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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

Abstract

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.

Résumé

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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References

Akaike, H., and Krishnaiah, P.R. 1977. On entropy minimization principle. In Applications of statistics. North Holland, Amsterdam. pp. 27−42.
Artuso, R., Bovet, S., and Streilein, A. 2003. Practical Methods for the Verification of Countrywide Terrain and Surface Models. In 3-D Reconstruction from Airborne Laserscanner and InSAR Data. ISPRS Working Group III/3, Dredsen, GER.
Baibing L. 2006. A new approach to cluster analysis: the clustering-function-based method. J. R. Stat. Soc. Series B Stat. Methodol. 68(3): 457–476.
Bechtold, W.A., and Patterson, P.L. 2005. The enhanced forest inventory and analysis program - National sampling design and estimation procedures. Gen. Tech. Rep. SRS-80.
Brändli, U.-B. 2010. Schweizerisches Landesforstinventar. Ergebnisse der dritten Erhebung 2004–2006.
Breidenbach J. and Astrup R. 2012. Small area estimation of forest attributes in the Norwegian National Forest Inventory. Eur. J. For. Res. 131(4): 1255–1267.
Breidt, F.J. 2004. Small area estimation for natural resource surveys. In Monitoring Science & Technology Symposium, Denver, CO.
Burnham, K.P., and Anderson, D.R. 2002. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. 2nd ed. Springer, New York.
Chambers, R.L., and Clark, R.G. 2012. An introduction to model-based survey sampling with applications. Oxford University Press, New York.
Chandra, H., Salvati, N., and Chambers, R. 2007. Small Area Estimation for Spatially Correlated Populations – A Comparison of Direct and Indirect Model-Based Methods. Working Paper.
Chandra H., Salvati N., Chambers R., and Tzavidis N. 2012. Small area estimation under spatial nonstationarity. Comput. Stat. Data Anal. 56(10): 2875–2888.
Chatfield C. 1995. Model Uncertainty, Data Mining and Statistical Inference. J. R. Stat. Soc. Series A Stat. Soc. 158(3): 419–466.
Christensen W.F., Dillner A.M., Schauer J.J., and Reese C.S. 2007. Clustering composition vectors using uncertainty information. Environmetrics, 18(8): 859–869.
Claeskens, G., and Hjort, N.L. 2008. Model selection and model averaging. Cambridge University Press, Cambridge.
Cliff, A.D., and Ord, J.K. 1981. Spatial Processes. Pion, London.
Cochran, W.G. 1977. Sampling techniques. Wiley, New York.
Corona P., Chirici G., and Marchetti M. 2002. Forest ecosystem inventory and monitoring as a framework for terrestrial natural renewable resource survey programmes. Plant Biosyst. 136(1): 69–82.
Cressie, N.A.C. 1993. Statistics for spatial data. Revised edition. 2nd ed. Wiley, New York.
Datta D.S. and Lahiri P. 2000. A unified measure of uncertainty of estimated best linear unbiased predictors in small area estimation problems. Stat. Sin. 10(2): 613–627.
Datta, G.S. 2009. Chapter 32 − Model-Based Approach to Small Area Estimation. In Handbook of Statistics. Edited by C.R. Rao. Elsevier. pp. 251−288.
Datta G.S., Hall P., and Mandal A. 2011. Model Selection by Testing for the Presence of Small-Area Effects, and Application to Area-Level Data. J. Am. Stat. Assoc. 106(493): 362–374.
Deville J.-C. 1999. Variance estimation for complex statistics and estimators: Linearization and residual techniques. Surv. Meth. 25(2): 193–203.
Draper D. 1995. Assessment and propagation of model uncertainty. J. R. Stat. Soc. Series B Stat. Methodol. 57(1): 45–97.
Draper, N.R., and Smith, H. 1981. Applied Regression Analysis. Wiley, New York.
