title: Linear and nonlinear growth models: describing a Bayesian perspective.
abstract: OBJECTIVE
  Conventional estimation of longitudinal growth models can produce inaccurate parameter estimates under certain research scenarios (e.g., smaller sample sizes and nonlinear growth patterns) and thus lead to potentially misleading interpretations of results (i.e., interpreting growth patterns that do not reflect the population patterns). The current article used patterns of change in cigarette and alcohol abuse prevalence and depression levels to demonstrate an alternative method for estimating growth models more accurately under these conditions, namely, via the Bayesian estimation framework. This article acts as an introduction and tutorial for implementing Bayesian methods when examining growth or change over time, particularly nonlinear growth.
  
  
  METHODS
  The National Longitudinal Survey of Youth 1997 database was used to highlight different linear and nonlinear (quadratic and logistic) growth models via growth curve modeling (GCM) and growth mixture modeling (GMM). The specific focus was on changes in cigarette/alcohol consumption and depression throughout adolescence and young adulthood. Specifically, a nationally representative group of individuals between the ages of 12 and 16 years were assessed at 4 time-points for levels of cigarette consumption, alcohol use, and depression.
  
  
  RESULTS
  The results for each example illustrated different patterns of linear and nonlinear growth via GCM and GMM through the versatile Bayesian estimation framework.
  
  
  CONCLUSIONS
  Growth models may benefit from the Bayesian perspective by incorporating prior information or knowledge into the model, especially when sample sizes are small or growth is nonlinear. A step-by-step tutorial for assessing various growth models via the Bayesian perspective is provided as online supplemental material.
authors.affiliation: Psychological Sciences, School of Social Sciences, Humanities, and Arts, University of California.
authors.forename: Sarah
authors.initials: S
authors.lastname: Depaoli
authors.affiliation: Psychological Sciences, School of Social Sciences, Humanities, and Arts, University of California.
authors.forename: Jonathan
authors.initials: J
authors.lastname: Boyajian
mesh_terms: D000293:Adolescent; D001499:Bayes Theorem; D005260:Female; D006801:Humans; D016014:Linear Models; D008137:Longitudinal Studies; D008297:Male; D015233:Models, Statistical