The separation of between-person and within-person components of individual change over time: A latent curve model with structured residuals.

Abstract

Objective Although recent statistical and computational developments allow for the empirical testing of psychological theories in ways not previously possible, one particularly vexing challenge remains: how to optimally model the prospective, reciprocal relations between two constructs as they developmentally unfold over time. Several analytic methods currently exist that attempt to model these types of relations, and each approach is successful to varying degrees. However, none provide the unambiguous separation of between-person and within-person components of stability and change over time, components that are often hypothesized to exist in the psychological sciences. The goal of our paper is to propose and demonstrate a novel extension of the multivariate latent curve model to allow for the disaggregation of these effects. Method We begin with a review of the standard latent curve models and describe how these primarily capture between-person differences in change. We then extend this model to allow for regression structures among the time-specific residuals to capture within-person differences in change. Results We demonstrate this model using an artificial data set generated to mimic the developmental relation between alcohol use and depressive symptomatology spanning five repeated measures. Conclusions We obtain a specificity of results from the proposed analytic strategy that are not available from other existing methodologies. We conclude with potential limitations of our approach and directions for future research.

Codevelopment of psychopathic features and alcohol use during emerging adulthood: Disaggregating between- and within-person change.

“…In order to investigate the relationship between features of psychopathy and alcohol use at multiple assessment points across the emerging adulthood developmental period, this study implemented a multivariate Latent Curve Model with Structured Residuals (LCM-SR; Curran et al, 2014) (see Figure 1). The LCM-SR model is a novel methodology that extends current analytic procedures by allowing more precise investigation into estimates of person-specific, “between-person” and time-specific, “within-person” processes among distinct constructs over time (Curran et al, 2014).…”

“…This structure results in these residuals being conceptualized as time-specific estimates of the deviation between the observed repeated measure and the underlying latent growth curve. This time-specific residual structure represents the within-person portion of the model (Curran et al, 2014). It is possible to incorporate both autoregressive and cross-lagged regressions in this within-person portion of the model, without affecting the underlying latent growth curve (which represents the between-person facet of the model).…”

“…Finally, we compared the fit of a series of models resulting from fixing and freeing parameters of the trajectory portion of the model (i.e., slope variance for alcohol use and psychopathic features) and the residual structure aspect of the model (i.e., concurrent time-specific correlations, autoregressions, and crosslags). All models were specified using maximum likelihood estimation with standard errors and a chi-square statistic that are robust to nonnormality (MLR) in Mplus 7 (Muthén & Muthén, 1998–2012) (also see Bollen & Curran, 2004, 2006; Curran et al, 2014; Morin, Maiano, Marsh, Janosz, and Nagengast, 2011). …”

“…This may include common factors that predate the use of alcohol and psychopathic features, such as a family history of substance use disorders or antisocial behavior. Therefore, between- and within- person effects each provide important, yet distinct types of information (for a more thorough review of these issues, see Curran & Bauer, 2011; Curran et al, 2014). To date, however, there are relatively few studies that have separated between- and within- person effects, particularly when considering these multiple developmental processes.…”

The dynamics of the development of mathematics skills: A comparison of theories of developing intelligence.

“…These correlations, or 'structured residuals' (cf. Curran et al, 2014) reflect the possible effects of: (1) a possible larger set of variables that influence growth in both measured domains, which are not included in the analyzed data set (e.g., working memory, processing speed, reasoning) and/or (2) a mismatch between measurement density during data collection and the time steps with which natural development unfolds (see Appendix B). Both of these mechanisms may be present in our sample.…”