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National forest inventories in the service of small area estimation of stem volume

Publication: Canadian Journal of Forest Research
12 May 2014


This study introduces five facets that can improve inference in small area estimation (SAE) problems: (1) model groups, (2) test of area effects, (3) conditional EBLUPs, (4) model selection, and (5) model averaging. Two contrasting case studies with data from the Swiss and Norwegian national forest inventories demonstrate the five facets. The target variable of interest was mean stem volume per hectare on forested land in 108 Swiss forest districts (FD) and in 14 Norwegian municipalities (KOM) in the County of Vestfold. Auxiliary variables from airborne laser scanning (Switzerland) and photogrammetric point clouds (Vestfold) with full coverage and a resolution of 25 m × 25 m (Switzerland) and 16 m × 16 m (Vestfold) were available. Only the data metric mean canopy height was statistically significant. Ten linear fixed-effects models and three mixed linear models were assessed. Area effects were statistically significant in the Swiss case but not in Vestfold case. A model selection based on AIC favored separate linear regression models for each FD and a single common regression model in Vestfold. Model averaging increased, on average, an estimated variance by 15%. Reported estimates of uncertainty were consistently larger than corresponding unconditional EBLUPs.


Cette étude présente cinq aspects qui peuvent améliorer l’inférence dans les cas d’estimations pour de petites régions géographiques: (1) les groupes de modèles; (2) les tests de l’effet de région; (3) les meilleures prédictions empiriques linéaires sans biais (EBLUP) conditionnelles; (4) la sélection de modèles; et (5) la combinaison de modèles. Deux études de cas contrastantes, utilisant des données des inventaires forestiers nationaux de la Suisse et de la Norvège sont utilisées pour démontrer ces cinq aspects. La variable d’intérêt ciblée était le volume moyen à l’hectare par tige des terrains forestiers de 108 Districts forestiers (DF) de la Suisse et de 14 municipalités du Comté de Vestfold en Norvège. Des variables auxiliaires provenant de couvertures complètes de balayage laser aéroporté (Suisse) et de nuages de points photogrammétriques (Vestfold), avec une résolution de 25 m × 25 m (Suisse) et de 16 m × 16 m (Vestfold) étaient disponibles. La hauteur moyenne du couvert forestier était la seule donnée métrique statistiquement significative. Dix modèles linéaires à effets fixes et trois modèles linéaires mixtes ont été évalués. Les effets de région étaient statistiquement significatifs dans le cas de la Suisse mais pas dans le cas du Vestfold. Une sélection de modèle sur la base du critère d’information d’Akaike a préféré des modèles de régression linéaires séparés pour chaque DF, mais un seul modèle de régression commun pour le Vestfold. La combinaison de modèles a augmenté la variance estimée de 15 % en moyenne. Les estimations d’incertitude rapportées étaient toujours plus grandes que les meilleures prédictions empiriques linéaires sans biais non conditionnelles correspondantes. [Traduit par la Rédaction]

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Published In

cover image Canadian Journal of Forest Research
Canadian Journal of Forest Research
Volume 44Number 9September 2014
Pages: 1079 - 1090


Received: 30 October 2013
Accepted: 9 May 2014
Accepted manuscript online: 12 May 2014
Version of record online: 12 May 2014


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Key Words

  1. model groups
  2. tests of area effect
  3. model selection
  4. model averaging
  5. conditional EBLUP


  1. groupes de modèles
  2. tests de l’effet de région
  3. sélection de modèles
  4. combinaison de modèles
  5. meilleure prédiction empirique linéaire sans biais (EBLUP) conditionnelle



Steen Magnussen
Natural Resources Canada, Canadian Forest Service, 506 West Burnside Road, Victoria, BC V8Z 1M5, Canada.
Daniel Mandallaz
Chair of Land Use Engineering, ETH Zurich, CH 8092 Zurich, Switzerland.
Johannes Breidenbach
Norwegian Forest and Landscape Institute, Postboks 115, 1431 Ås, Norway.
Adrian Lanz
Swiss Federal Research Institute, WSL, Zürcherstrasse 111, 8903 Birmensdorf ZH, Switzerland.
Christian Ginzler
Swiss Federal Research Institute, WSL, Zürcherstrasse 111, 8903 Birmensdorf ZH, Switzerland.

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