Study Length, Change Process Separability, Parameter Estimation, and Model Evaluation in Hybrid Autoregressive-Latent Growth Structural Equation Models for Longitudinal Data

Considering between- and within-person relations in auto-regressive cross-lagged panel models for developmental data

Longitudinal data can provide inferences at both the between-person and within-person levels of analysis, but only to the extent that the statistical models chosen for data analysis are specified to adequately capture these distinct sources of association. The present work focuses on auto-regressive cross-lagged panel models, which have long been used to examine time-lagged reciprocal relations and mediation among multiple variables measured repeatedly over time. Unfortunately, many common implementations of these models fail to distinguish between-person associations among individual differences in the variables' amounts and changes over time, and thus confound between-person and within-person relations either partially or entirely, leading to inaccurate results. Furthermore, in the increasingly complex model variants that continue to be developed, what is not easily appreciated is how substantial differences in interpretation can be created by what appear to be trivial differences in model specification. In the present work, we aimed to (a) help analysts become better acquainted with the some of the more common model variants that fall under this larger umbrella, and (b) explicate what characteristics of one's data and research questions should be considered in selecting a model. Supplementary Materials include annotated model syntax and output using Mplus, lavaan in R, and sem in Stata to help translate these concepts into practice.

Demystifying longitudinal data analyses using structural equation models in school psychology

Structural equation models (SEM) are a method of latent variable analysis that offer a high degree of flexibility in terms of modeling methods for applied research questions. Recent advancements associated with longitudinal SEM have unlocked innovative ways to decompose variance and to estimate mean trends over time (e.g., Allison et al., 2017; Berry & Willoughby, 2017; Hamaker et al., 2015; McArdle & Nesselroade, 2014). However, these longitudinal methods are not necessarily readily accessible to scholars seeking to advance theory and practice in school psychology. Importantly, not all longitudinal data are the same and not all longitudinal SEMs are the same; thus, analytic approaches must be appropriately matched to specific research aims to meaningfully inform school psychology theory and practice. The present article highlights recent advances in longitudinal SEMs, clarifies their similarities to other-perhaps more familiar-methods, and matches their applications to specific types of research questions. The intent of this work is to promote careful thinking about the correspondence between estimands, developmental theory, and practical applications to foster specificity in testing quantitative questions in school psychology research and advance a more rigorous evaluation of longitudinal trends relevant to research and practice in the field.