Estevao V.M. and Särndal C.-E. 2004. Borrowing strength is not the best technique within a wide class of design-consistent domain estimators. J. Off. Stat. 20(4): 645–669.
Everitt, B.S., Landau, S., and Leese, M. 2001. Cluster Analysis. 4th ed. Arnold, London.
Faes C., Molenberghs G., Aerts M., Verbeke G., and Kenward M.G. 2009. The Effective Sample Size and an Alternative Small-Sample Degrees-of-Freedom Method. Am. Stat. 63(4): 389–399.
Freeman E. and Moisen G. 2007. Evaluating Kriging as a Tool to Improve Moderate Resolution Maps of Forest Biomass. Environ. Monit. Assess. 128(1): 395–410.
Fuller W.A. 1975. Regression analysis for sample survey. Sankhya, 37(3): 117–132.
Fuller, W.A. 2009. Sampling Statistics. Wiley, New York.
Gallaun H., Zanchi G., Nabuurs G.J., Hengeveld G., Schardt M., and Verkerk P.J. 2010. EU-wide maps of growing stock and above-ground biomass in forests based on remote sensing and field measurements. For. Ecol. Manage. 260(3): 252–261.
Ghosh M. and Rao J.N.K. 1994. Small area estimation: an appraisal. Stat. Sci. 9: 55–93.
Gillespie A.J. 1999. Rationale for a national annual forest inventory program. J. For. 97(12): 16–20.
Gjertsen, A.K., Tomppo, E., and Tomter, S. 1999. National forest inventory in Norway: Using sample plots, digital maps, and satellite images. In. IEEE.
Goerndt M.E., Monleon V.J., and Temesgen H. 2011. A comparison of small-area estimation techniques to estimate selected stand attributes using LiDAR-derived auxiliary variables. Can. J. For. Res. 41(6): 1189–1201.
Goerndt M.E., Monleon V.J., and Temesgen H. 2013. Small-Area Estimation of County-Level Forest Attributes Using Ground Data and Remote Sensed Auxiliary Information. For. Sci. 59(5): 536–548.
Gregoire T.G. 1998. Design-based and model-based inference in survey sampling: Appreciating the difference. Can. J. For. Res. 28(10): 1429–1447.
Hansen, M.H., Hurwitz, W.N., and Madow, W.G. 1953. Sample survey methods and theory. John Wiley, New York.
Hastie T., Tibshirani R., Friedman J., and Franklin J. 2005. The elements of statistical learning: data mining, inference and prediction. Math. Intel. 27(2): 83–85.
Holm S. 1979. A simple sequentially rejective multiple test procedure. Scand. J. Stat. 6: 65–70.
Jiang J. and Lahiri P. 2006a. Estimation of finite population domain means: A model-assisted empirical best prediction approach. J. Am. Stat. Assoc. 101(473): 301–311.
Jiang J. and Lahiri P. 2006b. Mixed Model Prediction and Small Area Estimation. Test, 15(1): 1–96.
Jiang J., Nguyen T., and Rao J.S. 2011. Best Predictive Small Area Estimation. J. Am. Stat. Assoc. 106(494): 732–745.
Kangas A. 1996. Small-area estimates using model-based methods. Can. J. For. Res. 26(5): 758–766.
Katila M. 2006. Empirical errors of small area estimates from the multisource national forest inventory in eastern Finland. Silv. Fenn. 40(4): 729–742.
Katila, M., and Tomppo, E. 2006. Sampling, simulation on multi-source output forest maps − an application for small areas. Edited by M.E. Caetano and M. Painho. Portugese Geographic Institute, Lisbon.
Kaufmann, E. 1999. Vorrat, Zuwachs, Nutzung. In Schweiyerisches Landesforstinventar − Methoden und Modelle der Zweitaufnahme 1993−1995. Edited by P. Brassel and H. Lischke. Eidgenössissche Forschungsanstalt Wald Schnee Landschaft, Birmensdorf. pp. 162−196.
Lehtonen, R., and Veijanen, A. 2009. Design-based Methods of Estimation for Domains and Small Areas. In Handbook of Statistics. Edited by C.R. Rao. Elsevier. pp. 219−249.
Lehtonen R. and Vejanen A. 2012. Small area poverty estimation by model calibration. J. Indian Soc. Agric. Stat. 66(1): 125–133.
Lehtonen R., Särndal C.-E., and Veijanen A. 2003. The effect of model choice in estimation for domains, including small domains. Surv. Meth. 29(1): 33–44.
