Balancing vs modeling approaches to weighting in practice

There are two seemingly unrelated approaches to weighting in observational studies. One of them maximizes the fit of a model for treatment assignment to then derive weights-we call this the modeling approach. The other directly optimizes certain features of the weights-we call this the balancing approach. The implementations of these two approaches are related: the balancing approach implicitly models the propensity score, while instances of the modeling approach impose balance conditions on the covariates used to estimate the propensity score. In this article, we review and compare these two approaches to weighting. Previous review papers have focused on the modeling approach, emphasizing the importance of checking covariate balance. However, as we discuss, the dispersion of the weights is another important aspect of the weights to consider, in addition to the representativeness of the weighted sample and the sample boundedness of the weighted estimator. In particular, the dispersion of the weights is important because it translates into a measure of effective sample size, which can be used to select between alternative weighting schemes. In this article, we examine the balancing approach to weighting, discuss recent methodological developments, and compare instances of the balancing and modeling approaches in a simulation study and an empirical study. In practice, unless the treatment assignment model is known, we recommend using the balancing approach to weighting, as it systematically results in better covariate balance with weights that are minimally dispersed. As a result, effect estimates tend to be more accurate and stable.