An estimation strategy to protect against over-estimating precision in a LiDAR-based prediction of a stand mean

https://doi.org/10.17221/120/2018-JFSCitation:Magnussen S. (2018): An estimation strategy to protect against over-estimating precision in a LiDAR-based prediction of a stand mean. J. For. Sci., 64: 497-505.
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A prediction of a forest stand mean may be biased and its estimated variance seriously underestimated when a model fitted for an ensemble of stands (stratum) does not hold for a specific stand. When the sampling design cannot support a stand-level lack-of-fit analysis, an analyst may opt to seek a protection against a possibly serious over-estimation of precision in a predicted stand mean. This study propose an estimation strategy to counter this risk by an inflation of the standard model-based estimator of variance when model predictions suggest non-trivial random stand effects, a spatial distance-dependent autocorrelation in model predictions, or both. In a simulation study, the strategy performed well when it was most needed, but equally over-inflated variance in settings where less protection was appropriate.

References:
Binder David A. (1983): On the Variances of Asymptotically Normal Estimators from Complex Surveys. International Statistical Review / Revue Internationale de Statistique, 51, 279- https://doi.org/10.2307/1402588
 
Black P.E. (2006): Manhattan distance. Available at https://www.nist.gov/dads/HTML/manhattanDistance.html (accessed Sept 6, 2018).
 
Breidenbach Johannes, Astrup Rasmus (2012): Small area estimation of forest attributes in the Norwegian National Forest Inventory. European Journal of Forest Research, 131, 1255-1267 https://doi.org/10.1007/s10342-012-0596-7
 
Breidenbach Johannes, McRoberts Ronald E., Astrup Rasmus (2016): Empirical coverage of model-based variance estimators for remote sensing assisted estimation of stand-level timber volume. Remote Sensing of Environment, 173, 274-281 https://doi.org/10.1016/j.rse.2015.07.026
 
Breidenbach Johannes, Magnussen Steen, Rahlf Johannes, Astrup Rasmus (2018): Unit-level and area-level small area estimation under heteroscedasticity using digital aerial photogrammetry data. Remote Sensing of Environment, 212, 199-211 https://doi.org/10.1016/j.rse.2018.04.028
 
Breidenbach J., Kublin E., McGaughey R., Andersen H.E., Reutebuch S. (2008): Mixed-effects models for estimating stand volume by means of small footprint airborne laser scanner data. Photogrammetric Journal of Finland, 21: 4–15.
 
Chambers R.L. (2011): Which sample survey strategy? A review of three different approaches. Pakistan Journal of Statistics, 27: 337–357.
 
Chambers R.L., Clark R.G. (2012): An Introduction to Model-based Survey Sampling with Applications. New York, Oxford University Press: 265.
 
Chilès J.P., Delfiner P. (1999): Geostatistics: Modeling Spatial Uncertainty. New York, Wiley: 695.
 
Claeskens G., Hjort N.L. (2008): Model Selection and Model Averaging. Cambridge, Cambridge University Press: 332.
 
Czaplewski R.L., Reich R.M., Bechtold W.A. (1994): Spatial autocorrelation in growth of undisturbed natural pine stands across Georgia. Forest Science, 40: 314–328.
 
Dai Wen (2004): Asymptotics of the sample mean and sample covariance of long-range-dependent series. Journal of Applied Probability, 41, 383-392 https://doi.org/10.1239/jap/1082552213
 
Donner Allan (1986): A Review of Inference Procedures for the Intraclass Correlation Coefficient in the One-Way Random Effects Model. International Statistical Review / Revue Internationale de Statistique, 54, 67- https://doi.org/10.2307/1403259
 
Draper N.R., Smith H. (1998): Applied Regression Analysis. New York, Wiley: 736.
 
Fernández-Landa Alfredo, Fernández-Moya Jesús, Tomé Jose Luis, Algeet-Abarquero Nur, Guillén-Climent María Luz, Vallejo Roberto, Sandoval Vicente, Marchamalo Miguel (2018): High resolution forest inventory of pure and mixed stands at regional level combining National Forest Inventory field plots, Landsat, and low density lidar. International Journal of Remote Sensing, 39, 4830-4844 https://doi.org/10.1080/01431161.2018.1430406
 
Finley Andrew O., Banerjee Sudipto, Ek Alan R., McRoberts Ronald E. (2008): Bayesian multivariate process modeling for prediction of forest attributes. Journal of Agricultural, Biological, and Environmental Statistics, 13, 60-83 https://doi.org/10.1198/108571108X273160
 
