Ağaçların Çap-Boy Modellemesine İlişkin Otokorelasyon Probleminin Giderilmesinde Karışık Etkili Doğrusal Olmayan Regresyon Modelleri ile Otoregresif Regresyon Modellerinin Etkinliğinin Karşılaştırılması

Yıl 2019, Cilt 5, Sayı 1, 17 - 27, 07.08.2019

İlker ERCANLI Doğa EYÜBOĞLU

Öz

Ağaçların çap-boy ilişkilerinin modellenmesinde, Doğrusal Olmayan Regresyon modeli yanında Karışık Etkili Doğrusal Olmayan Regresyon modeli ile AR(1), AR(2), MA(1), MA(2), ARMA (1,1) ve ARMA (2,2) gibi çeşitli Otoregresif modellerin tahmin başarılıları ve farklı yapıdaki meşcerelerden elde edilen hiyerarşik verilerin kullanımıyla oluşan Otokorelasyon sorununa çözüm sunma kapasiteleri karşılaştırılmıştır.  Doğrusal Olmayan Regresyon Analizine ait başarı ölçütlerine göre   (RMSE=1.761, RMSE% =12.450, R²=0.838, AIC=316.167 ve BIC=912.207), gerek Otoregresif modelleme gerekse Karışık Etkili Doğrusal Olmayan Regresyon Modellemesinin kullanım ile önemli oranda iyileşmeler elde edilmiştir. En başarılı olarak belirlenen a parametresi rasgele olan Karışık Etkili Regresyon Modelinde, RMSE değeri; 1.174, RMSE% değeri; 8.300, R²değeri;0.928, AIC değeri; 93.959 ve BIC değeri ise; 689.999 olarak hesaplanmış ve bu bakımdan da RMSE değerinde % 33.33, RMSE% değerinde % 33.33, R² değerinde % 10.74, AIC değerinde % 70.28 ce BIC değerinde % 24.36 iyileşme elde edilmiştir. Tahmin başarı ölçütlerindeki iyileşmeler yanında Karışık Etkili Regresyon Modeli ile çeşitli Otoregresif modellere ilişkin hesaplanan Durbin-Watson katsayısı 2’ye yakın olarak elde edilmiş ve test sonucu olarak da herhangi bir Otokorelasyon saptanmamıştır.

