Interpreting effect sizes when controlling for stability effects in longitudinal autoregressive models: Implications for psychological science

Effect sizes in longitudinal studies often are dramatically smaller than effect sizes in cross-sectional studies. Indeed, autoregressive models (which are often used in longitudinal studies but not in cross-sectional studies) control for past levels on the outcome (i.e., stability effects) in order to predict change in levels of the outcome over time and thus may greatly reduce the magnitude of the effect of a predictor on the outcome. Unfortunately, however, there have been no attempts to differentiate guidelines for interpreting effect sizes for longitudinal studies versus cross-sectional studies. Consequently, longitudinal effect sizes that fall below the universal guidelines for "small" may be incorrectly dismissed as trivial, when they might be meaningful. In the current paper, we first review the present guidelines for interpreting effect sizes. Next, we discuss several examples of how controlling for stability effects can dramatically attenuate effect sizes of other predictors, in order to support our argument that the current guidelines may be misleading for interpreting longitudinal effects. Finally, we conclude by making recommendations for researchers regarding the interpretation of effect sizes in longitudinal autoregressive models.