Data integration of non-probability and probability samples with deterministic predictive mean matching

We study deterministic predictive mean matching mass imputation estimators to integrate data from probability and non-probability samples.

We consider two approaches: predicted-to-predicted (PMM~A) and predicted-to-observed (PMM~B) matching.

We prove the consistency of mean estimators, derive a variance decomposition, and propose estimators of variance.

We establish consistency of the PMM~A estimator under model misspecification and underline key differences from the nearest neighbour method.

Our PMM~B approach can be employed with non-parametric regression techniques, such as kernel regression, and the analytical expression for variance applies to nearest neighbour matching for non-probability samples.

Extensive simulation studies compare properties of the proposed estimators with existing alternatives and examine the effects of model misspecification.

The paper concludes with an empirical study on the integration of job vacancy survey and vacancies submitted to public employment offices (admin and online data).

Open-source software is available.