Determine whether lapse-rate attenuation is approximately linear

Determine whether attenuation of the frustrated-arm scores as a function of lapse rate is approximately linear, so that linear residualization remains valid for the confirmatory cross-domain analysis.

Background

The proposed cross-domain analysis removes a general response-consistency factor by linearly residualizing the signed obstruction margin against a control score. This adjustment is valid only if the confounding effect of lapses on the frustrated-arm scores is adequately represented by a linear relation.

The paper considers a possible nonlinear attenuation of the form $(1-\lambda)^p$. Simulations indicate that curvature can materially affect the margin and the calibration of the confirmatory test, particularly when $p=3$. The authors therefore identify the empirical shape of the lapse-rate relationship as an unresolved issue that must be assessed before relying on the planned analysis.