Finley Andrew O., Banerjee Sudipto, Waldmann Patrik, Ericsson Tore (2009): Hierarchical Spatial Modeling of Additive and Dominance Genetic Variance for Large Spatial Trial Datasets. Biometrics, 65, 441-451 https://doi.org/10.1111/j.1541-0420.2008.01115.x
 
Fortin Mathieu, Manso Rubén, Calama Rafael (2016): Hybrid estimation based on mixed-effects models in forest inventories. Canadian Journal of Forest Research, 46, 1310-1319 https://doi.org/10.1139/cjfr-2016-0298
 
Grafström Anton, Ringvall Anna Hedström (2013): Improving forest field inventories by using remote sensing data in novel sampling designs. Canadian Journal of Forest Research, 43, 1015-1022 https://doi.org/10.1139/cjfr-2013-0123
 
Gregoire Timothy G., Næsset Erik, McRoberts Ronald E., Ståhl Göran, Andersen Hans-Erik, Gobakken Terje, Ene Liviu, Nelson Ross (2016): Statistical rigor in LiDAR-assisted estimation of aboveground forest biomass. Remote Sensing of Environment, 173, 98-108 https://doi.org/10.1016/j.rse.2015.11.012
 
Gupta A.K., Nagar D.K. (1999): Matrix Variate Distributions. Boca Raton, Chapman & Hall/CRC: 384.
 
Harvey A.C. (1981): Time Series Models. Oxford, Phillip Allan: 229.
 
Hausman J. A. (1978): Specification Tests in Econometrics. Econometrica, 46, 1251- https://doi.org/10.2307/1913827
 
Hodges James S., Reich Brian J. (2010): Adding Spatially-Correlated Errors Can Mess Up the Fixed Effect You Love. The American Statistician, 64, 325-334 https://doi.org/10.1198/tast.2010.10052
 
Holm S. (1979): A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6: 65–70.
 
Hughes John, Haran Murali (2013): Dimension reduction and alleviation of confounding for spatial generalized linear mixed models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 75, 139-159 https://doi.org/10.1111/j.1467-9868.2012.01041.x
 
Johnston J., DiNardo J. (1997): Econometric Methods. New York, McGraw-Hill: 480.
 
Junttila Virpi, Finley Andrew O., Bradford John B., Kauranne Tuomo (2013): Strategies for minimizing sample size for use in airborne LiDAR-based forest inventory. Forest Ecology and Management, 292, 75-85 https://doi.org/10.1016/j.foreco.2012.12.019
 
Kangas Annika, Myllymäki Mari, Gobakken Terje, Næsset Erik (2016): Model-assisted forest inventory with parametric, semiparametric, and nonparametric models. Canadian Journal of Forest Research, 46, 855-868 https://doi.org/10.1139/cjfr-2015-0504
 
Kangas Annika, Astrup Rasmus, Breidenbach Johannes, Fridman Jonas, Gobakken Terje, Korhonen Kari T., Maltamo Matti, Nilsson Mats, Nord-Larsen Thomas, Næsset Erik, Olsson Håkan (2017): Remote sensing and forest inventories in Nordic countries – roadmap for the future. Scandinavian Journal of Forest Research, 33, 397-412 https://doi.org/10.1080/02827581.2017.1416666
 
Kessy Agnan, Lewin Alex, Strimmer Korbinian (2018): Optimal Whitening and Decorrelation. The American Statistician, 72, 309-314 https://doi.org/10.1080/00031305.2016.1277159
 
Köhl M., Magnussen S. (2014): Sampling in forest inventories. In: Köhl M., Pancel L. (eds): Tropical Forestry Handbook. Berlin, Heidelberg, Springer: 1–50.
 
Magnussen S. (2001): Fast pre-survey computation of the mean spatial autocorrelation in large plots composed of a regular array of secondary sampling units. Mathematical Modelling and Scientific Computing, 13: 204–217.
 
Magnussen Steen (2017): A New Mean Squared Error Estimator for a Synthetic Domain Mean. Forest Science, 63, 1-9 https://doi.org/10.5849/forsci.16-056
 
Magnussen Steen, Breidenbach Johannes (2017): Model-dependent forest stand-level inference with and without estimates of stand-effects. Forestry: An International Journal of Forest Research, 90, 675-685 https://doi.org/10.1093/forestry/cpx023
 
Magnussen Steen, Breidenbach Johannes, Mauro Fransisco (2017): The challenge of estimating a residual spatial autocorrelation from forest inventory data. Canadian Journal of Forest Research, 47, 1557-1566 https://doi.org/10.1139/cjfr-2017-0247
 
Magnussen S., Frazer G., Penner M. (2016a): Alternative mean-squared error estimators for synthetic estimators of domain means. Journal of Applied Statistics, 43: 2550–2573.
 
