Statistical efficiency of model-informed geographic sampling designs

Daniel A. Griffith
School of Social Sciences, University of Texas @ Dallas, Richardson, Texas, USA, P.O. Box 830688, GR31, 75083-0688
Tel. : + 001 972 883 4950; Fax : + 001 883 6297
dagriffith@utdallas.edu

Abstract

As spatial autocorrelation latent in georeferenced data increases, the amount of duplicate information contained in these data also increases, whether an entire population or some type of random sample drawn from that population is being analyzed, resulting in incorrect sample size calculations being given by conventional power and sample size calculation formulae. Griffith (2005) exploits this context to formulate equations for estimating the necessary sample size needed to obtain some predetermined level of precision for an analysis of georeferenced data when implementing a tessellation stratified random sampling design, labeling this approach model-informed, since a model of latent spatial autocorrelation is required. Spatial autocorrelation is accounted for in these power and sample size calculation equations by using the following spatial statistical model specifications: (1) simultaneous autoregressive; (2) geostatistical semivariogram; and, (3) spatial filter. Sample size results are somewhat sensitive to which model is employed to capture spatial autocorrelation effects. This paper addresses issues of efficiency associated with each of these models in  the presence of spatial autocorrelation effects. It summarizes results  from a set of simulation experiments following experimental design guidelines spelled out by Overton and Stehman (1993) that explore continuous linear, quadratic, and sinusoidal response surfaces. 

Keywords: autoregressive model, geostatistical model, spatial autocorrelation, spatial filter model, spatial sampling

In: Caetano, M. and Painho, M. (eds). Proceedings of the 7th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, 5 – 7 July 2006, Lisboa, Instituto Geográfico Português

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