Advertisement

Spatiotemporal Balanced Sampling Design for Longitudinal Area Surveys

  • Zhonglei Wang
  • Zhengyuan ZhuEmail author
Article
  • 12 Downloads

Abstract

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.

Keywords

Annual change Annual status Environmental survey Regression estimator Variance estimator 

Notes

Acknowledgements

We are grateful to the associate editor and three referees for the detailed and constructive comments. This research was supported in part by the Natural Resources Conservation Service of the U.S. Department of Agriculture. By personal communication, Anton Grafström independently developed the hierarchical local pivotal method and used it to split the Swedish NFI sample for the years 2018–2022; see function hlpm of Grafström and Lisic (2018) for details.

Supplementary material

13253_2019_350_MOESM1_ESM.pdf (168 kb)
Supplementary material 1 (pdf 168 KB)

References

  1. Bellhouse, D. R. (1977). Some optimal designs for sampling in two dimensions. Biometrika 64, 605–611.MathSciNetCrossRefzbMATHGoogle Scholar
  2. Benedetti, R., Piersimoni, F., Postiglione, P. et al. (2015). Sampling Spatial Units for Agricultural Surveys. Berlin: Springer.CrossRefzbMATHGoogle Scholar
  3. Breidt, F. J. (1995). Markov chain designs for one-per-stratum spatial sampling. In Proceedings of the Section on Survey Research Methods (pp. 356–361). Washington, DC: American Statistical Association.Google Scholar
  4. Breidt, F. J. and Fuller, W. A. (1999). Design of supplemented panel surveys with application to the National Resources Inventory. Journal of Agricultural, Biological, and Environmental Statistics 4, 391–403.MathSciNetCrossRefGoogle Scholar
  5. Cochran, W. G. (1977). Sampling Techniques. New York: Wiley.zbMATHGoogle Scholar
  6. Cressie, N. A. C. (2015). Statistics for Spatial Data, revised edn. New York: Wiley.zbMATHGoogle Scholar
  7. Deville, J.-C. and Tille, Y. (1998). Unequal probability sampling without replacement through a splitting method. Biometrika 85, 89–101.MathSciNetCrossRefzbMATHGoogle Scholar
  8. Duncan, G. J. and Kalton, G. (1987). Issues of design and analysis of surveys across time. International Statistical Review 55, 97–117.CrossRefGoogle Scholar
  9. Dunn, R. and Harrison, A. R. (1993). Two-dimensional systematic sampling of land use. Journal of the Royal Statistical Society, Series C (Applied Statistics) 42, 585–601.MathSciNetGoogle Scholar
  10. Eilers, P. H. C. and Marx, B. D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science 11, 89–102.MathSciNetCrossRefzbMATHGoogle Scholar
  11. Fancy, S. G., Gross, J. E. and Carter, S. L. (2009). Monitoring the condition of natural resources in US national parks. Environmental Monitoring and Assessment 151, 161–174.CrossRefGoogle Scholar
  12. Fuller, W. (2009). Sampling Statistics. Hoboken: Wiley.CrossRefzbMATHGoogle Scholar
  13. Fuller, W. A. and Breidt, F. J. (1999). Estimation for supplemented panels. Sankhyā: The Indian Journal of Statistics, Series B 58–70.Google Scholar
  14. Grafström, A. and Lisic, J. (2018). Balanced sampling: Balanced and spatially balanced sampling. R package version 1.5.4. https://CRAN.R-project.org/package=BalancedSampling
  15. Grafström, A., Lundström, N. L. P. and Schelin, L. (2012). Spatially balanced sampling through the pivotal method. Biometrics 68, 514–520.MathSciNetCrossRefzbMATHGoogle Scholar
  16. Grafström, A. and Schelin, L. (2014). How to select representative samples. Scandinavian Journal of Statistics 41, 277–290.MathSciNetCrossRefzbMATHGoogle Scholar
  17. Grafström, A., Zhao, X., Nylander, M. and Petersson, H. (2017). A new sampling strategy for forest inventories applied to the temporary clusters of the Swedish national forest inventory. Canadian Journal of Forest Research 47(9), 1161–1167.CrossRefGoogle Scholar
  18. Hardin, J. W. and Hilbe, J. M. (2002). Generalized Estimating Equations. London: Chapman & Hall/CRC.CrossRefzbMATHGoogle Scholar
  19. Horvitz, D. G. and Thompson, D. J. (1952). A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association 47, 663–685.MathSciNetCrossRefzbMATHGoogle Scholar
  20. Jessen, R. J. (1942). Statistical investigation of a sample survey for obtaining farm facts. Iowa Agricultural Experiment Station Research Bulletin 304, 54–59.Google Scholar
