An Examination of Initial Condition Specification in Autoregressive Latent Trajectory Models

TitleAn Examination of Initial Condition Specification in Autoregressive Latent Trajectory Models
Publication TypeJournal Article
Year of Publication2016
AuthorsOu, L, Chow, S-M, Ji, L, Molenaar, PCM
JournalMultivariate Behavioral Research

Bollen and Curran (Bollen & Curran, 2004; Curran & Bollen, 2001) presented the Autoregressive Latent Trajectory (ALT) model as a synthesis of the autoregressive model and the latent growth curve model. A challenge when estimating ALT models is to decide how to specify the initial conditions associated with the first available time point. Among the initial condition specifications (ICSs) considered in the literature are the predetermined and ongoing endogenous specifications (Curran & Bollen, 2001; Bollen & Curran, 2004; Hamaker, 2005; Jongerling & Hamaker, 2011). The former treats the first time point as predetermined and allows the process under study to conform to different longitudinal structures prior to, and after the first collected observation; the latter is used to describe an ALT process that has started in the distant past. One other specification that is commonly assumed in empirical applications is that the ALT process simply starts at the first time point and has no prior history. Unfortunately, the rationales for adopting one of these specifications over the others, their conditions of equivalence, and the effects of using covariates to predict individual differences in the presence of different ICs are poorly understood. In this study, we show analytically that a variety of ICSs is in fact nested within the predetermined ICS. We further demonstrate how likelihood ratio tests may be used to test hypotheses concerning unconditional and conditional ICSs using a subsample (N=3995) of longitudinal family income data from the National Longitudinal Survey of Youth (Bureau of Labor Statistics, 2013).