Empirical evaluation of confidence and prediction intervals for spatial models of forest structure in Jalisco, Mexico

Abstract

In recent years there has been an increasing interest in developing spatial statistical models for data sets that are seemingly spatially independent. This lack of spatial structure makes it difficult, if not impossible to use optimal predictors such as ordinary kriging for modeling the spatial variability in the data. In many instances, the data still contain a wealth of information that could be used to gain flexibility and precision in estimation. In this paper we propose using a combination of regression analysis to describe the large-scale spatial variability in a set of survey data and a tree-based stratification design to enhance the estimation process of the small-scale spatial variability. With this approach, sample units (i.e., pixel of a satellite image) are classified with respect to predictions of error attributes into homogeneous classes, and the classes are then used as strata in the stratified analysis. Independent variables used as a basis of stratification included terrain data and satellite imagery. A decision rule was used to identify a tree size that minimized the error in estimating the variance of the mean response and prediction uncertainties at new spatial locations. This approach was applied to a set of n=937 forested plots from a state-wide inventory conducted in 2006 in the Mexican State of Jalisco. The final models accounted for 62% to 82% of the variability observed in canopy closure (%), basal area (m²·ha⁻¹), cubic volumes (m³·ha⁻¹) and biomass (t·ha⁻¹) on the sample plots. The spatial models provided unbiased estimates and when averaged over all sample units in the population, estimates of forest structure were very close to those obtained using classical estimates based on the sampling strategy used in the state-wide inventory. The spatial models also provided unbiased estimates of model variances leading to confidence and prediction coverage rates close to the 0.95 nominal rate.

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