A multivariate growth curve model for three-level data.

Abstract

One of the most vexing challenges that has faced the behavioral sciences over the past century has been how to optimally measure, summarize, and predict individual variability in stability and change over time. It has long been known that a multitude of advantages are associated with the collection and analysis of repeated measures data; indeed, longitudinal data have become nearly requisite in many disciplines within the behavioral sciences. The challenge of how to best empirically capture individual change cuts across every aspect of the empirical research endeavor, including study design, psychometric measurement, subject sampling, data analysis, and substantive interpretation. Although many textbooks have been devoted to each of these research dimensions, here we have the much more modest goal of exploring just one specific type of longitudinal data analytic method: the multivariate growth model.Given our love of jargon in the social sciences, our field has coined a rather large number of terms to describe patterns of intraindividual change over time. These terms include (but are not limited to) growth, curve, trajectory, and path, among many others. Whether the term is growth models, growth trajectories, growth curves, latent trajectories, developmental curves, latent curves, time paths, or latent developmental growth curve time path trajectories of growth, 1 all tend to refer to the same thing. Namely, repeated measures are collected on a This research was partially funded by a grant from the Army Research Institute awarded to Patrick Sweeney; additional research team members included Kurt Dirks and Paul Lester. Sample computer code may be obtained from http://www.unc.edu/~curran 1 OK, so we made up that last one.

Grassland ecosystem responses to climate change and human activities within the Three-River Headwaters region of China

“…The solid line in this figure marks the 95% confidence interval (CI) for the estimated effect of variables at the three-level model; thus, those that do not overlap this line can be considered significantly different from zero. The dots denote point estimates for parameter values 47 , 48 , 93 . This figure was created using the software R ( http://www.Rproject.org/ ) 94 and the library sjPlot 93 .…”

“…The results of this analysis reveal that the most distinct feature of our MLM compared with other longitudinal approaches is the consideration of data in terms of the hierarchical structuring of repeated measures nested within higher level groups 47 , 48 . This feature means that MLMs can be used to assess variance related to rates of change in individual cases and to test whether, or not, these rates differ depending on the characteristics of higher-level groups 49 .…”

Growth Modeling in a Diagnostic Classification Model (DCM) Framework–A Multivariate Longitudinal Diagnostic Classification Model

“…The generalized multivariate GCM was applied to measure the changes in mastery statuses of attributes over time. First, as suggested by MacCallum et al ( 1997 ), Curran et al ( 2012 ), and Hoffman ( 2015 ), a synthesized variable was created, which was a composite of multiple outcome variables ( in the current study), then a series of dummy variables as exogenous predictors were adopted to control which specific outcomes were referenced within different parts of the model. Let dv rt denote the synthesized variable, which contained individual r ′ s mastery statuses for three attributes across four measurement occasions.…”

The mediating effect of family cohesion in reducing patient symptoms and family distress in a culturally informed family therapy for schizophrenia: A parallel-process latent-growth model.

“…Ignoring dependency due to nesting can bias parameter estimates, standard errors, and degrees of freedom (Bauer, Gottfredson, Dean, & Zucker, 2013; Kenny & Judd, 1986; Tasca, Illing, Joyce, & Ogrodniczuk, 2009). Moreover, multivariate growth models allow for the examination of complex residual variance components that can be key to understanding stability and change (Curran et al, 2012). Unlike a pre-post analysis, a growth model provides flexibility in modeling heterogeneity in growth at the individual and/or family level.…”