  21. Lackey, L. G. and Stein, E. D. (2015). Evaluating alternative temporal survey designs for monitoring wetland area and detecting changes over time in California. JAWRA Journal of the American Water Resources Association 51, 388–399.CrossRefGoogle Scholar
  22. Lai, M.-J. and Wang, L. (2013). Bivariate penalized splines for regression. Statistica Sinica 23, 1399–1417.MathSciNetzbMATHGoogle Scholar
  23. Lisic, J. and Grafström, A. (2018). Samplingbigdata: Sampling methods for big data. R package version 1.0.0. https://CRAN.R-project.org/package=SamplingBigData
  24. Lisic, J. J. and Cruze, N. B. (2016). Local pivotal methods for large surveys. In Proceedings of the Fifth International Conference on Establishment Surveys.Google Scholar
  25. Lister, A. J. and Scott, C. T. (2009). Use of space-filling curves to select sample locations in natural resource monitoring studies. Environmental Monitoring and Assessment 149, 71–80.CrossRefGoogle Scholar
  26. McDonald, T. (2003). Review of environmental monitoring methods: Survey designs. Environmental Monitoring and Assessment 85, 277–292.CrossRefGoogle Scholar
  27. Munholland, P. L. and Borkowski, J. J. (1996). Simple latin square sampling \(+ 1\): A spatial design using quadrats. Biometrics 52, 125–136.CrossRefzbMATHGoogle Scholar
  28. Nusser, S., Breidt, F. and Fuller, W. (1998). Design and estimation for investigating the dynamics of natural resources. Ecological Applications 8, 234–245.CrossRefGoogle Scholar
  29. Nusser, S. M. and Goebel, J. J. (1997). The National Resources Inventory: A long-term multi-resource monitoring programme. Environmental and Ecological Statistics 4, 181–204.CrossRefGoogle Scholar
  30. Olsen, A. R., Kincaid, T. M. and Payton, Q. (2012). Spatially balanced survey designs for natural resources. In R. A. Gitzen, J. J. Millspaugh, A. B. Cooper and D. S. Licht (Eds.), Design and Analysis of Long-term Ecological Monitoring Studies. Cambridge: Cambridge University Press, pp. 126–150. (Cambridge Books Online).CrossRefGoogle Scholar
  31. Patterson, H. D. (1950). Sampling on successive occasions with partial replacement of units. Journal of the Royal Statistical Society, Series B (Methodology) 12, 241–255.zbMATHGoogle Scholar
  32. Ramsay, T. (2002). Spline smoothing over difficult regions. Journal of the Royal Statistical Society: Series B (Methodology) 64, 307–319.MathSciNetCrossRefzbMATHGoogle Scholar
  33. Schreuder, H. T., Ernst, R. L. and Ramirez-Maldonado, H. (2004). Statistical Techniques for Sampling and Monitoring Natural Resources. Fort Collins: US Department of Agriculture, Forest Service, Rocky Mountain Research Station.CrossRefGoogle Scholar
  34. Scott, C. T. (1998). Sampling methods for estimating change in forest resources. Ecological Applications 8, 228–233.CrossRefGoogle Scholar
  35. Stevens, D. L. and Olsen, A. R. (2004). Spatially balanced sampling of natural resources. Journal of the American Statistical Association 99, 262–278.MathSciNetCrossRefzbMATHGoogle Scholar
  36. Theobald, D. M., Stevens, D. L., White, D., Urquhart, N. S., Olsen, A. R. and Norman, J. B. (2007). Using GIS to generate spatially balanced random survey designs for natural resource applications. Environmental Management 40(1), 134–146.CrossRefGoogle Scholar
  37. United States Department of Agriculture. (2014). 2014 National Resources Inventory Rangeland Resource Assessment. Website. Last checked: December 5, 2017.Google Scholar
  38. Urquhart, N. S., Paulsen, S. G. and Larsen, D. P. (1998). Monitoring for policy-relevant regional trends over time. Ecological Applications 8, 246–257.Google Scholar
  39. Wahba, G. (1990). Spline Models for Observational Data. Philadelphia: SIAM.CrossRefzbMATHGoogle Scholar
  40. Wikle, C. K. and Royle, J. A. (1999). Space: Time dynamic design of environmental monitoring networks. Journal of Agricultural, Biological, and Environmental Statistics 489–507.Google Scholar
  41. Yan, J. and Fine, J. (2004). Estimating equations for association structures. Statistics in Medicine 23(6), 859–874.CrossRefGoogle Scholar

Copyright information

© International Biometric Society 2019

Authors and Affiliations

  1. 1.MOE Key Laboratory of Econometrics, Wang Yanan Institute for Studies in Economics and School of EconomicsXiamen UniversityXiamenPeople’s Republic of China
  2. 2.Department of StatisticsIowa State UniversityAmesUSA

Personalised recommendations