非线性模型对数回归的偏差校正及与加权回归的对比分析

本文结合大样本的立木生物量实测数据,对非线性模型对数回归的偏差校正问题进行了探讨,并与加权回归结果进行了对比分析。首先,分析了对数回归产生偏差的内在原因,并提出了一个新的校正因子,同时对另外3个偏差校正因子一并进行了检验,结果表明本文和Baskerville(1972)提出的校正因子,能保证与加权回归估计结果趋于一致;然后,对非线性加权回归中基于普通回归残差推导的权函数与通用权函数(W＝1/f(x)²)的拟合效果进行了对比分析,结果表明二者基本相当,而通用权函数更具有广泛的适应性。建议对带有异方差的非线性模型,最好直接采用加权回归进行估计;当按照通用权函数进行估计其总相对误差超出一定范围时,应该根据普通回归估计的残差推导效果最佳的权函数后再进行加权回归。     

An empirical comparison of two subject-specific approaches to dominant heights modeling: The dummy variable method and the mixed model method

The varying (local) parameter(s) in site index models can be treated as fixed or random. Two primary subject-specific approaches to height modeling, the dummy variable method (fixed individual effects) and the mixed model method (random individual effects), were compared using Chapman–Richards type models fitted to second-rotation loblolly pine (Pinus taeda L.) data from a designed experiment. For height prediction of new growth series, tested on our validation subset data, the mixed model provides a new (local) parameter prediction method (termed as mixed predictor), which generally performed better than the traditional method of recovering local parameters (the least squares (LS) predictor we used). However, using the LS predictor, both the dummy variable estimation method and mixed model estimation showed almost identical prediction results. With multiple pairs of height–age measurements, no big difference was found in empirical site index prediction between the LS and mixed predictor. Theoretically, one main advantage of the mixed model approach is the ability of its mixed predictor to predict several local parameters using a single height–age pair. However, our empirical results failed to support this point.     

A common near infrared—based partial least squares regression model for the prediction of wood density of Pinus pinaster and Larix?×?eurolepis

Wood density is defined as the ratio of mass to volume and therefore in principle it should be possible to calculate a unique partial least squares regression (PLS-R) model for several species. PLS-R models for wood density based on X-ray microdensity data were calculated for each species Pinus pinaster and Larix × eurolepis and for both species together. After cross-validation and test set validation the data sets were combined and final models were calculated. The common model gave a residual prediction deviation (RPD) of 3.1, a range error ratio (RER) of 11.7, and a SEP/SEC of 1.06. The single models for Pinus pinaster and Larix?×?eurolepis gave RPD’s of 3.5 and 3.2, RER’s of 13 and 11, and a SEP/SEC of 1.2. To the best knowledge of the authors all obtained PLS-R models are the first ones that fulfil the requirements according to AACC Method 39-00 (AACC in AACC Method, 39-00:15, 1999) to be used at least for screening (RPD?≥?2.5). Although this method and the defined limits were developed for the analysis of grains they can be used as a rough rule of thumb until limits for wood are available. The improvement of the PLS-R models, compared to published results, might be due to three facts (1) the higher number of scans collected for a single spectrum, (2) that the samples were better represented by the NIR spectra and X-ray microdensity values, and (3) that the sites for the measurement of NIR spectra and X-ray microdensity were coincided as strictly as possibly.     

Models for predicting lumber bending MOR and MOE based on tree and stand characteristics in black spruce

In this study, a stepwise method was introduced to identify the best variables for predicting lumber static bending modulus of elasticity (MOE) and modulus of rupture (MOR) based on stand and tree characteristics in black spruce (Picea mariana). In the initial development of the technique, the two equations were fitted independently using ordinary least squares (OLS). A test for cross-equation correlation using black spruce data showed highly significant correlation between the two equations. Since the cross-equation correlation exists between the two equations, more efficient parameter estimation can be achieved through joint-generalized least squares, better known as seemingly unrelated regression (SUR). A simultaneous system of two equations was derived for black spruce. The two methods were evaluated and compared for some statistical parameters. The results indicated that there is a small difference between the two methods, but parameter estimates from seemingly unrelated regression estimation had smaller standard errors in all cases as compared to those from ordinary least squares estimates. Therefore, the system estimation methods theoretically perform better for simultaneously interdependent systems of equations and the appropriate system estimation approaches are recommended for estimating coefficients in simultaneously interdependent systems of forestry equations.     

