DOI QR코드

DOI QR Code

임의효과를 이용한 충남지역 소나무림의 바이오매스 모형 개발

The Development of Biomass Model for Pinus densiflora in Chungnam Region Using Random Effect

  • 표정기 (한국임업진흥원 산림탄소인증센터) ;
  • 손영모 (국립산림과학원 산림산업연구과)
  • Pyo, Jungkee (Forest Carbon and Certification Center, Korea Forestry Promotion Institute) ;
  • Son, Yeong Mo (Division of Forest Industry Research, National Institute of Forest Science)
  • 투고 : 2016.10.13
  • 심사 : 2017.02.09
  • 발행 : 2017.06.30

초록

본 연구의 목적은 임의효과(random effect)를 이용하여 충남지역 임령-바이오매스 모형을 개발하고 임의효과의 적용성을 평가하는데 있다. 충남지역 소나무림의 임령에 따른 바이오매스 모형 개발을 위해 임분 구조를 고려하여 전국의 중부지방소나무 임분에서 30개소(150그루)를 조사하고 임령과 바이오매스 자료를 수집하였다. 모형 개발에서 중부지방소나무의 임령-바이오매스 관계는 고정효과(fixed effect)이고 지역간 차이를 임의효과로 설정하였다. 임의효과에 따른 모형의 적합도를 검정하기 위해 아카이케의 정보기준(Akaike Information Criterion, AIC)을 참고하고 지역간 차이에 따른 분산-공분산 행렬과 오차항을 추정하였다. 추정된 공분산은 -1.0022, 오차항은 0.6240이고 분산-공분산 행렬을 이용한 임의효과 모형의 AIC는 377.7을 나타내어 선행 연구와 이질적인 차이는 없었다. 이러한 결과는 범주형 자료의 임의효과가 모형 개발에 반영된 결과로 판단된다. 본 연구의 결과는 임의효과를 이용하여 일부지역에 국한되어 개발되었던 바이오매스 모형 연구에 활용이 가능하다.

The purpose of this study was to develop age-biomass model in Chungnam region containing random effect. To develop the biomass model by species and tree component, data for Pinus densiflora in central region is collected to 30 plots (150 trees). The mixed model were used to fixed effect in the age-biomass relation for Pinus densiflora, with random effect representing correlation of survey area were obtained. To verify the evaluation of the model for random effect, the akaike information criterion (abbreviated as, AIC) was used to calculate the variance-covariance matrix, and residual of repeated data. The estimated variance-covariance matrix, and residual were -1.0022, 0.6240, respectively. The model with random effect (AIC=377.2) has low AIC value, comparison with other study relating to random effects. It is for this reason that random effect associated with categorical data were used in the data fitting process, the model can be calibrated to fit the Chungnam region by obtaining measurements. Therefore, the results of this study could be useful method for developing biomass model using random effects by region.

