Regression to the mean in latent change score models: an example involving breastfeeding and intelligence

Latent change score models are often used to study change over time in observational data. However, latent change score models may be susceptible to regression to the mean. In the present study, we investigate regression to the mean in the case of breastfeeding and intelligence of children. Earlier observational studies have identified a positive association between breastfeeding and child intelligence, even when adjusting for maternal intelligence. Here, we used latent change score modeling to analyze intergenerational change in intelligence, both from mothers to children and backward from children to mothers, in the 1979 National Longitudinal Survey of Youth (NLSY79) dataset (N = 6283). When analyzing change from mothers to children, breastfeeding was found to have a positive association with intergenerational change in intelligence, whereas when analyzing backward change from children to mothers, a negative association was found. These discrepant findings highlight a hidden flexibility in the analytical space and call into question the reliability of earlier studies of breastfeeding and intelligence using observational data.

Coupling Effects of Depression and Functional Disability: Using Bivariate Latent Change Score Model

The purpose of the study was to examine the coupling effect of depression and functional disability over four time points using the data from the Health and Retirement Study (HRS). The sample included participants who survived to 98 years or older (N = 458). Four alternative latent change score models were computed to examine the univariate and bivariate effects among depressive symptoms (CES-D) and functional disabilities (ADL): No-coupling, univariate model of ADL to change in CES-D, univariate model of CES-D to change in ADL, and bivariate model. As hypothesized, the no-coupling model did not fit the data well, χ2 (26) = 164.86, CFI = 0.85, RMSEA = 0.11. Model 2, ADL predicting change in CES-D, did not fit the data well, χ2 (25) = 164.18, CFI = 0.85, RMSEA = 0.11. Model 3, CES-D predicting change in ADL, also did not fit the data, χ2 (25) = 148.06, CFI = 0.87, RMSEA = 0.10. The bivariate model fit the data well, χ2 (21) = 66.94, CFI = 0.95, RMSEA = 0.07, and was the best fitting model. All level to change effects were significant in model 4. One’s CES-D at prior waves was positively associated with change in ADL at subsequent waves, and ADL at prior waves was positively associated with change in CES-D at subsequent waves. In conclusion, there is a significant coupling effect between depressive symptoms and ADL over time. Future health policies should monitor older adults’ mental and functional health simultaneously for their possible spillover effects.

lcsm: An R package and tutorial on latent change score modelling

Latent change score models (LCSMs) are used across disciplines in behavioural sciences to study how constructs change over time. LCSMs can be used to estimate the trajectory of one construct (univariate) and allow the investigation of how changes between two constructs (bivariate) are associated with each other over time. This paper introduces the R package lcsm, a tool that aims to help users understand, analyse, and visualise different latent change score models. The lcsm package provides functions to generate model syntax for basic univariate and bivariate latent change score models with different model specifications. It is also possible to visualise different model specifications in simplified path diagrams. An interactive application illustrates the main functions of the package and demonstrates how the model syntax and path diagrams change based on different model specifications. This R package aims to increase the transparency of reporting analyses and to provide an additional resource to learn latent change score modelling.

Clarifying the Implicit Assumptions of Two-Wave Mediation Models via the Latent Change Score Specification: An Evaluation of Model Fit Indices

Statistical mediation analysis is used to investigate mechanisms through which a randomized intervention causally affects an outcome variable. Mediation analysis is often carried out in a pretest-posttest control group design because it is a common choice for evaluating experimental manipulations in the behavioral and social sciences. There are four different two-wave (i.e., pretest-posttest) mediation models that can be estimated using either linear regression or a Latent Change Score (LCS) specification in Structural Equation Modeling: Analysis of Covariance, difference and residualized change scores, and a cross-sectional model. Linear regression modeling and the LCS specification of the two-wave mediation models provide identical mediated effect estimates but the two modeling approaches differ in their assumptions of model fit. Linear regression modeling assumes each of the four two-wave mediation models fit the data perfectly whereas the LCS specification allows researchers to evaluate the model constraints implied by the difference score, residualized change score, and cross-sectional models via model fit indices. Therefore, the purpose of this paper is to provide a conceptual and statistical comparison of two-wave mediation models. Models were compared on the assumptions they make about time-lags and cross-lagged effects as well as statistically using both standard measures of model fit (χ2, RMSEA, and CFI) and newly proposed T-size measures of model fit for the two-wave mediation models. Overall, the LCS specification makes clear the assumptions that are often implicitly made when fitting two-wave mediation models with regression. In a Monte Carlo simulation, the standard model fit indices and newly proposed T-size measures of model fit generally correctly identified the best fitting two-wave mediation model.

Dangers of including outcome at baseline as a covariate in latent change score models

Latent change score modelling is a version of structural equation modelling for measuring change between measurements. It seems quite common to regress change on the initial value included in the calculation of the change score (i.e. ΔY (= Y2 – Y1) is regressed on Y1). However, similarly as in simpler regression analyses, this procedure may make findings susceptible to the influence of regression to the mean. This suspicion was verified in the present simulations. An empirical application, including re-analyses of previously published data, indicated that previously claimed reciprocal promoting effects of vocabulary and matrix reasoning on each other’s longitudinal development may actually be due to regression to the mean. Researchers are recommended not to regress change on the initial value included in the calculation of the change score when employing latent change score modelling, or at least to verify findings with analyses omitting this parameter.

Temporal Dynamics Between Faculty Goals, Burnout/Engagement, and Performance in Teaching and Research: A Latent Change Score Approach

Motivation is posited to be central for faculty members’ professional experiences and performance. To this end, achievement goals have been associated with burnout/engagement and performance at work. However, the few studies that have examined this topic were cross-sectional and only considered one of the two equally important work domains of faculty members. In the present research, we analyze the temporal relationships between achievement goals and burnout/engagement as well as performance and investigate the domain specificity of goal pursuit by considering goals for teaching and goals for research. To this end, we conducted a longitudinal study including 681 German faculty members that were surveyed four times over a total of two years. Multivariate Latent Change Score modeling attested that in both domains, mastery-approach goals were positively related to subsequent development of performance, while performance was also positively related to subsequent development of mastery goals, creating a double positive loop. Performance goals and work-avoidance goals were differentially associated with performance in both domains, indicating that the effects of goals can be bound to different contextual features. For overall burnout/engagement, our results implied that for its development, primarily research goals mattered (with performance-avoidance and work-avoidance goals being risk factors), while high burnout levels were associated with subsequent reduction of adaptive mastery-approach goals in both domains. This highlights the relevance of achievement goals for burnout/engagement and performance of faculty and employees in general, and sheds light on their complex temporal dynamics that can also meaningfully inform achievement goal research in other contexts.

Dynamical Properties and Conceptual Interpretation of Latent Change Score Models

Latent Change Score models (LCS) are a popular tool for the study of dynamics in longitudinal research. They represent processes in which the short-term dynamics have direct and indirect consequences on the long-term behavior of the system. However, this dual interpretation of the model parameters is usually overlooked in the literature, and researchers often find it difficult to see the connection between parameters and specific patterns of change. The goal of this paper is to provide a comprehensive examination of the meaning and interpretation of the parameters in LCS models. Importantly, we focus on their relation to the shape of the trajectories and explain how different specifications of the LCS model involve particular assumptions about the mechanisms of change. On a supplementary website, we present an interactive Shiny App that allows users to explore different sets of parameter values and examine their effects on the predicted trajectories. We also include fully explained code to estimate some of the most relevant specifications of the LCS model with the R-packages lavaan and OpenMx.