Comparison of treewise and standwise forest simulators by means of quantile regression

Predicting forest development under varying treatment schedules forms the basis of forest management planning. The actual growth predictions are made with a forest simulator which includes growth equations and additional models for predicting a number of varying tree, forest and site properties. Forest growth simulators typically include either tree-level or stand-level growth models, but these two approaches have not been thoroughly compared. We set out here to compare these two approaches with the SIMO simulator framework in a small data set from southern Finland based on 60 sample plots in 30 stands, the development of which was known for 20 years. The stands chosen were very dense, so that the simulators could be tested under extreme conditions. The results show that the stand-level model is more accurate in almost all cases and its computational burden is much lower. It could therefore be advisable to use tree-level models for short-term predictions, which would ensure detailed information on forest structure for planning the near-future operations. Stand-level models would be more advisable in longer term predictions, especially when accurate volume estimates are considered more important than the forest structure. The errors observed in these simulators were analysed further by quantile regression, which allows empirical estimates of confidence intervals to be obtained for the simulator.     

Fast measurement of starch content in cold-treated seedlings by infrared spectra

Despite the importance of starch for tree growth, methodological challenges in starch analysis slow down the research on its ecological importance. In this study, a rapid monitoring method was developed for measuring starch content in Pinus taeda L. seedlings after cold treatments. A linear mixed-effects model was used to analyze the effects of cold treatments, seedling tissue types and their interaction on starch content. Mid-infrared (MIR) and near-infrared (NIR) spectra were surveyed, and the results were analyzed using partial least squares regression to determine the starch content. The determination coefficient for calibration and residual predictive deviation were compared between MIR and NIR models to assess the variability of the established models. The results showed that the effects of cold treatments, seedling tissue types and their interaction on starch content were significant. Compared to MIR spectra, NIR spectra is more suitable to estimate starch content in the seedlings. Using NIR spectra, roots provided the most accurate estimates of starch content. The presented guidelines regarding data accuracy as a function of MIR/NIR spectra of samples represent an important methodological reference for starch quantification, which will improve the understanding of the fundamental role of starch in seedlings against environmental forces.     

Modelling primary branch growth based on a multilevel nonlinear mixed‑effects model: a Pinus koraiensis plantation case study in north‑east China

On the basis of a multilevel nonlinear mixed?effects model approach, branch diameter and length growth models were developed for a Pinus koraiensis plantation in north?east China. The models developed were able to better capture the residual variation successfully by partitioning the residual variance into plot?, tree? and branch? level variations via random parameter modeling at the three levels. In addition to random effects, various time series correlation structures were evaluated to account for residual autocorrelation, and the AR(1) and ARMA(1,1) structures were selected for the branch diameter and length growth models, respectively. Model validation results using an independent data set confirmed that multilevel mixed models with an appropriate correlation structure produced more accurate and precise branch?specified diameter and length predictions. Overall, the models were suitable in describing the trends and inherent variability of crown profile and good enough to be included in growth simulation systems for Pinus koraiensis plantations.     

Predicting species-specific basal areas in urban forests using airborne laser scanning and existing stand register data

The aim of this work was to examine how well species-specific stand attributes can be predicted using a combination of airborne laser scanning (ALS) and existing stand register data in urban forests. In this context, the ability of three data combinations: ALS data and stand register data, ALS data and digital aerial images and all of these combined, was tested in the prediction of species-specific basal areas. We divided tree species into seven and three different tree species strata and applied two prediction methods: (1) regression method, in which the predicted total basal area was divided into tree species based on tree species proportions from stand register data, and (2) the nearest neighbour (NN) method, in which tree species proportions were used as predictor variables for species-specific basal areas. Prediction models were built based on training data of 205 field plots, and the accuracy of the models was tested based on validation data of 52 forests stands. Our results showed that species-specific predictions of seven tree species were more accurate when tree species proportions from stand register data were used in the prediction. Both the regression and the NN method provided reasonable accuracy. This study showed that tree species information from existing stand register data could be used as an alternative for aerial images in ALS-based forests inventories. The use of ALS data together with stand register data and small field data could also be economically beneficial in an inventory of urban forests.     

