title: (Re)evaluating the Implications of the Autoregressive Latent Trajectory Model Through Likelihood Ratio Tests of Its Initial Conditions.
abstract: The autoregressive latent trajectory (ALT) model synthesizes the autoregressive model and the latent growth curve model. The ALT model is flexible enough to produce a variety of discrepant model-implied change trajectories. While some researchers consider this a virtue, others have cautioned that this may confound interpretations of the model's parameters. In this article, we show that some-but not all-of these interpretational difficulties may be clarified mathematically and tested explicitly via likelihood ratio tests (LRTs) imposed on the initial conditions of the model. We show analytically the nested relations among three variants of the ALT model and the constraints needed to establish equivalences. A Monte Carlo simulation study indicated that LRTs, particularly when used in combination with information criterion measures, can allow researchers to test targeted hypotheses about the functional forms of the change process under study. We further demonstrate when and how such tests may justifiably be used to facilitate our understanding of the underlying process of change using a subsample (N = 3,995) of longitudinal family income data from the National Longitudinal Survey of Youth.
authors.affiliation: a The Pennsylvania State University.
authors.forename: Lu
authors.initials: L
authors.lastname: Ou
authors.affiliation: a The Pennsylvania State University.
authors.forename: Sy-Miin
authors.initials: SM
authors.lastname: Chow
authors.affiliation: a The Pennsylvania State University.
authors.forename: Linying
authors.initials: L
authors.lastname: Ji
authors.affiliation: a The Pennsylvania State University.
authors.forename: Peter C M
authors.initials: PCM
authors.lastname: Molenaar
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005190:Family; D006801:Humans; D007182:Income; D016013:Likelihood Functions; D008137:Longitudinal Studies; D009010:Monte Carlo Method; D015999:Multivariate Analysis; D017711:Nonlinear Dynamics; D012044:Regression Analysis; D014481:United States
keywords: Autoregressive latent trajectory model; initial condition; latent growth curve models