Sample-related invariance is an important topic in psychometric research. The generalizability of findings in a broad range of application samples requires equivalence of interpretations based on the measurement outcomes across respective samples. Contextual factors like gender, age, culture, ethnicity, socio-economical status etc. may affect the meaning and interpretation of psychological measures. Sample-related invariance is frequently investigated using Multiple-Group Mean and Covariance Structure (MGMCS) analyses. This method builds upon natural or artifical categories of contextual variables. Many contextual variables are continuous variables and their categorization is associated with an information loss and potentially overly simplistic data analyses. We present and discuss two complementary analytical approaches – Latent Moderated Structural (LMS) Equations and Local Structural Equation Models (LSEM). Both approaches allow treating contextual factors as continuous variables and are appropriate to detect non-linear relations. The use of these methods is exemplified based on real data. We investigated measurement equivalence of a battery of cognitive tests across age (N = 448; age range 18-82 years). Based on a higher-order factor model of cognitive abilities factorial equivalence could be established – contradicting the agededifferentiation hypothesis. Advantages and disadvantages of MGMCS, LMS, and LSEM and further implementations beyond aging-research are discussed.