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

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Title: Hierarchical models for small area estimation using zero-inflated forest inventory variables: comparison and implementation.
Authors: White, Grayson W.1,2,3 (AUTHOR) gwhite@reed.edu, Finley, Andrew O.1,2 (AUTHOR), Yamamoto, Josh K.4 (AUTHOR), Green, Jennifer L.2 (AUTHOR), Frescino, Tracey S.5 (AUTHOR), MacFarlane, David W.1 (AUTHOR), Andersen, Hans-Erik6 (AUTHOR), Domke, Grant M.7 (AUTHOR)
Source: Canadian Journal of Forest Research. 4/9/2026, Vol. 56, p1-17. 17p.
Subject Terms: *Biomass estimation, *Forest surveys, Small area statistics, Frequentist statistics, Spatial variation, Statistics, Multilevel models, Bayesian analysis
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. [ABSTRACT FROM AUTHOR]
Copyright of Canadian Journal of Forest Research is the property of Canadian Science Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Hierarchical models for small area estimation using zero-inflated forest inventory variables: comparison and implementation.
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  Data: <searchLink fieldCode="AR" term="%22White%2C+Grayson+W%2E%22">White, Grayson W.</searchLink><relatesTo>1,2,3</relatesTo> (AUTHOR)<i> gwhite@reed.edu</i><br /><searchLink fieldCode="AR" term="%22Finley%2C+Andrew+O%2E%22">Finley, Andrew O.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Yamamoto%2C+Josh+K%2E%22">Yamamoto, Josh K.</searchLink><relatesTo>4</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Green%2C+Jennifer+L%2E%22">Green, Jennifer L.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Frescino%2C+Tracey+S%2E%22">Frescino, Tracey S.</searchLink><relatesTo>5</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22MacFarlane%2C+David+W%2E%22">MacFarlane, David W.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Andersen%2C+Hans-Erik%22">Andersen, Hans-Erik</searchLink><relatesTo>6</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Domke%2C+Grant+M%2E%22">Domke, Grant M.</searchLink><relatesTo>7</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Canadian+Journal+of+Forest+Research%22">Canadian Journal of Forest Research</searchLink>. 4/9/2026, Vol. 56, p1-17. 17p.
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  Data: *<searchLink fieldCode="DE" term="%22Biomass+estimation%22">Biomass estimation</searchLink><br />*<searchLink fieldCode="DE" term="%22Forest+surveys%22">Forest surveys</searchLink><br /><searchLink fieldCode="DE" term="%22Small+area+statistics%22">Small area statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Frequentist+statistics%22">Frequentist statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Spatial+variation%22">Spatial variation</searchLink><br /><searchLink fieldCode="DE" term="%22Statistics%22">Statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Multilevel+models%22">Multilevel models</searchLink><br /><searchLink fieldCode="DE" term="%22Bayesian+analysis%22">Bayesian analysis</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: 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. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Canadian Journal of Forest Research is the property of Canadian Science Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1139/cjfr-2025-0175
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      – Code: eng
        Text: English
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        PageCount: 17
        StartPage: 1
    Subjects:
      – SubjectFull: Biomass estimation
        Type: general
      – SubjectFull: Forest surveys
        Type: general
      – SubjectFull: Small area statistics
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      – SubjectFull: Frequentist statistics
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      – SubjectFull: Spatial variation
        Type: general
      – SubjectFull: Statistics
        Type: general
      – SubjectFull: Multilevel models
        Type: general
      – SubjectFull: Bayesian analysis
        Type: general
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      – TitleFull: Hierarchical models for small area estimation using zero-inflated forest inventory variables: comparison and implementation.
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              Text: 4/9/2026
              Type: published
              Y: 2026
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