Different inference procedures are proposed in the literature to correct for selection bias that might be introduced with non-random selection mechanisms. A class of methods to correct for selection bias is to apply a statistical model to predict the units not in the sample (super-population modeling). Other studies use calibration or Statistical Matching (statistically match nonprobability and probability samples). To date, the more relevant methods are weighting by Propensity Score Adjustment (PSA).
    The Propensity Score Adjustment method was originally developed to construct weights by estimating response probabilities and using them in Horvitz–Thompson type estimators. This method is usually used by combining a non-probability sample with a reference sample to construct propensity models for the non-probability sample. Calibration can be used in a posterior way to adding information of auxiliary variables.
    Propensity scores in PSA are usually estimated using logistic regression models. Machine learning classification algorithms can be used as alternatives for logistic regression as a technique to estimate propensities.
    The package 'NonProbEst' implements some of these methods and thus provides a wide options to work with data coming from a non-probabilistic sample.

Provides pseudo-weighted estimates of means and
    prevalences for finite population inference from nonprobability
    samples using auxiliary information from one or multiple probability
    reference surveys. The package supports estimation with multiple
    reference surveys, allowing auxiliary information to be combined
    when no single survey contains all variables relevant to
    participation. Optional cumulative precalibration can be applied to
    align weighted totals of shared variables across surveys. Methods
    are based on the generalized estimating equations framework of
    Landsman et al. (2026) <doi:10.1002/sim.70403> for correcting
    participation bias. For a single reference survey, the package
    implements the raking ratio calibration method and includes the
    adjusted logistic propensity (ALP) method of Wang, Valliant, and Li
    (2021) <doi:10.1002/sim.9122>, as well as the Chen-Li-Wu (CLW)
    method of Chen, Li, and Wu (2020) <doi:10.1080/01621459.2019.1677241>.
    Analytic variance estimation uses Taylor linearization and accounts
    for complex sampling designs in the reference surveys via integration
    with the 'survey' package.