Search

Model fit criteria for structural equation models rely on asymptotic behavior. As such, corrections are applied when fitting models to small samples (N ≤ 100). However, these corrections are based ...

Structural equation model trees (SEM Trees) allow for the construction of decision trees with structural equation models fit in each of the nodes. Based on covariate information, SEM Trees can be u...

Understanding causal effects of a treatment is often of interest in the social sciences. When treatments cannot be randomly assigned, researchers must ensure that treated and untreated participants are balanced on covariates before estimating treatment effects. Conventional practices are useful in matching such that treated and untreated participants have similar average values on their covariates. However, situations arise in which a researcher may instead want to match on model parameters. We propose an algorithm, Causal Mplus Trees, which uses decision trees to match on structural equation model parameters and estimates conditional average treatment effects in each node. We provide a proof of concept using two small simulation studies and demonstrate its application using COVID-19 data.

Over the past 40 years there have been great advances in the analysis of individual change and the analyses of between-person differences in change. While conditional growth models are the dominant approach, exploratory models, such as growth mixture models and structural equation modeling trees, allow for greater flexibility in the modeling of between-person differences in change. We continue to push for greater flexibility in the modeling of individual change and its determinants by combining growth mixture modeling with structural equation modeling trees to evaluate how measured covariates predict class membership using a recursive partitioning algorithm. This approach, referred to as growth mixture modeling with membership trees, is illustrated with longitudinal reading data from the Early Childhood Longitudinal Study with the MplusTrees package in R.

Longitudinal research is often interested in identifying correlates of heterogeneity in change. This paper compares three approaches for doing so: the mixed-effects model (latent growth curve model), the growth mixture model, and structural equation model trees. Each method is described, with special focus given to how each structures heterogeneity, attributes that heterogeneity to covariates, and the kinds of research questions each can be used to address. Each approach is used to analyze data from the National Longitudinal Survey of Youth to understand the similarities and differences between methods in the context of empirical data. Specifically, changes in weight across adolescence are examined, as well as how differences in these change patterns can be explained by sex, race, and mother's education. Recommendations are provided for how to select which approach is most appropriate for analyzing one's own data.

There has been a great deal of work in the literature on the equivalence between the mixed-effects modeling and structural equation modeling (SEM) frameworks in specifying growth models (Willett & ...

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.

This chapter proposes to examine the performance of measures of model fit for the latent change score model in small samples with missing data. Structural equation modeling is a flexible modeling framework that encompasses a broad set of statistical models. The empirical example demonstrated that the framework within which a model is fit can lead to opposing results even when comparing models using the likelihood ratio test. The missing data correction used should be of the form such that it, in effect, deactivates itself when data are complete. Otherwise, it should adequately characterize the quality of the observed information in the data. Such a small sample corrections would be of great use to researchers with small samples wishing to evaluate how well longitudinal models fit their data. The chapter concludes with a discussion of the results accompanied by some thoughts on how future research should proceed.

The growth mixture model has become increasingly popular, given the willingness to acknowledge developmental heterogeneity in populations. Typically, linear growth mixture models, based on polynomials or piecewise functions, are used in substantive applications and evaluated quantitatively through simulation. Growth mixture models that follow inherently nonlinear trajectories, referred to as nonlinear mixed-effects mixture models, have received comparatively little attention—likely due to estimation complexity. Previous work on the estimation of these models has involved multistep routines (Kelley, 2008), maximum likelihood estimation (MLE) via the E-M algorithm (Harring, 2005, 2012), Taylor series expansion and MLE within the structural equation modeling framework (Grimm, Ram, & Estabrook, 2010), and MLE by adaptive Gauss–Hermite quadrature (Codd & Cudeck, 2014). This article proposes and evaluates the use of Bayesian estimation with OpenBUGS (Lunn, Spiegelhalter, Thomas, & Best, 2009), a free program, a...