nonprobsampling: Inference for Nonprobability Samples Using Multiple Reference Surveys
Source:R/nonprobsampling-package.R
nonprobsampling-package.Rdnonprobsampling implements pseudo-weighting methods for finite population inference from nonprobability samples, such as convenience samples, volunteer cohorts, and opt-in panels. Because the participation mechanism in a nonprobability sample is unknown, unadjusted estimates of population means and prevalences may be biased. The package addresses this issue by leveraging auxiliary information from one or more probability reference surveys to estimate participation probabilities and using their inverses as pseudo-weights to obtain bias-corrected estimates of finite population means and prevalences.
Details
The package implements the generalized estimating equation framework of Landsman et al. (2026). Pseudo-weights are obtained by solving estimating equations that equate auxiliary variable totals estimated from the nonprobability sample with the corresponding totals estimated from one or more probability reference surveys. Totals from the nonprobability sample are computed using estimated pseudo-weights, whereas totals from the reference surveys are computed using the known survey sampling weights.
Several one reference methods arise as special cases of this framework under different choices of the weight and estimating functions:
the raking ratio calibration method of Landsman et al. (2026);
the adjusted logistic propensity (ALP) method of Wang, Valliant, and Li (2021);
the Chen–Li–Wu (CLW) method of Chen, Li, and Wu (2020).
A key feature of the package is the multi-reference extension of the calibration method. This extension enables the integration of auxiliary information across multiple surveys when no single reference survey contains all variables relevant to participation (Landsman et al., 2026), with an optional cumulative precalibration step to preserve information on the relationships between overlapping and unique auxiliary variables across reference surveys.
Variance estimation is based on Taylor linearization. The resulting analytic variance estimator accounts for uncertainty from pseudo-weight estimation and for the sampling designs of the reference surveys through integration with the survey package. The package also supports bootstrap-based variance estimation when bootstrap weights are provided with the reference surveys.
Typical workflow
Estimation is carried out in two steps:
est_pw()estimates pseudo-weights using the nonprobability sample and one or more reference survey design objects. This step fits the participation model and stores the internal quantities needed for subsequent estimation. It does not require an outcome variable.pwmean()uses the object returned byest_pw()to estimate a pseudo-weighted mean or prevalence for an outcome, either overall or by category. It also returns the standard error and confidence interval.
Numerical settings for solving the estimating equations can be specified with
pw_solver_control().
Datasets
The package includes example datasets for demonstrating one reference and
multiple reference analyses: sc is a nonprobability sample,
sp1 and sp2 are probability reference surveys,
and sp1_bootstrap contains replicate weights for
sp1. See the package vignette for worked examples.
References
Chen, Y., Li, P., and Wu, C. (2020). Doubly robust inference with nonprobability survey samples. Journal of the American Statistical Association, 115(532), 2011–2021. doi:10.1080/01621459.2019.1677241
Landsman, V., Wang, L., Carrillo-Garcia, I., Mitani, A. A., Smith, P. M., Graubard, B. I., Bui, T., and Carnide, N. (2026). Correction for participation bias in nonprobability samples using multiple reference surveys. Statistics in Medicine, 45(3–5). doi:10.1002/sim.70403
Wang, L., Valliant, R., and Li, Y. (2021). Adjusted logistic propensity weighting methods for population inference using nonprobability volunteer-based epidemiologic cohorts. Statistics in Medicine, 40(24), 5237–5250. doi:10.1002/sim.9122