키워드

참고문헌

  1. Budhathoki, C.B., Lynch, T.B. and Guldin, J.M. 2008. A Mixed-effects model for the dbh-height relationship of shortleaf pine(Pinus echinata Mill.). Southern Journal of Applied Forestry 32(1): 5-11.
  2. Clutter, J.L., Fortson, J.C. Pienaar, L.V., Brister, G.H. and Bailey, R.L. 1983. Timber Management - A Quantitative Approach. John Wiley and Sons. pp. 31-58.
  3. Choi, J.S. 2016. Estimable functions of mixed models. The Korean Journal of Applied Statistics 29(2): 291-299.
  4. Jeong, S.O. and Shin, K.I. 2013. Semiparametric and nonparameteric mixed effects models for small area estimation. The Korean Journal of Applied Statistics 26(1): 71-79. https://doi.org/10.5351/KJAS.2013.26.1.071
  5. Jo, J.N. and Chang, U.J. 2013. A statistical analysis of the fat mass repeated measures data using mixed model. Journal of the Korean Data and Information Science Society 24(2): 303-310. https://doi.org/10.7465/jkdi.2013.24.2.303
  6. Kim, H. 1999. Review of repeated measures data analysis and PROC MIXED. Journal of the Korean Society of Health Statistics 24(1): 7-15.
  7. Lappi, J. 1997. A longitudinal analysis of height/diameter curves. Forest Science 43(4): 555-570.
  8. Lappi, J. and Bailey, R.L. 1988. A height prediction model with random stand and tree parameter: An alternative to traditional site index methods. Forest Science 34(4): 907-927.
  9. Lee, Y.J., Coble, D.W., Pyo, J.K., Kim, S.H., Lee, W.K. and Choi, J.K. 2009. A Mixed-effects height-diameter model for Pinus densiflora trees in Gangwon province, Korea. Journal of Korean Forest Society 98(2): 178-182.
  10. Lee, Y.J. 2015. Review of mixed-effects models. The Korean Journal of Applied Statistics 28(2): 123-136. https://doi.org/10.5351/KJAS.2015.28.2.123
  11. Liang, J. and Picard, N. 2013. Matrix model of forest dynamics: An overview and outlook. Forest Science 59(3): 359-378. https://doi.org/10.5849/forsci.11-123
  12. Liu, X.Q., Rong, J.Y. and Liu, X.Y. 2008. Best linear unbiased prediction for linear combinations in general mixed linear models. Journal of Multivariate Analysis 99: 1503-1517. https://doi.org/10.1016/j.jmva.2008.01.004
  13. Lynch, T.B., Holly, A.G. and Stevenson, D.J. 2005. A random-parameter height-dbh model for Cherrybark oak. Southern Journal of Applied Forestry 29(1): 22-26.
  14. Mcculloch, C.E., Searle, S.R. and Neuhaus, J.M. 2008. Generalized, Linear, and Mixed Models. John Wiley and Sons, Incorporation. pp. 7-10.
  15. Pyo, J.K., Lee, S.T., Seo, K.Y. and Lee, K.J. 2015. Applicability evaluation of a mixed model for the analysis of repeated inventory data: A case on Quercus variabilis stands in Gangwon region. Journal of Korea Forest Society 104(1): 111-116. https://doi.org/10.14578/jkfs.2015.104.1.111
  16. Robinson, G.K. 1991. That BLUP is a good thing: The estimation of random effects. Statistical Science 6(1): 15-51. https://doi.org/10.1214/ss/1177011926
  17. Ryu, J.S. and Cho, J.S. 2016. The wage determinants of the vocational high school graduates using mixed effects mode. Journal of the Korean Data and Information Science Society 27(4): 935-946. https://doi.org/10.7465/jkdi.2016.27.4.935
  18. SAS Institute, Inc. 2014. SAS/STAT 9.4 User′s Guide. SAS Institute, Incorporation. Cary. North Carolina. pp. 489.
  19. Searle, S.R. 1982. Matrix algebra useful for statistics. John Wiley and Sons, Incorporation. pp. 200-201.
  20. Sharma, M. and 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. https://doi.org/10.1016/j.foreco.2007.05.006
  21. Trincado, G. and Burkhart, H.E. 2006. A generalized approach for modeling and localizing stem profile curves. Forest Science 52: 670-682.
  22. Trincado, G., Vanderschaaf, C.L. and 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. https://doi.org/10.1007/s10342-006-0141-7
  23. Vanderschaaf, C. 2008. Stand level height-diameter mixed effects models: parameters fitted using Loblolly pine but calibrated for sweetgum. Proceeding of the 16th central hardwoods forest conference. pp. 386-393.
  24. Vargas-larreta, B., Castedo-dorado, F., Alvarez-gonzalez, J.G., Barrio-anta, M. and Cruz-cobos, F. 2009. A generalized height-diameter model with random coefficients for uneven-aged stands in El Salto, Durango (Mexico). Forestry 82(4): 445-462. https://doi.org/10.1093/forestry/cpp016
  25. Zhang, Y. and Borders, B.E. 2004. Using a system mixedeffects modeling method to estimates tree compartment biomass for intensively managed loblolly pines-an allometric approach. Forest Ecology and Management 194: 145-157. https://doi.org/10.1016/j.foreco.2004.02.012