Magnussen S., Mandallaz D., Lanz A., Ginzler C., Næsset E., Gobakken T. (2016b): Scale effects in survey estimates of proportions and quantiles of per unit area attributes. Forest Ecology and Management, 364: 122–129.
 
Maltamo Matti, Mehtätalo Lauri, Vauhkonen Jari, Packalén Petteri (2012): Predicting and calibrating tree attributes by means of airborne laser scanning and field measurements. Canadian Journal of Forest Research, 42, 1896-1907 https://doi.org/10.1139/x2012-134
 
Maltamo M., Bollandsas O. M., Vauhkonen J., Breidenbach J., Gobakken T., Naesset E. (2010): Comparing different methods for prediction of mean crown height in Norway spruce stands using airborne laser scanner data. Forestry, 83, 257-268 https://doi.org/10.1093/forestry/cpq008
 
Mauro F., Monleon V.J., Temesgen H., Ruiz L.A. (2017): Analysis of spatial correlation in predictive models of forest variables that use LiDAR auxiliary information. Canadian Journal of Forest Research, 47, 788-799 https://doi.org/10.1139/cjfr-2016-0296
 
Mauro F., Molina I., García-Abril A., Valbuena R., Ayuga-Téllez E. (2016): Remote sensing estimates and measures of uncertainty for forest variables at different aggregation levels. Environmetrics, 27, 225-238 https://doi.org/10.1002/env.2387
 
Meini Beatrice (2004): The Matrix Square Root from a New Functional Perspective: Theoretical Results and Computational Issues. SIAM Journal on Matrix Analysis and Applications, 26, 362-376 https://doi.org/10.1137/S0895479803426656
 
Melville Gavin, Stone Christine, Turner Russell (2015): Application of LiDAR data to maximise the efficiency of inventory plots in softwood plantations. New Zealand Journal of Forestry Science, 45, - https://doi.org/10.1186/s40490-015-0038-7
 
Næsset Erik (2007): Practical large-scale forest stand inventory using a small-footprint airborne scanning laser. Scandinavian Journal of Forest Research, 19, 164-179 https://doi.org/10.1080/02827580310019257
 
Nanos Nikos, Calama Rafael, Montero Gregorio, Gil Luis (2004): Geostatistical prediction of height/diameter models. Forest Ecology and Management, 195, 221-235 https://doi.org/10.1016/j.foreco.2004.02.031
 
Paciorek Christopher J. (2010): The Importance of Scale for Spatial-Confounding Bias and Precision of Spatial Regression Estimators. Statistical Science, 25, 107-125 https://doi.org/10.1214/10-STS326
 
Rao J., Hidiroglou M. (2003): Confidence interval coverage properties for regression estimators in uni-phase and two-phase sampling. Journal of Official Statistics, 19: 17–30.
 
Saarela S., Grafström A., Ståhl G., Kangas A., Holopainen M., Tuominen S., Nordkvist K., Hyyppä J. (2015a): Model-assisted estimation of growing stock volume using different combinations of LiDAR and Landsat data as auxiliary information. Remote Sensing of Environment, 158: 431–440.
 
Saarela S., Schnell S., Grafström A., Tuominen S., Nordkvist K., Hyyppä J., Kangas A., Ståhl G. (2015b): Effects of sample size and model form on the accuracy of model-based estimators of growing stock volume. Canadian Journal of Forest Research, 45: 1524–1534.
 
Searle S.R. (1982): Matrix Algebra Useful for Statistics. New York, Wiley: 438.
 
Searle S.R., Casella G., McCulloch C.E. (1992): Variance Components. New York, Wiley: 501.
 
Thaden H., Kneib T. (2017): Structural equation models for dealing with spatial confounding. The American Statistician, 72: 1–14.
 
Viana H., Aranha J., Lopes D., Cohen Warren B. (2012): Estimation of crown biomass of Pinus pinaster stands and shrubland above-ground biomass using forest inventory data, remotely sensed imagery and spatial prediction models. Ecological Modelling, 226, 22-35 https://doi.org/10.1016/j.ecolmodel.2011.11.027
 
Wulder M., Coops N., Hudak A., Morsdorf F., Nelson R., Newnham G., Vastaranta M. (2013): Status and prospects for LiDAR remote sensing of forested ecosystems. Canadian Journal of Remote Sensing, 39: S1–S5.
 
Zhang Lianjun, Liu Chuangmin, Davis Craig J (2004): A mixture model-based approach to the classification of ecological habitats using Forest Inventory and Analysis data. Canadian Journal of Forest Research, 34, 1150-1156 https://doi.org/10.1139/x04-005
 
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