This article focuses on the implementation of propensity score matching for clustered data. Different approaches to reduce bias due to cluster-level confounders are considered and compared using Monte Carlo simulations. We investigated methods that exploit the clustered structure of the data in two ways: in the estimation of the propensity score model (through the inclusion of fixed or random effects) or in the implementation of the matching algorithm. In addition to a pure within-cluster matching, we also assessed the performance of a new approach, 'preferential' within-cluster matching. This approach first searches for control units to be matched to treated units within the same cluster. If matching is not possible within-cluster, then the algorithm searches in other clusters. All considered approaches successfully reduced the bias due to the omission of a cluster-level confounder. The preferential within-cluster matching approach, combining the advantages of within-cluster and between-cluster matching, showed a relatively good performance both in the presence of big and small clusters, and it was often the best method. An important advantage of this approach is that it reduces the number of unmatched units as compared with a pure within-cluster matching. We applied these methods to the estimation of the effect of caesarean section on the Apgar score using birth register data. Copyright © 2016 John Wiley & Sons, Ltd.

Propensity score matching (PSM) and propensity score weighting (PSW) are popular tools to estimate causal effects in observational studies. We address two open issues: how to estimate propensity scores and assess covariate balance. Using simulations, we compare the performance of PSM and PSW based on logistic regression and machine learning algorithms (CART; Bagging; Boosting; Random Forest; Neural Networks; naive Bayes). Additionally, we consider several measures of covariate balance (Absolute Standardized Average Mean (ASAM) with and without interactions; measures based on the quantile‐quantile plots; ratio between variances of propensity scores; area under the curve (AUC)) and assess their ability in predicting the bias of PSM and PSW estimators. We also investigate the importance of tuning of machine learning parameters in the context of propensity score methods. Two simulation designs are employed. In the first, the generating processes are inspired to birth register data used to assess the effect of labor induction on the occurrence of caesarean section. The second exploits more general generating mechanisms. Overall, among the different techniques, random forests performed the best, especially in PSW. Logistic regression and neural networks also showed an excellent performance similar to that of random forests. As for covariate balance, the simplest and commonly used metric, the ASAM, showed a strong correlation with the bias of causal effects estimators. Our findings suggest that researchers should aim at obtaining an ASAM lower than 10% for as many variables as possible. In the empirical study we found that labor induction had a small and not statistically significant impact on caesarean section.

This paper addresses some recent developments in the field of management science and economics of well-being, trying to prove a link between working conditions and subjective well-being. Using the fifth round of the European Social Survey, which is the most recent set of data with a module focusing on the interrelations between work, family and well-being, this paper uses an instrumental variable approach to estimate the effect of job satisfaction on subjective Well-being. The direction of the relationship between these two variables has always been controversial because of endogeneity. Results, also exploring the role of working contract and welfare systems, allow for isolating a considerable influence on job satisfaction in increasing people's subjective well-being. Results are robust even if the restriction condition is violated. Job satisfaction increases subjective well-being even if the instrumental variables are not uncorrelated with the error of the main equation.

Matching is a well known technique to balance covariates distribution between treated and control units in non-experimental studies. In many fields, clustered data are a very common occurrence in the analysis of observational data and the clustering can add potentially interesting information. Matching algorithms should be adapted to properly exploit the hierarchical structure. In this article we present the CMatching package implementing matching algorithms for clustered data. The package provides functions for obtaining a matched dataset along with estimates of most common parameters of interest and model-based standard errors. A propensity score matching analysis, relating math proficiency with homework completion for students belonging to different schools (based on the NELS-88 data), illustrates in detail the use of the algorithms.

This article presents a Bayesian semi-parametric approach for modeling the occurrence of cesarean sections using a sample of women delivering in 20 hospitals of Sardinia (Italy). A multilevel logistic regression has been fitted on the data using a Dirichlet process prior for modeling the random-effects distribution of the unobserved factors at the hospital level. Using the estimated random effects at the hospital level, a partition of the hospitals in terms of similar medical practice has been obtained that identifies different profiles of hospitals in terms of caesarean section risks. The limited number of clusters may be useful for suggesting policy implications that help to reduce the heterogeneity of caesarean delivery risks