Lehtonen R., Särndal C.-E., and Veijanen A. 2005. Does the model Matter? Comparing model-Assisted and Model-Dependent estimators of class frequencies for domains. Statistics in Transition, 7(3): 649–673.
Little R.J.A. 2004. To model or not to model? Competing modes of inference for finite population sampling. J. Am. Stat. Assoc. 99(466): 546–556.
Lohr S.L. and Prasad N.G.N. 2003. Small area estimation with auxiliary survey data. Can. J. Stat. 31(4): 383–396.
Longford, N.T. 2005. Missing data and small-area estimation. Springer, New York.
Magnussen S., Naesset E., and Gobakken T. 2013. Prediction of tree-size distributions and inventory variables from cumulants of canopy height distributions. Forestry, 86(5): 583–595.
Maltamo M., Packalén P., Suvanto A., Korhonen K.T., Mehtätalo L., and Hyvönen P. 2009. Combining ALS and NFI training data for forest management planning: A case study in Kuortane, Western Finland. Eur. J. For. Res. 128(3): 305–317.
Mandallaz, D. 2008. Sampling techniques for forest inventories. Chapman and Hall, Boca Raton, Florida.
Mandallaz D. 2013. Design-based properties of some small-area estimators in forest inventory with two-phase sampling. Can. J. For. Res. 43(5): 441–449.
Mandallaz D., Breschan J., and Hill A. 2013. New regression estimators in forest inventories with two-phase sampling and partially exhaustive information: a design-based Monte Carlo approach with applications to small-area estimation. Can. J. For. Res. 43(11): 1023–1031.
Mayr A., Fenske N., Hofner B., Kneib T., and Schmid M. 2012. Generalized additive models for location, scale and shape for high dimensional data-a flexible approach based on boosting. J. R. Stat. Soc. Series C Appl. Stat. 61(3): 403–427.
McRoberts R.E. 2011. Estimating forest attribute parameters for small areas using nearest neighbors techniques. For. Ecol. Manage. 272: 3–12.
McRoberts R.E. and Tomppo E.O. 2007. Remote sensing support for national forest inventories. Remote Sens. Environ. 110: 412–419.
McRoberts R.E., Tomppo E.O., and Næsset E. 2010. Advances and emerging issues in national forest inventories. Scand. J. For. Res. 25(4): 368–381.
Molina E.A., Smith T.M.F., and Sugden R.A. 2001. Modelling Overdispersion for Complex Survey Data. Int. Stat. Rev. 69(3): 373–384.
Molina I., Salvati N., and Pratesi M. 2009. Bootstrap for estimating the MSE of the spatial EBLUP. Comput. Stat. 24(3): 441–458.
Olsen A.R., Sedransk J., Edwards D., Gotway C.A., Liggett W., Rathburn S., Reckhow K.H., and Young L.J. 1999. Statistical issues for monitoring ecological and natural resources in the United States. Environ. Monit. Assess. 54: 1–45.
Opsomer J.D., Claeskens G., Ranalli M.G., Kauermann G., and Breidt F.J. 2008. Non-parametric small area estimation using penalized spline regression. J. R. Stat. Soc. Series B Stat. Methodol. 70(1): 265–286.
Pawitan Y., Calza S., and Ploner A. 2006. Estimation of false discovery proportion under general dependence. Bioinformatics, 22(24): 3025–3031.
Petrucci A., Pratesi M., and Salvati N. 2005. Geographic information in small area estimation: Small area models and spatially correlated random area effects. Statistics in Transition, 7(3): 609–623.
Pfeffermann D. 2002. Small area estimation - New developments and directions. Int. Stat. Rev. 70(1): 125–143.
Pfeffermann D. 2013. New important developments in small area estimation. Stat. Sci. 28: 40–68.
Pinheiro, J.C., and Bates, D.M. 2000. Mixed-effects models in S and S-plus. Springer, New York.
Pratesi M. and Salvati N. 2008. Small area estimation: the EBLUP estimator based on spatially correlated random area effects. Stat. Methods Appl. 17(1): 113–141.
