Beyond scalar invariance: Evaluating the validity of person-level score comparisons

Scalar invariance is widely regarded as essential for comparing test-score means across groups. However, it is less clear when test scores can be meaningfully compared at the individual level — specifically, whether individuals from different groups who share the same observed score have the same expected value of the latent trait. I show that scalar invariance alone is insufficient for meaningful person-level comparisons based on sum scores. In addition to scalar invariance, person comparison invariance requires equality of latent variable means and omega coefficients across groups. Nevertheless, non-invariance effects can be relatively small if the omega coefficients are high and similar in magnitude across groups. I relate person comparison invariance to predictive invariance and provide R code to test person comparison invariance and to visualise the effects of non-invariance.