title: On the Mathematical Relationship Between Latent Change Score and Autoregressive Cross-Lagged Factor Approaches: Cautions for Inferring Causal Relationship Between Variables.
abstract: The present paper focuses on the relationship between latent change score (LCS) and autoregressive cross-lagged (ARCL) factor models in longitudinal designs. These models originated from different theoretical traditions for different analytic purposes, yet they share similar mathematical forms. In this paper, we elucidate the mathematical relationship between these models and show that the LCS model is reduced to the ARCL model when fixed effects are assumed in the slope factor scores. Additionally, we provide an applied example using height and weight data from a gerontological study. Throughout the example, we emphasize caution in choosing which model (ARCL or LCS) to apply due to the risk of obtaining misleading results concerning the presence and direction of causal precedence between two variables. We suggest approaching model specification not only by comparing estimates and fit indices between the LCS and ARCL models (as well as other models) but also by giving appropriate weight to substantive and theoretical considerations, such as assessing the justifiability of the assumption of random effects in the slope factor scores.
authors.affiliation: a University of Tsukuba.
authors.forename: Satoshi
authors.initials: S
authors.lastname: Usami
authors.affiliation: b University of Southern California.
authors.forename: Timothy
authors.initials: T
authors.lastname: Hayes
authors.affiliation: b University of Southern California.
authors.forename: John J
authors.initials: JJ
authors.lastname: McArdle
mesh_terms: D000368:Aged; D000369:Aged, 80 and over; D000375:Aging / Q000523:psychology; D035841:Behavioral Research / Q000379:methods*; D006801:Humans; D008137:Longitudinal Studies; D008875:Middle Aged; D015233:Models, Statistical; D011594:Psychometrics / Q000379:methods*; D015203:Reproducibility of Results
keywords: autoregressive cross-lagged model; causality; latent change score model; longitudinal data