In social psychology, some research questions address a comparison of individuals belonging to different social or relational contexts. As measurement invariance literature has indicated, before comparing two or more groups (gender, cultures, and relationship types), the question of whether a measurement of the construct used for the comparison is invariant must be verified. Measurement invariance helps to assure the validity of the measurement and the construct equivalence across groups. However, when non-independent data are used for comparison (the same individual provides data for his or her different relationship types), the standard multigroup analyses for testing measurement invariance are not accurate. The current study presents a modified correlated uniqueness model that may be applied in these specific cases. As an example, we analyzed the invariance of the Intimate Disclosure scale and the Conflict scale in mother–child, father–child, and romantic relationships of young adults. Results indicate a partial invariance: only configural invariance, factor loading invariance, and factor covariance invariance were found. The consequences for validity of the measurement are then discussed. Copyright © 2014 John Wiley & Sons, Ltd.