Abstract
National forest inventories in many countries combine expensive ground plot data with remotely-sensed information to improve precision in estimators of forest parameters. A simple post-stratified estimator is often the tool of choice because it has known statistical properties, is easy to implement, and is intuitive to the many users of inventory data. Because of the increased availability of remotely-sensed data with improved spatial, temporal, and thematic resolutions, there is a need to equip the inventory community with a more diverse array of statistical estimators. Focusing on generalized regression estimators, we step the reader through seven estimators including: Horvitz Thompson, ratio, post-stratification, regression, lasso, ridge, and elastic net. Using forest inventory data from Daggett county in Utah, USA as an example, we illustrate how to construct, as well as compare the relative performance of, these estimators. Augmented by simulations, we also show how the standard variance estimator suffers from greater negative bias than the bootstrap variance estimator, especially as the size of the assisting model grows. Each estimator is made readily accessible through the new R package, mase. We conclude with guidelines in the form of a decision tree on when to use which an estimator in forest inventory applications.
Highlights
The US Forest Service Forest Inventory and Analysis Program (FIA) is tasked with monitoring status and trends in forested ecosystems across the U.S It provides estimates of numerous forest attributes in a variety of domains, such as county, state, and regional levels
Here we describe building the post-stratified estimator based on a single categorical variable, the strata can be created by binning a mix of quantitative and categorical variables
Model selection is appropriate under a logistic model and the elastic net (LENET), lasso (LLASSO), or ridge (LRIDGE) penalization can be added to the criterion for the logistic regression coefficient estimates
Summary
The US Forest Service Forest Inventory and Analysis Program (FIA) is tasked with monitoring status and trends in forested ecosystems across the U.S It provides estimates of numerous forest attributes in a variety of domains, such as county, state, and regional levels. Using only the FIA plot data, it is possible to construct unbiased estimators for the forest attributes of interest Such estimators potentially suffer from a large degree of variability, especially when the number of ground plots in the domain of interest is small. Similar to the use of penalized regression in the predictive modeling approach, penalized methods have been introduced in the calibration literature [16,17,18] and applied to forest inventory data [19]. See [34] for more details on the multi-phase regression estimator and [35] for the post-stratified estimator employed by forestinventory Another software option is the survey package which contains a large collection of estimation techniques, including the regression estimator and allows for a wide variety of sampling designs [36,37].
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