Applying multilevel regression weighting when only population margins are available

Abstract

Reliable survey data is needed to be able to infer survey findings to the general population. However, self-selection or panel attrition of the survey respondents may bias survey estimations. To tackle these challenges, weighting adjustments have been established to correct for different inclusion probabilities and to reduce bias in the survey. These strategies adjust the survey data to match known population statistics (e.g., means and proportions). The usefulness of weighting strategies depends on the benchmarks of the variables available from official statistics or other highly reliable sources, for instance, whether population information on the weighting variables is available as joint distributions of all variables or as margins only. While complex weighting strategies have been developed for poststratification using joint distributions (for example multilevel regression and poststratification), these methods are not applicable when only population margins are available. In this paper, we propose two practical approaches that combine the multilevel regression weighting method with weighting algorithms using marginal population distributions only. In a simulation study, we applied both approaches to volunteer samples.

Um Selektion in Befragungsdaten auszugleichen, werden üblicherweise Gewichtungsverfahren angewendet. Deren Nützlichkeit hängt auch davon ab, ob Bevölkerungsinformationen zu den Gewichtungsvariablen als gemeinsame Verteilungen aller Merkmale oder nur als Randverteilungen der einzelnen Merkmale verfügbar sind. In der Praxis liegen häufig nur Randverteilungen vor, wodurch komplexe Verfahren wie MrP nicht verwendet werden können. In diesem Artikel werden zwei praktische Ansätze vorgeschlagen, die die MrP-Idee so adaptieren, dass sie auch mit Randverteilungen verwendet werden kann.