Hierarchical models for small area estimation using zero-inflated forest inventory variables: comparison and implementation

Abstract

National Forest Inventory (NFI) data are typically limited to sparse networks of sample locations due to cost constraints. While design-based estimators provide reliable forest parameter estimates for large areas, there is increasing interest in model-based small area estimation (SAE) methods to improve precision for smaller spatial, temporal, or biophysical domains. SAE methods can be broadly categorized into area- and unit-level models, with unit-level models offering greater flexibility, making them the focus of this study. Ensuring valid inference requires satisfying model distributional assumptions, which is particularly challenging for NFI variables that exhibit positive support and zero-inflation, such as forest biomass, carbon, and volume. Here, we evaluate nine candidate estimators, including two-stage unit-level hierarchical Bayesian models, single-stage Bayesian models, and two-stage frequentist models, for estimating forest biomass at the county level in Nevada and Washington, United States. Estimator performance is assessed using repeated sampling from simulated populations and unit-level cross-validation with FIA data. Results show that small area estimators incorporating a two-stage approach to account for zero-inflation, county-specific random intercepts and residual variances, and spatial random effects yield the most accurate and well-calibrated county-level estimates, with spatial effects providing the greatest benefits when spatial autocorrelation is present in the underlying population.