Probability Sampling Designs: Principles for Choice of Design and Balancing

TL;DR

This paper formalizes three principles—randomization, overrepresentation, and restriction—for selecting probability sampling designs, and reviews balanced sampling within a model-assisted framework, highlighting new spatial sampling methods and their advantages.

Contribution

It introduces a systematic approach to choosing sampling designs based on formal principles and reviews the role of balanced sampling and spatial methods within this framework.

Findings

Balanced sampling can be optimal under certain models.

New spatial sampling methods offer practical advantages.

The principles guide improved inference in sampling design.

Abstract

The aim of this paper is twofold. First, three theoretical principles are formalized: randomization, overrepresentation and restriction. We develop these principles and give a rationale for their use in choosing the sampling design in a systematic way. In the model-assisted framework, knowledge of the population is formalized by modelling the population and the sampling design is chosen accordingly. We show how the principles of overrepresentation and of restriction naturally arise from the modelling of the population. The balanced sampling then appears as a consequence of the modelling. Second, a review of probability balanced sampling is presented through the model-assisted framework. For some basic models, balanced sampling can be shown to be an optimal sampling design. Emphasis is placed on new spatial sampling methods and their related models. An illustrative example shows the advantages of the different methods. Throughout the paper, various examples illustrate how the three principles can be applied in order to improve inference.