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Abstract:
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Covariate nonoverlap is challenge for causal inference. Several weighting methods exist that result in an inference population with overlap, including weight truncation (Crump) and smooth overlap weighting functions (e.g., Li et al.'s overlap weight and also Li & Green's matching weight), which are our focus. These methods are propensity score (PS) centric, where the weight is a function of the PS. With a more general view of weighting as combining covariate distributions of groups, we obtain a new interpretation of these weighting schemes that involves weighted negative power means of group-specific covariate densities, where group weights are tied to the power parameter. With Li et al.'s method, for example, power parameter rho=-1 and group weight is inverse group size, an interesting feature. For matching weight, rho = -infty. With this recognition, we propose two families of flexible overlap weighting (FOW) schemes. Family #1 is a simple generalization allowing any non-positive rho; this retains a PS weighting representation, and rho=0 is a nice choice. Family #2 decouples group weight omega from rho; this allows flexible user choice, and we note some intuitive omega values.
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