A new technique for handling non-probability samples based on model-assisted kernel weighting

Abstract

Surveys are going through massive changes, and the most important innovation is the use of non-probability samples. Non-probability samples are increasingly used for their low research costs and the speed of the attainment of results, but these surveys are expected to have strong selection bias caused by several mechanisms that can eventually lead to unreliable estimates of the population parameters of interest. Thus, the classical methods of statistical inference do not apply because the probabilities of inclusion in the sample for individual members of the population are not known. Therefore, in the last few decades, new possibilities of inference from non-probability sources have appeared.

Statistical theory offers different methods for addressing selection bias based on the availability of auxiliary information about other variables related to the main variable, which must have been measured in the non-probability sample. Two important approaches are inverse probability weighting and mass imputation. Other methods can be regarded as combinations of these two approaches.

This study proposes a new estimation technique for non-probability samples. We call this technique model-assisted kernel weighting, which is combined with some machine learning techniques. The proposed technique is evaluated in a simulation study using data from a population and drawing samples using designs with varying levels of complexity for, a study on the relative bias and mean squared error in this estimator under certain conditions. After analyzing the results, we see that the proposed estimator has the smallest value of both the relative bias and the mean squared error when considering different sample sizes, and in general, the kernel weighting methods reduced more bias compared to based on inverse weighting. We also studied the behavior of the estimators using different techniques such us generalized linear regression versus machine learning algorithms, but we have not been able to find a method that is the best in all cases. Finally, we study the influence of the density function used, triangular or standard normal functions, and conclude that they work similarly.

A case study involving a non-probability sample that took place during the COVID-19 lockdown was conducted to verify the real performance of the proposed methodology, obtain a better estimate, and control the value of the variance.