We introduce hierarchically regularized entropy balancing as an extension to entropy balancing, a reweighting method that adjusts weights for control group units to achieve covariate balance in observational studies with binary treatments. Our proposed extension expands the feature space by including higher-order terms (such as squared and cubic terms and interactions) of covariates and then achieves approximate balance on the expanded features using ridge penalties with a hierarchical structure. Compared with entropy balancing, this extension relaxes model dependency and improves the robustness of causal estimates while avoiding optimization failure or highly concentrated weights. It prevents specification searches by minimizing user discretion in selecting features to balance on and is also computationally more efficient than kernel balancing, a kernel-based covariate balancing method. We demonstrate its performance through simulations and an empirical example. We develop an open-source R package, hbal, to facilitate implementation.

Imputing missing values is an important preprocessing step in data analysis, but the literature offers little guidance on how to choose between imputation models. This letter suggests adopting the imputation model that generates a density of imputed values most similar to those of the observed values for an incomplete variable after balancing all other covariates. We recommend stable balancing weights as a practical approach to balance covariates whose distribution is expected to differ if the values are not missing completely at random. After balancing, discrepancy statistics can be used to compare the density of imputed and observed values. We illustrate the application of the suggested approach using simulated and real-world survey data from the American National Election Study, comparing popular imputation approaches including random forests, hot-deck, predictive mean matching, and multivariate normal imputation. An R package implementing the suggested approach accompanies this letter.

Weighting techniques are employed to generalize results from survey experiments to populations of theoretical and substantive interest. Although weighting is often viewed as a second-order methodological issue, these adjustment methods invoke untestable assumptions about the nature of sample selection and potential heterogeneity in the treatment effect. Therefore, although weighting is a useful technique in estimating population quantities, it can introduce bias and also be used as a researcher degree of freedom. We review survey experiments published in three major journals from 2000–2015 and find that there are no standard operating procedures for weighting survey experiments. We argue that all survey experiments should report the sample average treatment effect (SATE). Researchers seeking to generalize to a broader population can weight to estimate the population average treatment effect (PATE), but should discuss the construction and application of weights in a detailed and transparent manner given the possibility that weighting can introduce bias.

Mitochondrial DNA sequences consisting of 645 sites from the 12S rRNA and 16S rRNA genes were used to estimate the phylogeny of 15 of the 32 species of spiny-footed lizards Acanthodactylus. The resultant tree has similarities to that produced from a differentially weighted data set of 32 morphological characters but there are also significant differences. However, combined analysis of molecular and morphological data sets produces the same tree topology as DNA sequence alone. The molecular data confirm that there are distinct eastern and western clades within Acanthodactylus, but place A. boskianus in the former while the A. scutellatus group constitutes a third clade. Species for which only morphological information is available were integrated with the combined tree to give a provisional phylogeny for 31 species. This phylogeny indicates that the ancestor of existing Acanthodactylus probably originated in south-west Asia and that North Africa was invaded by more than one lineage of the genus. It also suggests that soft aeolian sand habitats may have been independently occupied more than once. Molecular data provide independent evidence that the differential weighting of morphological characters in past analyses was appropriate.