Lord's paradox in latent change score modeling: An example involving facilitating longitudinal effects between intelligence and academic achievement

It has been claimed that intelligence causes academic achievement to increase over time, and that also, conversely, academic achievement causes intelligence to increase over time. This bidirectional facilitating longitudinal effect between intelligence and academic achievement rests on observed associations between initial intelligence and the change in academic achievement between an initial and a subsequent measurement, and vice versa. Here, we demonstrate, through simulating empirical data used in previous research, that such longitudinal associations may be due to regression toward the mean rather than a true facilitating effect. Regression toward the mean occurs due to the conditioning of change on the initial value on the outcome variable. Researchers should be aware of this fallacy and are recommended to verify their findings with analyses without adjustment for an initial value on the outcome.