长白落叶松林分进界模型的研究

利用吉林省汪清林业局金沟岭林场落叶松林分连续观测数据,以计数类模型为基础,分别利用Poisson回归模型、负二项模型、零膨胀模型和Hurdle模型拟合林木进界株数,并通过AIC值,Pearson残差图以及Vuong检验对这些模型进行了详细分析比较.结果表明:Poisson回归模型不适用于模拟林木枯损株数;负二项回归模型相对于Poisson回归模型比较适用,但是对于零枯损过多的数据,这两类模型拟合效果较差;零膨胀模型和Hurdle模型对这类数据有很好的解决办法,而且,零膨胀负二项模型拟合效果最好.     

基于气象因子的马尾松毛虫发生率空间格局研究

[目的]为预测未来我国马尾松毛虫的潜在变化趋势,以2002-2012年全国范围内马尾松毛虫的地级逐年平均发生率作为预测指标,[方法]运用偏最小二乘回归方法,获得马尾松毛虫平均发生率与相关气象因子的回归方程,并结合地理空间数据与未来气象数据,得到马尾松毛虫平均发生率空间格局模型.[结果]表明:以筛选后的12个气象因子建立的马尾松毛虫平均发生率空间格局模型精度达到86.98%,具有较强的可靠性.据此预测2020s,2050s,2080s的马尾松毛虫平均发生率空间格局,并与2002-2012年的空间格局相比,结果显示:华东及华中地区虫害中度和重度发生面积均明显增加,有扩散的趋势;华东地区的轻度发生面积总体为缩减;而华南部分地区虫害轻度发生面积扩增.[结论]以偏最小二乘回归方法所得的空间格局模型具有实际预测意义,可以预测我国未来马尾松毛虫平均发生率的变化趋势.     

Kernel regression methods for the prediction of wood properties of Pinus taeda using near infrared spectroscopy

Near infrared diffuse reflectance spectra collected in 10-mm sections were used for the estimation of air-dry density (AD), microfibril angle (MFA), stiffness (MOE), tracheid coarseness (COARS), and tracheid wall thickness (WTHICK) in wood radial strip samples obtained at breast height (1.4 m) from 60 Pinus taeda trees. Calibration models were developed using traditional partial least squares (PLS) and kernel regression. The kernel methods included radial basis functions-partial least squares (RBF-PLS) and least-squares support vector machines (LS-SVM). RBF-PLS and LS-SVM models outperformed PLS-CV calibrations in terms of fit statistics. MFA and MOE, two properties that exhibited nonlinearity, showed the most significant improvements compared to PLS. In terms of predictive ability RBF-PLS performed better than PLS for the prediction of MFA, MOE, and COARS. LS-SVM showed better prediction statistics in all cases, except for WTHICK that gave similar statistics compared to PLS and was superior to RBF-PLS. By adding statistically significant factors to the PLS regressions, it was possible to capture some of the nonlinear features of the data and improve the predictive ability of the PLS models.     

华北落叶松人工林差分地位指数模型构建

以阴山山地苏木山林场华北落叶松人工林为研究对象,利用43株解析木数据,基于Richards方程构建差分地位指数模型。结果表明:差分模型拟合结果明显优于基础模型,R²均在0.96以上,RMSE在0.86~0.96之间,MAE在0.42以下。ADA法推导的模型,以b或c为自由参数拟合结果要好于以a为自由参数;GADA法推导的模型,假设自由参数c与变量X₀成线性关系更合理。通过统计分析、残差分析和地位指数曲线簇比较,采用GADA法,假设自由参数a=e^X₀,c=c₁+c₂X₀所推导的差分模型为最佳模型,满足生物学和统计学两方面的要求。地位指数越大,优势木树高及其连年生长量的极值也越大,到达拐点的时间也越早。研究结果可为华北落叶松人工林立地质量科学评价提供依据。     

