Triangulation can be useful depending on what you wish to achieve: Further elaborations and a reply to Lucas et al. (2024)

There is a debate about statistical models for analyzing longitudinal data. Models based on cross-lagged effects may give false positive results under certain conditions. We have proposed a triangulation method where cross-lagged effects of a predictor (X) on a subsequent score on an outcome (Y2) when adjusting for a prior score (Y1) are scrutinized by estimating a reversed effect of X on Y1 when adjusting for Y2 and an effect of X on the Y2-Y1 difference. Lucas et al. conducted simulations and reported that our triangulation method may flag genuine causal effects of X on Y2 when adjusting for Y1 as spurious and concluded that the triangulation method is not valid. Here we respond to this criticism. We show that the simulations and conclusions by Lucas et al. are focused on the ability of the test to avoid type II errors. Here we complement this view with a discussion about type I errors. Further, we show that the criticism by Lucas et al. appears to be founded on an assumption that causality is best viewed as an adjusted effect of X on the Y2-Y1 difference. We argue that it may often be better to view causality as a crude (i.e., unadjusted) effect of X on the Y2-Y1 difference. Therefore, we continue to claim that our triangulation method may be a useful tool to scrutinize causal claims based on adjusted cross-lagged effects.