. The simulation results show that the primary sources of differences in parameter estimates across models are model parameters related to the slope factor scores in the LCS model (specifically, the correlation between the intercept factor and the slope factor scores) as well as the size of the data (specifically, the number of time points and sample size). Among several model selection procedures, correct selection rates were higher when using model fit indexes (i.e., comparative fit index, root mean square error of approximation) than when using a likelihood ratio test or any of several information criteria (i.e., Akaike’s information criterion, Bayesian information criterion, consistent AIC, and sample-size-adjusted BIC). [ABSTRACT FROM AUTHOR]

In this article, we introduce and demonstrate the application of a newly developedRpackageRAMpathfor tracing path diagrams and conducting structural longitudinal data analysis.RAMpathwas developed to preserve the essential features of the classic DOS version of the RAMpath program (McArdle & Boker, 1990) and ease data analysis done through structural equation modeling (SEM). The applicability ofRAMpathis demonstrated through a mediation model, a MIMIC model, several latent growth curve models, a univariate latent change score model, and a bivariate latent change score model. In addition to performing regular SEM analysis,RAMpathhas unique features. First, it can generate path diagrams according to a given model. Second, it can display path tracing rules through path diagrams and decompose total effects into their respective direct and indirect effects as well as decompose variances and covariances into individual bridges. Furthermore,RAMpathcan fit dynamic system models automatically based on latent change scores and generate vector field plots based on results obtained from a bivariate dynamic system.RAMpathis provided as an open-sourceRpackage. [ABSTRACT FROM AUTHOR]

The scientific literature consistently supports a negative relationship between adolescent depression and educational achievement, but we are certainly less sure on the causal determinants for this robust association. In this article we present multivariate data from a longitudinal cohort-sequential study of high school students in Hawai‘i (following McArdle, 2008; McArdle, Johnson, Hishinuma, Miyamoto, & Andrade, 2001). We first describe the full set of data on academic achievements and self-reported depression. We then carry out and present a progression of analyses in an effort to determine the accuracy, size, and direction of the dynamic relationships among depression and academic achievement, including gender and ethnic group differences. We apply 3 recently available forms of longitudinal data analysis: (a)Dealing with incomplete data—We apply these methods to cohort-sequential data with relatively large blocks of data that are incomplete for a variety of reasons (Little & Rubin, 1987; McArdle & Hamagami, 1992). (b)Ordinal measurement models(Muthén & Muthén, 2006)—We use a variety of statistical and psychometric measurement models, including ordinal measurement models, to help clarify the strongest patterns of influence. (c)Dynamic structural equation models(DSEMs; McArdle, 2008). We found the DSEM approach taken here was viable for a large amount of data, the assumption of an invariant metric over time was reasonable for ordinal estimates, and there were very few group differences in dynamic systems. We conclude that our dynamic evidence suggests that depression affects academic achievement, and not the other way around. We further discuss the methodological implications of the study. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

With few exceptions. the dynamics underlying the mood structures of individuals with Parkinson's Disease have consistently been overlooked. Based on 12 participants' daily self-reports over 72 days, we identified 10 participants whose covariance matrices for positive and negative affect were similar enough to warrant pooling. Dynamic factor models that included factor autoregression and cross-regressions were fitted to the pooled, lagged covariance matrix representing approximately 700 occasions of measurement. Although results from the pooled data indicated that both positive and negative affect had a strong lag-1 autoregressive impact on current positive and negative affect, most individuals showed stronger autoregressive effects for positive than negative affect when examined individually. There was also a weak cross-regression effect of positive affect on negative affect, but the reverse was not true. Through model lining, we demonstrated that failure to incorporate lagged relations among factors could lead to an overestimation of concurrent correlations among latent factors. Implications of the findings in relation to the orthogonality of positive and negative affect are discussed. [ABSTRACT FROM AUTHOR]

This article offers different examples of how to fit latent growth curve (LGC) models to longitudinal data using a variety of different software programs (i.e., LISREL, Mx, Mplus, AMOS, SAS). The article shows how the same model can be fitted using both structural equation modeling and multilevel software, with nearly identical results. even in the ease of models of latent growth fitted to incomplete data. The general purpose of this article is to provide a demonstration that integrates programming features from different software. The most immediate coal is to help researchers implement these LGC models as a useful way to test hypotheses of growth. [ABSTRACT FROM AUTHOR]

Structural equation models are presented as alternative models for examining longitudinal data. The models include (a) a cross-lagged regression model, (b) a factor model based on latent growth curves, and (c) a dynamic model based on latent difference scores. The illustrative data are on motivation and perceived competence of students during their first semester in high school. The 3 models yielded different results and such differences were discussed in terms of the conceptualization of change underlying each model. The last model was defended as the most reasonable for these data because it captured the dynamic interrelations between the examined constructs and, at the same time, identified potential growth in the variables. [ABSTRACT FROM AUTHOR]

Focuses on the application of latent growth curves for analyzing the development of height. Frequency of height measurement; Significance of the integration of growth curve and structural equation model in estimating the curves spanning the entire range of sexes; Ability of the different model to discern the growth of the abuse and the control sample.