When Are Asymmetric Fixed-Effects Models Within-Person Tests of Reversibility? Heterogeneous Responses and Bidirectional Support

Asymmetric fixed-effects models are increasingly used in sociological research to test whether an effect reverses when a time-varying predictor changes direction. Because these models rely on within-person change, directional asymmetry is often interpreted as evidence of within-person irreversibility. This study shows that this interpretation requires an additional cross-person homogeneity assumption. I reparameterize Allison’s (2019) cumulative asymmetric fixed-effects model exactly as a model of current state and total movement, revealing that the specification pools current-state responses across individuals. When those responses are heterogeneous and systematically related to who moves upward versus downward, pooled asymmetry can arise even when every individual’s response is perfectly reversible. I derive this mover-composition result and characterize what remains identifiable when individual state responses are unrestricted. A common path response—the additional response associated with accumulated movement conditional on current state—can then be identified only from within-person bidirectional movement, provided that the resulting variation is not absorbed by period effects. Monte Carlo simulations and a reanalysis of Allison’s wage example illustrate the resulting assumption–support–precision trade-off and show that relevant support depends on the structure of observed trajectories, not simply on the number of directional transitions.