What is causal about individual differences? : A comment on Weinberger

Weinberger (2015) claims that if a latent variable is a cause, it must be a within-subject cause. In addition, Weinberger suggests that this fact refutes the conclusion of Borsboom, Mellenbergh, and Van Heerden (2003), who stated that standard psychometric models have a causal interpretation that is cast strictly in a between-subjects sense: individual differences in the latent variable may cause individual differences in test scores, while the latent variable has no causal relevance at the level of the individual. Weinberger's argument elucidates the status of causal relations in latent variable models, and clearly spells out the strong assumptions that underlie the use of such models. However, contrary to Weinberger's claims, a pure individual-differences reading of the causal model is possible. This interpretation relies on the fact that, for latent variable models, shifts of the person relative to the latent dimension can either be interpreted as a change of the individual, or as a shift of the population relative to the individual. The latter interpretation does not require us to place assumptions on what interventions would do intra-individually, but nevertheless is consistent with a causal interpretation along the lines suggested by Weinberger.