Estimating canopy closure density and above-ground tree biomass using partial least square methods in Chinese boreal forests

Boreal forests play an important role in global environment systems. Understanding boreal forest ecosystem structure and function requires accurate monitoring and estimating of forest canopy and biomass. We used partial least square regression (PLSR) models to relate forest parameters, i.e. canopy closure density and above ground tree biomass, to Landsat ETM+ data. The established models were optimized according to the variable importance for projection (VIP) criterion and the bootstrap method, and their performance was compared using several statistical indices. All variables selected by the VIP criterion passed the bootstrap test (p<0.05). The simplified models without insignificant variables (VIP <1) performed as well as the full model but with less computation time. The relative root mean square error (RMSE%) was 29% for canopy closure density, and 58% for above-ground tree biomass. We conclude that PLSR can be an effective method for estimating canopy closure density and above-ground biomass.     

High accuracy rapid prediction and feasibility of on-site nondestructive estimation of Para rubber quality by spectroscopic methods

The aim of this study was to investigate convenient spectroscopic evaluation method of Para rubber quality. Ultra violet–near infrared (UV–NIR 370–1085 nm) spectra of latex were measured in transmittance mode. Calibrations for total solid content (TSC) and dry rubber content (DRC) were developed using spectral data set with aid of partial least square regression analysis using 57 samples. UV–NIR spectra of latex provided good regression models between measured and predicted values of TSC and DRC with determination coefficient for cross-validation of 0.96 and 0.97, respectively. The ranks were 2 and 1, respectively. This study suggests high accuracy in-line quality control of latex using UV–NIR spectroscopy. The long wavelength NIR spectra of bark were scanned to check the feasibility of on-site evaluation of latex quality by measuring the NIR spectra of standing tree. From the observation of near infrared spectra, it was shown that there was more latex signal in outer part of wood bark than in inner part of wood bark. This result suggests that the focal point should be on the outer part of bark to get the signal of latex when we measure the spectra of standing tree.     

基于TM影像和统计分析的林分参数估测研究

林业研究中的主要兴趣点之一在于通过经验或半经验模型建立林分参数与遥感影像数据间的相互关系来估测林分参数.基于覆盖美国佛罗里达州东北Duval县的遥感数据和两块样地清查数据,论文探讨了所选林分参数与TM影像光谱DN值间的相关性.相关性分析结果表明,单波段或植被指数对林分参数的解释能力低于50%,为此构建了林分参数与影像多波段间多元回归模型来估测林分参数.预测结果通过另一组数据验证,除林分密度外,其它参数估测可信度达75%以上.论文最后探讨了预测模型不足和需改进的地方,并指出该研究有助于更好地理解影像光谱值和林分参数间的关系.图1表2参9.     

Modelling dominant height growth from national forest inventory individual tree data with short time series and large age errors

We developed dominant height growth models for Norway spruce (Picea abies (L.) Karst.) and Scots pine (Pinus sylvestris L.) in Norway using national forest inventory (NFI) data. The data were collected for a different purpose which potentially causes problems for dominant height growth modelling due to short time series and large age errors. We used the generalized algebraic difference approach and fitted 15 different models using nested regression techniques. Despite the potential problems of NFI data the models fitted to these data were unbiased for most of the age and site index range covered by the NFI data when tested against independent data from long-term experiments (LTE). Biased predictions for young stands and better site indices that are better represented in the LTE data, led us to fit models to a combined data set for unbiased predictions across the total data range. The models fitted to the combined data that were unbiased with little residual variation when tested against an independent data set based on stem analysis of 73 sample trees from southeastern Norway. No indications of regional differences in dominant height growth across Norway were detected. We tested whether the better growing conditions during the short time series (22 years) of the NFI data had affected our dominant height growth models relative to long-term growing conditions, but found only minor bias. The combination with LTE data that have been collected during a longer period (91 years) reduced this potential bias. The dominant height growth models presented here can be used as potential height growth models in individual tree-based forest growth models or as site index models.     