Anahtar Kelimeler

Çap-Boy Tahmini, Otokorelasyon, Karışık Etkili Regresyon Modeli

Kaynakça

• Adame, P., Cañellas, I., Roig, S., del Rio, M. 2006. Modeling dominant height growth and site index curves for Rebollo oak (Quercus pyrenaica Willd.). Annals of Forest Science, 63, 929–940.Adame, P., del Río, M., Cañellas, I., 2008. A mixed nonlinear height–diameter model for pyrenean oak (Quercus pyrenaica Willd.). Forest Ecology and Management, 256, 88–98Avery, T. E., Burkhart, H. E. 1983. Forest Measurements, Mcgraw-Hill Series in Forest Resources, Mcgraw-Hill Book Company, New York, 331 p.Bravo-Oviedo, A., del Río, M., Montero, G. 2007. Geographic variation and parameter assessment in generalized algebraic difference site index modeling. Forest Ecology and Management, 247, 107-119.Budhathoki, C. B., Lynch, T. B., Guldin, J. M. 2008. A mixed-effects model for dbh–height relationship of shortleaf pine (Pinus echinata Mill.). Southern Journal of Applied Forestry, 32, 5–11.Calama, R., Montero, G. 2004. Interregional nonlinear height– diameter model with random coefficients for stone pine in Spain. Canadian Journal of Forest Research, 34, 150–163.Castedo-Dorado, F., Diéguez-Aranda, U., Barrio, M., Sánchez, M. and von Gadow, K. 2006. A generalized height-diameter model including random components for radiata pine plantations in northeastern Spain. Forest Ecology and Management, 229, 202 – 213.Cieszewski, C. J., Strub, M. ve Zasada, M. J. 2007. New Dynamic Site Equation That Fits Best The Schwappach For Scots Pine (Pinus Slyvestris L.) in Centarl Europe, Forest Ecology and Management, 23, 83-93.Cieszewski, C. J., Strub, M. 2008. Generalized algebraic difference approach derivation of dynamic site equations with polymorphism and variable asymptotes from exponential and logarithmic functions. Forest Science 54: 303-315.Crecente-Campo, F., Tomé, M., Soares, P., Diéguez-Aranda, U. 2010. A generalized nonlinear mixed-effects height-diameter model for Eucalyptus globulus L. in northwestern Spain. Forest Ecology and Management, 259, 943-952.Davis, S. L., Johnson, K. N., Bettinger, P. S., Howard, T. E. 2001. Forest Management, McGraw-Hill, NewYork, 804 s.Diéguez-Aranda, U., Burkhart, H. E., Rodriguez-Soalleiro, R. 2005. Modeling dominant height growth of radiata pine (Pinus radiata D. Don) plantations in north-western Spain. Forest Ecology and Management, 215, 271–284.Diéguez-Aranda, U., Grandas-Arias, J. A., Álvarez-González, J. G., Gadow, K.V. 2006. Site Quality Curves For Birch Stands in North-Western Spain, Silva Fennica, 40, 4, 631-644.Ferguson, I. S., Leech, J. W. 1978. Generalized least squares estimation of yield functions. Forest Science, 24, 27–42.Fulton, M. R. 1999. Patterns in height–diameter relationship for selected tree species and sites in eastern Texas. Canadian Journal of Forest Research, 29, 1445–1448.Gadow, K. V., Hui, G.Y. 1999. Modelling Forest Development, Kluwer Academic Publishers, Dordrect, 213 p.Gadow K., Real P, Álvarez Gonzáles J. G. 2001. Modelización del Crecimiento y la Evolución de los Bosques. IUFRO World Series, Vol. 12, Vienna.Gregoire, T., Schabenberger, O., Barret, J. 1995. Linear modelling of irregularly spaced, unbalanced, longitudinal data from permanent-plot measurements. Canadian Journal of Forest Research, 25, 137-156.Fang, Z., Bailey, R. L. 1998. Height– diameter models for tropical forests on Hainan Island in southern China. Forest Ecology and Management, 110, 315-327.Fox, J., 1997. Applied Regression Analysis, Linear Models, and Related Methods. Thousand Oaks, CA: Sage.
• Huang, S., Titus, S. J., Wiens, D. P. 1992. Comparison of nonlinear heightdiameter functions for major Alberta tree species. Canadian Journal of Forest Research, 22, 1297–1304.Huang, S., Price, D., Titus, S. J. 2000. Development of ecoregion-based height– diameter models for white spruce in boreal forests. Forest Ecology and Management, 129, 125–141.