Improving Estimates of Natural Resources Using Model-Based Estimators: Impacts of Sample Design, Estimation Technique, and Strengths of Association

Abstract

Natural resource managers need accurate depictions of existing resources to make informed decisions. The classical approach to describing resources for a given area in a quantitative manner uses probabilistic sampling and design-based inference to estimate population parameters. While probabilistic designs are accepted as being necessary for design-based inference, many recent studies have adopted non-probabilistic designs that do not include elements of random selection or balance and have relied on models to justify inferences. While common, model-based inference alone assumes that a given model accurately depicts the relationship between response and predictors across all populations. Within complex systems, this assumption can be difficult to justify. Alternatively, models can be trained to a given population by adopting design-based principles such as balance and spread. Through simulation, we compare estimates of population totals and pixel-level values using linear and nonlinear model-based estimators for multiple sample designs that balance and spread sample units. The findings indicate that model-based estimators derived from samples spread and balanced across predictor variable space reduce the variability of population and unit-level estimators. Moreover, if samples achieve approximate balance over feature space, then model-based estimates of population totals approached simple expansion-based estimates of totals. Finally, in all comparisons made, improvements in estimation were achieved using model-based estimation over design-based estimation alone. Our simulations suggest that samples drawn from a probabilistic design, that are spread and balanced across predictor variable space, improve estimation accuracy.

Keywords

• sample design
• model-based estimation
• spread
• balance