Photosynthesis of a Scots pine shoot: a comparison of two models of shoot photosynthesis in direct and diffuse radiation fields

Two models of shoot photosynthesis, the needle surface element model (SEM) and needle volume element model (VEM), were tested against empirical data obtained from measurements of the photosynthetic response of twelve Scots pine (Pinus sylvestris L.) shoots in direct and diffuse radiation. The models assume that shoot photosynthesis is obtained as the integrated response of either all needle surface area elements (SEM) or all needle volume elements (VEM) of the shoot. The models differ in that needles are treated as optically black in SEM, whereas in VEM radiation penetrates into the needle. The photosynthetic response of a surface/volume element was described as a Blackman-type curve and the distributions of irradiance on the elements were derived by computer simulation, based on a model of shoot geometry. The parameters (initial slope and maximum rate) of the Blackman-curve of an element were estimated iteratively by the method of least squares, i.e., by minimizing the residual sum of squares of simulated and measured rates of shoot photosynthesis. The parameter estimation was done separately for direct and diffuse radiation, and the models were evaluated based on the notion that, for the "ideal" model, the estimated parameter values should be the same in direct and diffuse radiation. Both models produced shoot photosynthesis curves that agreed well with measurements, but there was a discrepancy in the estimated parameter values, indicating that differences in the photosynthetic response of shoots in direct and diffuse radiation could not be explained solely on the basis of the simulated irradiance distributions. The agreement was, however, much better for the volume element model, which accounts for penetration of radiation into the needles.     

Using optimization for fitting individual-tree growth models for uneven-aged stands

A convenient model type for simulating the dynamics of uneven-aged and uneven-sized stands of Finland is individual-tree model. This is because the stand structures are complex due to the presence of several tree species and irregular size distributions of trees. The required minimum set of models in this approach consists of species-specific individual-tree diameter increment models, individual-tree survival models, and ingrowth models. The development of these models needs data in which the diameter and survival of each tree of the sample plots is known for at least two time points. For this, the trees need to be numbered, which is tedious in uneven-aged forests due to the great number of small trees and the continuous ingrowth process. This study proposes a modelling approach that fits the above models but requires only the diameter distributions of the plots in the beginning and at the end of the measurement interval. The method uses non-linear optimization to derive such values for model parameters that, when the models are applied to the initial diameter distribution, the simulated stand development results in a diameter distribution which agrees with the measured ending distribution. The study showed that the method produces similar models and model parameters as regression analysis. Since the method is less demanding in terms of modelling data, it brings new data sets available for modelling the dynamics of uneven-aged stands and reduces the cost of collecting new data. The models fitted by the proposed optimization method were rather similar to the models developed earlier for Finnish uneven-aged forests.     

Estimation of forest parameters based on TM imagery and statistical analysis

One of the primary forestry research interests lies in estimating forest stand parameters by applying empirical or semi-empirical model to establish the relationship between the forest stand parameters and remote sensing data. Using remote sensing image and the inventory data from 2 compartments in northeast Florida, U.S.A., this paper explored the correlation between forest stand parameters and Landsat TM spectral digital number （DN） value. Results showed that less than 50% of the total variance could be explained by linear regression models with only either a single band or such vegetation indices as vegetation index （VI） or normalized difference vegetation index （NDVI） as predicators. In consequence, multi-linear regression models which synthesized more predicators were introduced to estimate forest parameters. Regression results were tested in terms of the other group of data, and verification showed a better capability of explaining over 75% variance except for forest density. The weakness and further improvement of prediction models were also discussed in the article. This paper is expected to provide a better understanding of the relationship between TM spectral and forest characteristics     

黄土丘陵区沙棘地上部生物量估测模型

根据沙棘生长因子与其地上部生物量间的相关关系,以生长因子为自变量,沙棘地上部生物量为因变量,应用主成分分析和多元回归分析方法,依据最优子集和平均残差平方和的优选原则,从单生长因子、双生长因子、多生长因子估测模型中,筛选出具有最优性质的沙棘地上部生物量估测模型,复相关系数为０．９４２１～０．９９５９,经检验均达十分显著水平。这一研究结果改进了非破坏性调查沙棘地上部生物量的方法。