Using residualized change versus difference scores for longitudinal research

Researchers interested in studying change over time are often faced with an analytical conundrum: Whether a residualized change model versus a difference score model should be used to assess the effect of a key predictor on change that took place between two occasions. In this article, the authors pose a motivating example in which a researcher wants to investigate the effect of cohabitation on pre- to post-marriage change in relationship satisfaction. Key features of this example include the likely self-selection of dyads with lower relationship satisfaction to cohabit and the impossibility of using experimentation procedures to attain equivalent groups (i.e., cohabitants vs. not cohabitants). The authors use this example of a nonrandomized study to compare the residualized change and difference score models analytically and empirically. The authors describe the assumptions of the models to explain Lord’s paradox; that is, the fact that these models can lead to different inferences about the effect under investigation. They also provide recommendations for modeling data from nonrandomized studies using a latent change score framework.