• Bayes factors;
  • Hierarchical models;
  • Laplace approximation;
  • Multilevel linear model;
  • Variance components

Summary.  Racial or ethnic disparities in birth weight are a large source of differential morbidity and mortality world wide and have remained largely unexplained in epidemiologic models. We assess the effect of maternal ancestry and census tract residence on infant birth weights in New York City and the modifying effects of race and nativity by incorporating random effects in a multilevel linear model. Evaluating the significance of these predictors involves a test of whether the variances of the random effects are equal to 0. This is problematic because the null hypothesis lies on the boundary of the parameter space. We generalize an approach for assessing random effects in the two-level linear model to a broader class of multilevel linear models by scaling the random effects to the residual variance and introducing parameters that control the relative contribution of the random effects. After integrating over the random effects and variance components, the resulting integrals that are needed to calculate the Bayes factor can be efficiently approximated with Laplace's method.