On valid descriptive inference from non-probability sample

ABSTRACT

We examine the conditions under which descriptive inference can be based directly on the observed distribution in a non-probability sample, under both the super-population and quasi-randomisation modelling approaches. Review of existing estimation methods reveals that the traditional formulation of these conditions may be inadequate due to potential issues of under-coverage or heterogeneous mean beyond the assumed model. We formulate unifying conditions that are applicable to both types of modelling approaches. The difficulties of empirically validating the required conditions are discussed, as well as valid inference approaches using supplementary probability sampling. The key message is that probability sampling may still be necessary in some situations, in order to ensure the validity of descriptive inference, but it can be much less resource-demanding given the presence of a big non-probability sample.

KEYWORDS:

• Non-informative selection
• prediction model
• calibration
• inverse propensity weighting
• sample matching
• model misspecification

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Li-Chun Zhang  http://orcid.org/0000-0002-3944-9484

Additional information

Notes on contributors

Li-Chun Zhang

Li-Chun Zhang is Professor of Social Statistics at University of Southampton, Senior Researcher at Statistics Norway, and Professor of Official Statistics at University of Oslo. His research interests include finite population sampling design and coordination, graph sampling, sample survey estimation, non-response, measurement errors, small area estimation, index number calculations, editing and imputation, register-based statistics, analysis of integrated data, statistical matching, record linkage, population size estimation.