J. For. Sci., 2018, 64(12):497-505 | DOI: 10.17221/120/2018-JFS

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

Steen MAGNUSSEN
Natural Resources Canada, Canadian Forest Service, Pacific Forestry Centre, Victoria, Canada

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.

Keywords: forest enterprise inventory; risk analysis; stand-effects; spatial autocorrelation; simulation

Published: December 31, 2018  Show citation

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MAGNUSSEN S. An estimation strategy to protect against over-estimating precision in a LiDAR-based prediction of a stand mean. J. For. Sci. 2018;64(12):497-505. doi: 10.17221/120/2018-JFS.
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    References

    1. Binder D.A. (1983): On the variances of asymptotically normal estimators from complex surveys. International Statistical Review, 51: 279-292. Go to original source...
    2. Black P.E. (2006): Manhattan distance. Available at https://www.nist.gov/dads/HTML/manhattanDistance.html (accessed Sept 6, 2018).
    3. Breidenbach J., Astrup R. (2012): Small area estimation of forest attributes in the Norwegian National Forest Inventory. European Journal of Forest Research, 131: 1255-1267. Go to original source...
    4. Breidenbach J., McRoberts R.E., Astrup R. (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. Go to original source... Go to PubMed...
    5. Breidenbach J., Magnussen S., Rahlf J., Astrup R. (2018): Unit-level and area-level small area estimation under heteroscedasticity using digital aerial photogrammetry data. Remote Sensing of Environment, 212: 199-211. Go to original source...
    6. 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.
    7. Chambers R.L. (2011): Which sample survey strategy? A review of three different approaches. Pakistan Journal of Statistics, 27: 337-357.
    8. Chambers R.L., Clark R.G. (2012): An Introduction to Modelbased Survey Sampling with Applications. New York, Oxford University Press: 265. Go to original source...
    9. Chilès J.P., Delfiner P. (1999): Geostatistics: Modeling Spatial Uncertainty. New York, Wiley: 695. Go to original source...
    10. Claeskens G., Hjort N.L. (2008): Model Selection and Model Averaging. Cambridge, Cambridge University Press: 332.
    11. 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. Go to original source...
    12. Dai W. (2004): Asymptotics of the sample mean and sample covariance of long-range-dependent series. Journal of Applied Probability, 41A: 383-392. Go to original source...
    13. Donner A. (1986): A review of inference procedures for the intraclass correlation coefficient in the one-way random effects model. International Statistical Review, 54: 67-82. Go to original source...
    14. Draper N.R., Smith H. (1998): Applied Regression Analysis. New York, Wiley: 736. Go to original source...
    15. Fernández-Landa A., Fernández-Moya J., Tomé J.L., AlgeetAbarquero N., Guillén-Climent M.L., Vallejo R., Sandoval V., Marchamalo M. (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: 1-15. Go to original source...
    16. Finley A.O., Banerjee S., Ek A.R., McRoberts R.E. (2008): Bayesian multivariate process modeling for prediction of forest attributes. Journal of Agricultural Biological and Environmental Statistics, 13: 60-83. Go to original source...
    17. Finley A.O., Banerjee S., Waldmann P., Ericsson T. (2009): Hierarchical spatial modeling of additive and dominance genetic variance for large spatial trial datasets. Biometrics, 65: 441-451. Go to original source... Go to PubMed...
    18. Fortin M., Manso R., Calama R. (2016): Hybrid estimation based on mixed-effects models in forest inventories. Canadian Journal of Forest Research, 46: 1310-1319. Go to original source...
    19. Grafström A., Ringvall A.H. (2013): Improving forest field inventories by using remote sensing data in novel sampling designs. Canadian Journal of Forest Research, 43: 1015-1022. Go to original source...
    20. Gregoire T.G., Naesset E., McRoberts R.E., Ståhl G., Andersen H.E., Gobakken T., Ene L., Nelson R. (2016): Statistical rigor in LiDAR-assisted estimation of aboveground forest biomass. Remote Sensing of Environment, 173: 98-108. Go to original source...
    21. Gupta A.K., Nagar D.K. (1999): Matrix Variate Distributions. Boca Raton, Chapman & Hall/CRC: 384.
    22. Harvey A.C. (1981): Time Series Models. Oxford, Phillip Allan: 229.
    23. Hausman J.A. (1978): Specification tests in econometrics. Econometrica: Journal of the Econometric Society, 46: 1251-1271. Go to original source...
    24. Hodges J.S., Reich B.J. (2010): Adding spatially-correlated errors can mess up the fixed effect you love. The American Statistician, 64: 325-334. Go to original source...
    25. Holm S. (1979): A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6: 65-70.
    26. Hughes J., Haran M. (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. Go to original source...
    27. Johnston J., DiNardo J. (1997): Econometric Methods. New York, McGraw-Hill: 480.
    28. Junttila V., Finley A.O., Bradford J.B., Kauranne T. (2013): Strategies for minimizing sample size for use in airborne LiDAR-based forest inventory. Forest Ecology and Management, 292: 75-85. Go to original source...
