Spatiotemporal Balanced Sampling Design for Longitudinal Area Surveys.

A spatially balanced sample can produce good estimates of finite population quantities when the study variable is dependent over a spatial region with respect to a super-population model. In many longitudinal surveys for monitoring natural resources, annual samples are taken in space to estimate both annual status and annual change. In this paper, we propose a spatiotemporal balanced sampling design with a repeated panel such that the sample for each year is spatially balanced, and the sample combined from consecutive years is also spatially balanced. We propose design-based regression estimators of the annual status and change, and the corresponding variance estimators are also derived. Simulation studies show that the spatial balance of a sample generated by the proposed spatiotemporal balanced sampling design is good, and design-based regression estimators work well. The proposed spatiotemporal balanced sampling design is tested on data from the National Resources Inventory rangeland on-site survey conducted in Texas from 2009 to 2013. For the study variable "average soil aggregate stability," the proposed sampling design and estimators are shown to have better performance compared with the original sample and estimators. Although the spatiotemporal balanced sampling design is proposed in a two-dimensional space, it can be generalized to higher dimensions easily. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]