The authors have evaluated a range of estimation methods for combining probability and nonprobability samples using Monte Carlo simulations as well as case studies. Our earlier evaluations show that Statistical Matching, Propensity Weighting, and Small Area Modeling all perform well. In particular, hybrid methods that combine multiple methods perform better than any single method. Based on further Monte Carlo simulations with the CCTC simulation data, now made available by NORC at the University of Chicago, this paper extends our earlier investigations to explore two promising hybrid methods: (1) Matching Propensity (MP) and (2) Matching Propensity with Small Area Modeling (MP-SM). The MP method features a two-way combination of Statistical Matching and Propensity Weighting, and the MP-SM method adds Small Area Modeling to the MP method, resulting in a three-way combination that is doubly robust. The simulations show that both hybrid methods result in substantial bias reduction. The MP-SM method leads to slightly more bias reduction, both overall and for small domains, but at the cost of much greater variance, which is consistent with our earlier observation that calibration to small area model estimates is effective in reducing bias, but the resulting weights are more variable. Overall, the MP method performs better based on our current simulation results. For variance estimation under the MP method, we propose a simple variance estimator that produces approximately unbiased variance estimates in our simulation experiments.
