Log-linear models for contingency tables are a key tool for the study of categorical inequalities in sociology. However, the conventional approach to model selection and specification suffers from at least two limitations: reliance on oftentimes equivocal diagnostics yielded by fit statistics, and the inability to identify patterns of association not covered by model candidates. In this article, we propose an application of Lasso regularization that addresses the aforementioned limitations. We evaluate our method through a Monte Carlo experiment and an empirical study of educational assortative mating in Chile, 1990-2015. Results demonstrate that our approach has the virtue, relative to ad hoc specification searches, of offering a principled statistical criterion to inductively select a model. Importantly, we show that in situations where conventional fit statistics provide conflicting diagnostics, our Lasso-based approach is consistent in its model choice, yielding solutions that are both predictive and parsimonious.