Calibration and optimal transport approaches for harmonizing survey weights

Originally, the construction of weighting systems to estimate parameters of interest in survey data does not depend on the variables of interest. However, recent research raises questions about the practice of using specific weighting systems for each variable of interest, thus deviating from the universal nature of the weights proposed by survey data processing methods. This article examines the challenge of harmonizing weights for variables with different weighting systems in survey data processing, by presenting and comparing two methods: one that creates a common weight for both variables using the calibration method, and one that uses optimal transport to match the variables. A simulation study is carried out to evaluate the performance of these methods in different sampling scenarios and with continuous and categorical variables. The results of the simulation study show that the optimal transport method for weight harmonization can provide accurate parameter estimates in different scenarios, particularly in situations where disparities between sample and population distributions are large. It therefore appears to be a more versatile solution.