Rao, J.N.K. 2003. Small area estimation. Wiley & Sons, Hoboken, New Jersey.
Royall, R. 2003. Interpreting a sample as evidence about a finite population. In Analysis of survey data. Edited by R.L. Chambers and C.J. Skinner. Wiley, Chichester. pp. 59−72.
Saei, A., and Chambers, R. 2003. Small area estimation: A review of methodsbased on the application of mixed models. Southampton Statistical Sciences Research Institute.
Salvati N., Tzavidis N., Pratesi M., and Chambers R. 2012. Small area estimation via M-quantile geographically weighted regression. Test, 21(1): 1–28.
Särndal C.-E. 2007. The calibration approach in survey theory and practice. Surv. Meth. 33(2): 99–119.
Särndal, C.E., Swensson, B., and Wretman, J. 1992. Model assisted survey sampling. Springer-Verlag, New York.
Shen X.T., Huang H.C., and Ye J. 2004. Inference after model selection. J. Am. Stat. Assoc. 99(467): 751–762.
Singh, A.C., and Yuan, P. 2010. Building-block BLUPs for aggregate level small area estimation for survey data. In Joint Statistical Meeting. American Statistical Association. p. 14.
Singh B.B., Shukla G.K., and Kundu D. 2005. Spatio-temporal models in small area estimation. Surv. Meth. 31(2): 183–195.
Sperlich S. and José Lombardía M. 2010. Local polynomial inference for small area statistics: estimation, validation and prediction. J. Nonparametr. Stat. 22(5): 633–648.
Ståhl G., Allard A., Esseen P.A., Glimskär A., Ringvall A., Svensson J., Sundquist S., Christensen P., Torell Å.G., Högström M., Lagerqvist K., Marklund L., Nilsson B., and Inghe O. 2011. National Inventory of Landscapes in Sweden (NILS)-scope, design, and experiences from establishing a multiscale biodiversity monitoring system. Env. Monit. Assess. 173(1–4): 579–595.
Steinmann K., Mandallaz D., Ginzler C., and Lanz A. 2013. Small area estimations of proportion of forest and timber volume combining Lidar data and stereo aerial images with terrestrial data. Scand. J. For. Res. 28(4): 373–385.
Tomppo, E. 1991. Satellite image-based national forest inventory of Finland. In Proceedings of the symposium on global and environmental monitoring, techniques and impacts. ISPRS, Victoria BC. pp. 419−424.
Tomppo E., Olsson H., Stahl G., Nilsson M., Hagner O., and Katila M. 2008. Combining national forest inventory field plots and remote sensing data for forest databases. Remote Sens. Environ. 112(5): 1982–1999.
Tomppo, E., Gschwantner, T., Lawrence, M., McRoberts, R., Gabler, K., Schadauer, K., Vidal, C., Lanz, A., Ståhl, G., and Cienciala, E. 2010. National Forest Inventories. In Pathways for Common Reporting. European Science Foundation.
Vaida F. and Blanchard S. 2005. Conditional Akaike information for mixed-effects models. Biometrika, 92(2): 351–370.
Vanclay J.K. and Skovsgaard J.P. 1997. Evaluating forest growth models. Ecol. Model. 98(1): 1–12.
Wald A. 1941. Asymptotically most powerful test of statistical hypotheses. Ann. Math. Stat. 12: 1–19.
Wolfram, S. 1999. The Mathematica Book. Wolfram Media/Cambridge University Press, Champaign, IL.
Wu C.B. 2003. Optimal calibration estimators in survey sampling. Biometrika, 90(4): 937–951.
Wulder M.A., White J.C., Nelson R.F., Næsset E., Ørka H.O., Coops N.C., Hilker T., Bater C.W., and Gobakken T. 2012. Lidar sampling for large-area forest characterization: A review. Remote Sens. Environ. 121(0): 196–209.

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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

History

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

Mots-clés

  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

Authors

Affiliations

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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