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Abstract:
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The design-based and model-based approaches to frequentist statistical inference rest on fundamentally different foundations. In the design-based approach, inference relies on random sampling. In the model-based approach, inference relies on distributional assumptions. We compare the approaches for finite population spatial data. We provide relevant background for the design-based and model-based approaches and then study their performance using simulations and an analysis of real mercury concentration data. We found that regardless of the strength of spatial dependence in the data, sampling plans that incorporate spatial locations (spatially balanced samples) generally outperform sampling plans that ignore spatial locations (non-spatially balanced samples). We also found that model-based approaches tend to outperform design-based approaches, even when the data are skewed. The performance gap between these approaches is small when spatially balanced samples are used but large when non-spatially balanced samples are used. We end by discussing further benefits and drawbacks of each approach, making recommendations for use based on the practitioner's goals.
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