Balanced two-stage equal probability sampling

Abstract

For two-stage sampling, equal probability sampling method (epsem) by πps-SRS is commonly used in practice. It also provides practical means for controlling cost and fieldwork allocation. In two-stage epsem, same number of elements are selected by SRS from each sampled PSU. As an alternative to this convention for two-stage epsem, one can also select same number of equal-sized sub-clusters by SRS from each sampled PSU. Furthermore, although HT-estimator is design unbiased, when a set of auxiliary variables is known, generalized regression (or GREG) estimator is also commonly used in practice.
A comparison of sampling strategies involving two-stage epsem by πps-SRS may provide a useful insights from practical viewpoint. Therefore, four sampling strategies involving two-stage epsem are compared under a two-level regression model which is a intuitive choice for two-stage sampling. A simulation study is also conducted to support theoretical comparison of the sampling strategies.

Cube method for balanced sampling was proposed for selection of PSU’s. In two-stage sampling design, cube method can be used when auxiliary variables are know at either PSU-level or at element level. Cube method aims to selected balanced samples with fixed first-order inclusion probabilities. It consists of two-phases: flight- and landing-phase. When its landing-phase is invoked, samples are not exactly balanced. A sampling procedure is proposed which aims to improve landing-phase of the cube method when it is not exactly balanced. In addition, a methodology for the estimation of sampling variance under balanced sampling is also proposed which found to be better than a variance estimator in literature. Simulation studies are conducted to investigate the performance of proposed sampling procedure and variance estimators.

When location data of sampling units is available, it is emphasized in literature to select spatially balanced samples as study variables are expected to have positive spatial autocorrelation. Since there are many spatially balanced sampling methods available, a comparative study of different spatially balanced sampling methods is conducted under a spatial super-population model with varying level of spatial autocorrelation. When both auxiliary and spatial variables are known, doubly balanced sampling is advocated in literature. Spatial or doubly balanced sampling can be used in two-stage sampling
depending on availability of spatial and auxiliary variables. Some variables of the study population may have negative spatial autocorrelation, as two-stage designs are often used for socio-economic surveys which include a variety of study variables. Four spatial sampling schemes are suggested to select spatially balanced samples when there are also some variables with negative spatial autocorrelation in the population. A variance estimation methodology is also suggested under the spatially balanced and doubly balanced sampling methods. Simulation studies are conducted to investigate the performance of proposed spatial sampling schemes and variance estimators.

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Identifiers

ORCID for Shoaib Ali: orcid.org/0000-0001-6221-9962

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

ORCID for Nikolaos Tzavidis: orcid.org/0000-0002-8413-8095

ORCID for Angela Luna Hernandez: orcid.org/0000-0001-8629-1918

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