Assortative mating, the process through which people interactively choose each other as spouses, is a complex, consequential and informative phenomenon. 1 It has important consequences for the structure of society, for inequality and integration, and it tells a lot about social structures, patterns of interactions and preferences. However, it is a complex process, and while tempting it is problematic to read preferences directly from the empirical outcomes. The mapping of preferences to outcomes in a process subject to constraints is not straightforward. Outcomes are constrained in complex ways, not least the gendered distribution of the characteristics of interest, the competition among peers for alters with the desired characteristics, and the fact that alters are agents with preferences too. Additionally, the fact that the process is dynamic, where the context changes continually, not only because of external historical reasons, but also endogenously, as the distribution of single people changes as others marry.Research on assortative mating has a long history of looking at the data, usually tables of spouse pairs classified by the characteristic of interest, and making inferences about the data generating processes in terms of homogamy preference, competition for desirable characteristics, female hypergamy preference, or relative desirability of different characteristics leading to status exchange. Earlier work tends to read directly from patterns in the tables, or simple summaries. But loglinear modelling of these tables, predominant in the literature since the 1980s, is markedly superior, by controlling for the marginal distributions and correlated characteristics. For instance, raw data may show lots of women marrying up, but loglinear analysis may correctly detect that this is explained entirely by a gendered distribution where men are higher on average.The research question that motivates this research is whether loglinear models of tables of achieved marriages correctly capture evidence of underlying preferences, such as homophily, competition, female hypergamy, or relative ranking of attributes in the context of status exchange. This is partly a question about loglinear models, but more fundamentally it concerns the extent to which the theoretical mechanisms leave detectable evidence in the resulting data, the tables of spouse pairs usually used in analysis.