Comparisons of group means, variances, correlations, and/or regression slopes involving psychological variables rely on an assumption of measurement invariance–that the latent variables under investigation have equivalent meaning and measurement across group. When measures are noninvariant, replicability suffers, as comparisons are either conceptually meaningless, or hindered by inflated Type I error rates. We propose that the failure to account for interdependence amongst dyad members when testing measurement invariance may be a potential source of unreplicable findings in relationship research. We develop fully dyadic versions of invariance-testing in an Actor-Partner Interdependence Model framework, and propose a Registered Report for gauging the extent of dyadic (non)invariance in romantic relationship research.