İyit, N., Genç, A., Arslan, F. 2006. Analysis of repeated measures for continuoes response data using General Linear Model and Mixed Models, Proceedings of the international conference on modeling and simulation, Konya, TURKEY, 937-942.Kalıpsız, A., 1984. Dendrometri, İstanbul Üniversitesi Orman Fakültesi Yayınları , İstanbul.Krumland, B. E., Wensel, L. C. 1978. A generalized height– diameter equation for coastal California species. Western Journal of Applied Forestry, 3, 113–115.Larsen, D. R., Hann, D. W. 1987. Height–diameter equations for seventeen tree species in southwest Oregon. Research paper 49. Oregon State University, Forest Research Laboratory, Corvallis, OR.Lei Y., Parresol B. R. 2001. Remarks on height-diameter modeling (Res Note SRS-10), USDA For Service, Southern Research Station, Asheville, NC.Lopez-Sanchez, C. A., Varela, J. G., Dorado, F. C., Alboreca, A. R., Soalleiro, R.R., Alvarez Gonzalez, J. G., Rodriguez, F. S. 2003. A height–diameter model for Pinus radiata D.Don in Galicia (Northwest Spain). Annals of Forest Science, 60, 237–245.Lynch, T. B, Holley A. G., Stevenson, D. J. 2005. A random-parameter height-dbh model for cherrybark oak., Southern Journal of Applied Forestry, 29, 22–26.Martin, F. C., Flewelling, J. W. 1998. Evaluation of tree height prediction models for stand inventory. Western Journal of Applied Forestry, 13, 109–119.Mehtätalo, L. 2004. A longitudinal height–diameter model for Norway spruce in Finland., Canadian Journal of Forest Research, 34,131–140.Monserud, R.A. 1984. Height Growth and Site Index Curves for Inland Douglas-Fir Based on Stem Analysis Data and Forest Habitat Type, Forest Science, 30, 943–965.Nanos, N., Calama, R., Montero, G., Gil, L. 2004. Geostatistical prediction of height/diameter models. Forest Ecology and Management, 195, 221–235.Nord-Larsen, T. 2006. Developing dynamic site index curves for European beech (Fagus sylvatica L.) in Denmark. Forest Science, 52, 173-181.Paulo, J. A., Tomé, J., Tomé, M. 2011. Nonlinear fixed and random generalized height–diameter models for Portuguese cork oak stands, Annals of Forest Science, 68, 295-309Parresol, B. R. 1992. Baldcypress height–diameter equations and their prediction confidence interval. Canadian Journal of Forest Research, 22, 1429– 1434.Parresol, B. R., Vissage, J. S. 1998. White Pine Site İndex for The Southern Forest Survey, USDA For. Serv. Res. Pap. SRS-10.Peng, C. 1999. Nonlinear height- diameter models for nine boreal forest tree species in Ontario (OFRI-Rep 155), Ministry of Natural Resources Institutes.Peng, C., Zhang, L., Liu, J. 2001. Developing and validating nonlinear height– diameter models for major tree species of Ontario’s boreal forests. Northern Journal of Applied Forestry, 18, 87–94.Robinson, A. P., Wykoff, W. R. 2004. Imputing missing height measures using a mixed-effects modeling strategy. Canadian Journal of Forest Research, 34, 2492–2500.SAS Institute Inc., 2004. SAS/STAT 9.1 User's Guide: statistics, Version 9.1, SAS Institute Inc., Cary, NC., 816 p. Saunders, M. R., Wagner, R. G. 2008. Long-term spatial and structural dynamics in Acadian mixedwood stands managed under various silvicultural systems. Canadian Journal of Forest Research, 38, 498–517.Schröder J., Álvarez-González J. G. 2001. Comparing the performance of generalized diameter-height equations for Maritime pine in Northwestern Spain. Forstwissenschaftliches Centralblatt vereinigt mit Tharandter forstliches Jahrbuch, 120, 18–23.Sharma, M., Zhang, S. Y. 2004. Height–diameter models using stand characteristics for Pinus banksiana and Picea mariana. Scandinavian Journal of Forest Research, 19, 442–451.Sharma, M., Parton, J. 2007. Height-diameter equations for boreal tree species in Ontario using a mixed-effects modeling approach. Forest Ecology and Management, 249, 187–198.Schnute, J., 1981. A versatile growth model with statistically stable parameters. Canadian Journal of Fisheries and Aquatic, 38, 1128-1140.Soares, P., Tomé, M. 2002. Height–diameter equation for first rotation eucalypt plantations in Portugal. Forest Ecology and Management, 166, 99–109.Temesgen, H., Gadow, K. V. 2004. Generalized height–diameter models—an application for major tree species in complex stands of interior British Columbia. European Journal of Forest Research, 123, 45–51.Trincado, G., VanderSchaaf , C. L., Burkhart , H. E. 2007. Regional mixed-effects height-diameter models for loblolly pine (Pinus taeda L.) plantations. European Journal of Forest Research, 126, 253 – 262.Vanclay, J. K. 1994. Modelling Forest Growth: Applications to Mixed Tropical Forests, CAB International, Department of Economics and Natural Resource, Royal Veterinary and Agricultural University, Copenhagen, Denmark, Wallingford, UK, 312 p.van Laar, A., Akça, A. 2007. Forest mensuration: in Managing Forest Ecosystems, Dordrecht, The Netherlands, Springer. 383 p.Ye, S. 2005. Covariance structure selection in linear mixed models for longitudinal data, M. Sc. Thesis, department of Bioinformatics and Biostatistics, University of Lousville, Kentucky, USA. Wykoff, W. R., Crookston, N. L., Stage, A.R.1982. User’s guide to the stand prognosis model. USDA For. Serv. Gen. Tech. Rep. INT-133.