A method to combine non-probability sample data with probability sample data in estimating spatial means of...

Area of Science:

• Environmental science
• Spatial statistics
• Geostatistics

Background:

• Estimating spatial means of environmental variables often relies on convenience or purposive sampling, which can compromise validity.
• Probability sampling can ensure validity but may be resource-intensive.

Purpose of the Study:

• To improve the precision of spatial mean estimators when using probability sampling.
• To investigate methods for incorporating non-probability sample data into spatial estimation frameworks.

Main Methods:

• Utilized probability sampling to ensure data validity.
• Employed interpolation techniques to transfer values from non-probability sample points to probability sample points.
• Applied difference and regression estimators using interpolated values as auxiliary variables.

Main Results:

• The proposed estimators are approximately unbiased, even with biased non-probability samples (e.g., preferential samples).
• Precision gains depend on the correlation between the target variable and the interpolated variable, influenced by non-probability sample density, coverage, and spatial continuity.
• Case studies showed significant precision improvements, with variance ratios of 0.68 and 0.80 for moderate and strong spatial clustering, respectively.

Conclusions:

• Combining probability and non-probability sampling with interpolation offers a robust approach to enhance spatial mean estimation.
• The regression estimator demonstrated substantial precision gains over the pi estimator, particularly with clustered non-probability samples.