Methods for Combining Probability and Nonprobability Samples Under Unknown Overlaps

Nonprobability (convenience) samples are increasingly sought to stabilize estimations for one or more population variables of interest that are performed using a randomized survey (reference) sample by increasing the effective sample size. Estimation of a population quantity derived from a convenience sample will typically result in bias since the distribution of variables of interest in the convenience sample is different from the population. A recent set of approaches estimates conditional (on sampling design predictors) inclusion probabilities for convenience sample units by specifying reference sample-weighted pseudo likelihoods. This paper introduces a novel approach that derives the propensity score for the observed sample as a function of conditional inclusion probabilities for the reference and convenience samples as our main result. Our approach allows specification of an exact likelihood for the observed sample. We construct a Bayesian hierarchical formulation that simultaneously estimates sample propensity scores and both conditional and reference sample inclusion probabilities for the convenience sample units. We compare our exact likelihood with the pseudo likelihoods in a Monte Carlo simulation study.Comment: 32 pages, 8 figure

Manganese Content Control in Weld Metal During MAG Welding

The influence of the welding current and method of gas shielding in MAG welding on the content of manganese is considered in the paper. Results of study of the welded specimens of steels 45 when applying welding wire of different formulas and different types of gas shielding (traditional shielding and double-jet shielding) are given. It is found that in MAG welding the value of the welding current and the speed of the gas flow from the welding nozzle have a considerable impact on the chemical composition of the weld metal. The consumable electrode welding under double-jet gas shielding provides the directed gas-dynamics in the welding area and enables controlling the electrode metal transfer and the chemical composition of a weld

Methods for combining probability and nonprobability samples under unknown overlaps

Nonprobability (convenience) samples are increasingly sought to reduce the estimation variance for one or more population variables of interest that are estimated using a randomized survey (reference) sample by increasing the effective sample size. Estimation of a population quantity derived from a convenience sample will typically result in bias since the distribution of variables of interest in the convenience sample is different from the population distribution. A recent set of approaches estimates inclusion probabilities for convenience sample units by specifying reference sample-weighted pseudo likelihoods. This paper introduces a novel approach that derives the propensity score for the observed sample as a function of inclusion probabilities for the reference and convenience samples as our main result. Our approach allows specification of a likelihood directly for the observed sample as opposed to the approximate or pseudo likelihood. We construct a Bayesian hierarchical formulation that simultaneously estimates sample propensity scores and the convenience sample inclusion probabilities. We use a Monte Carlo simulation study to compare our likelihood based results with the pseudo likelihood based approaches considered in the literature