When to Apply the Slope-to-Slope Path Time Centering? A Tutorial Guide for Parallel Process Latent Growth Curve Models

In parallel process latent growth curve models, the path linking the rates of change of two developmental processes is often the primary parameter of interest. We show that this slope-to-slope estimate can change substantially with the choice of time centering. We derive the complete transformation for all four cross-process paths and identify two conditions under which the slope-to-slope coefficient is distorted: a nonzero intercept-to-slope path and a nonzero predictor intercept–slope covariance. Using published data on emotional abuse and depressive symptoms, we illustrate a 71% shift in the estimate across centering conditions, with identical model fit. We present two equivalent approaches, aperture-adjusted time centering and a uniqueness factor approach, both yielding a time centering-invariant estimate, and provide annotated Mplus and lavaan syntax.