    29. Kangas A., Myllymäki M., Gobakken T., Naesset E. (2016): Model-assisted forest inventory with parametric, semiparametric, and nonparametric models. Canadian Journal of Forest Research, 46: 855-868. Go to original source...
    30. Kangas A., Astrup R., Breidenbach J., Fridman J., Gobakken T., Korhonen K.T., Maltamo M., Nilsson M., Nord-Larsen T., Naesset E. (2018): Remote sensing and forest inventories in Nordic countries - roadmap for the future. Scandinavian Journal of Forest Research, 33: 397-412. Go to original source...
    31. Kessy A., Lewin A., Strimmer K. (2018): Optimal whitening and decorrelation. The American Statistician, 72: 1-6. Go to original source...
    32. Köhl M., Magnussen S. (2014): Sampling in forest inventories. In: Köhl M., Pancel L. (eds): Tropical Forestry Handbook. Berlin, Heidelberg, Springer: 1-50. Go to original source...
    33. 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.
    34. Magnussen S. (2016): A new mean squared error estimator for a synthetic domain mean. Forest Science, 63: 1-9. Go to original source...
    35. Magnussen S., Breidenbach J. (2017): Model-dependent forest stand-level inference with and without estimates of stand-effects. Forestry: An International Journal of Forest Research, 90: 675-685. Go to original source...
    36. Magnussen S., Breidenbach J., Mauro F. (2017): The challenge of estimating a residual spatial autocorrelation from forest inventory data. Canadian Journal of Forest Research, 47: 1557-1566. Go to original source...
    37. 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. Go to original source...
    38. Magnussen S., Mandallaz D., Lanz A., Ginzler C., Naesset 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. Go to original source...
    39. Maltamo M., Mehtätalo L., Vauhkonen J., Packalén P. (2012): Predicting and calibrating tree attributes by means of airborne laser scanning and field measurements. Canadian Journal of Forest Research, 42: 1896-1907. Go to original source...
    40. Maltamo M., Bollandsås 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 (Oxford), 83: 257-268. Go to original source...
    41. Mauro F., Monleon V.J., Temesgen H., Ruíz L.Á. (2017): Analysis of spatial correlation in predictive models of forest variables that use LiDAR auxiliary information. Canadian Journal of Forest Research, 47: 788-799. Go to original source...
    42. Mauro F., Molina I., García-Abril A., Valbuena R., AyugaTéllez E. (2016): Remote sensing estimates and measures of uncertainty for forest variables at different aggregation levels. Environmetrics, 27: 225-238. Go to original source...
    43. Meini B. (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. Go to original source...
    44. Melville G., Stone C., Turner R. (2015): Application of LiDAR data to maximise the efficiency of inventory plots in softwood plantations. New Zealand Journal of Forestry Science, 45: 1-9. Go to original source...
    45. Naesset E. (2004): Practical large-scale forest stand inventory using a small-footprint airborne scanning laser. Scandinavian Journal of Forest Research, 19: 164-179. Go to original source...
    46. Nanos N., Calama R., Montero G., Gil L. (2004): Geostatistical prediction of height/diameter models. Forest Ecology and Management, 195: 221-235. Go to original source...
    47. Paciorek C.J. (2010): The importance of scale for spatialconfounding bias and precision of spatial regression estimators. Statistical Science :A Review Journal of the Institute of Mathematical Statistics, 25: 1-107. Go to original source... Go to PubMed...
    48. Rao J., Hidiroglou M. (2003): Confidence interval coverage properties for regression estimators in uni-phase and twophase sampling. Journal of Official Statistics, 19: 17-30.
    49. Saarela S., Grafström A., Ståhl G., Kangas A., Holopainen M., Tuominen S., Nordkvist K., Hyyppä J. (2015a): Modelassisted estimation of growing stock volume using different combinations of LiDAR and Landsat data as auxiliary information. Remote Sensing of Environment, 158: 431-440. Go to original source...
    50. 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. Go to original source...
    51. Searle S.R. (1982): Matrix Algebra Useful for Statistics. New York, Wiley: 438.
    52. Searle S.R., Casella G., McCulloch C.E. (1992): Variance Components. New York, Wiley: 501. Go to original source...
    53. Thaden H., Kneib T. (2017): Structural equation models for dealing with spatial confounding. The American Statistician, 72: 1-14. Go to original source...
    54. Viana H., Aranha J., Lopes D., Cohen W.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. Go to original source...
    55. 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. Go to original source...
    56. Zhang L.J., Liu C.M., Davis C.J. (2004): A mixture modelbased approach to the classification of ecological habitats using Forest Inventory and Analysis data. Canadian Journal of Forest Research, 34: 1150-1156. Go to original source...

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