We develop a new method, which assumes that marital preferences are characterized either by the scalar-valued measure developed by Liu and Lu (2006) for dichotomous assorted trait variables, or by the matrix-valued generalized Liu- Lu measure (proposed in this paper for polytomous ordered assorted trait variables). The new method transforms an observed contingency table into a counterfactual table while preserving its (generalized) Liu- Lu value. After studying some analytical properties of the new method, we illustrate its application by a counterfactual decomposition. We decompose changes in the prevalence of homogamy in the US between 1980 and 2010. Technically speaking, we map marital preferences represented by Liu- Lu matrices (together with another driver of marital patterns) to the scalar-valued change in the share of homogamous couples. We perform this decomposition with two alternative measures as well by applying two conventional transformation methods. Finally, we use survey evidences to support our claim that out of the three considered methods, the new transformation method is the most apt for identifying the role of marital preferences at shaping marriage patterns. These evidences are also in favor of measuring assortativity in
preferences à la Liu and Lu.