Agent-based simulations of marriage processes are used to investigate whetherloglinear models of tables of spouse pairs properly capture evidence of the preferences behind assortative mating. Can we tell what sort of mechanisms bring about the patterns we see? Is there a female hypergamy preference and do loglinear models capture it? Four different ideal-typical simulations of spouse choice processes are presented: homophily, competition, social segregation, time segregation. All produce "realistic" patterns of educational assortative mating. Imposing a simulated female hypergamy preference yields more asymmetric outcomes, directly detected in loglinear models. But the relationship between the size of the hypergamy estimate and the strength of the hypergamy differs according to the pairing mechanism. Notably, for homophily the estimate is lower, and for time-segregation higher. Indeed, for zero simulated hypergamy, the homophily simulation shows negative, and the time-segregation simulation positive, hypergamy. This is shown to be due to the dynamic nature of the simulations: as individuals pair off the distribution of single individuals changes. For homophily perfectly symmetric choices at each iteration sum into a table of spouse pairs in which loglinear models detect hypogamy. Conclusions: these biases are small, and depend on very large simulation populations. They are less likely to be detectable in typical survey data. However, we demonstrate a clear mechanism by which loglinear models of tables of spouse pairs can be biased. This suggests that if longitudinal data is available, a time dimension should be included in the loglinear models. Otherwise, this is another argument for preferring tables of recent marriages.
Data Information in Contingency Tables: A Fallacy of Hierarchical Loglinear Models
