We aim to find a way to effectively integrate a non-probability (voluntary) sample under the data framework, where the study variable is also observed in a probability sample of some statistical survey. The selection bias that arises from voluntary participation in the survey is corrected by estimating the inclusion into the sample probabilities (propensity scores) for the units in the non-probability sample. The estimators for the propensity scores are constructed using a parametric logistic regression model. We consider two modeling scenarios: with an assumption that the willingness to participate in the voluntary survey does not depend on the survey variable itself and that such a variable does contribute to whether the individual responds or not. The maximum likelihood method is applied in both scenarios to estimate the propensity scores. The estimators of the population mean based on the estimated propensity scores are linearly combined with the unbiased estimator using the probability sample data. We compare the constructed estimators in the simulation study, where we estimate the population proportions using data from the Population and Housing Census surveys.
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