森林林下植被生物量收获的样方选择和模型

在控制误差内寻求样方的最小面积和最少样方数量是植被生态学野外研究的重要问题。在综合考虑取样的边界效应和时间、劳力消耗的基础上,研究了在控制误差内测定森林林下植被生物量时应选择的最佳样方大小和数量,并找出最佳的自变量拟合了估算林下植被生物量的预测方程。结果表明,利用Wiegert的方法测定研究区林下植被生物量取样方案,得出0．25m。的小样方为最佳取样面积。但小样方受边界效应的影响很大,会产生过高的生物量估计。通过分析了边界效应的影响和生物量相对平均值的变化,得出2m×1m是本研究的最佳样方面积,而10个2m×1m的样方能把标准误差控制在生物量平均值的10％以内。灌木生物量回归方程所选取的3个自变量D^2H、CH和P日中,CH与灌木生物量的相关性和以CH为自变量的线性回归方程的拟合度较其他2个变量好。而以PH为自变量的灌木生物量预测方程在实际操作中能提高研究的简便性和效率。以PH为自变量的林下草本层单位面积生物量的预测方程分别为Wv=11．65＋4．25（PH）和wD=24．23＋6．85（PH）。     

微波协同酶法提取平菇柄多糖的工艺研究

为优化微波协同酶法提取平菇柄多糖的工艺条件,在单因素试验的基础上,选择提取时间、微波功率以及液料比为自变量,多糖得率为响应值,采用中心组合设计的方法,研究各自变量及其交互作用对多糖得率的影响。利用响应面分析方法,模拟得到二次多项式回归方程的预测模型,并确定平菇柄多糖提取工艺的最佳条件为:微波功率420 W,提取时间8 min,液料比55:1,在此条件下,最大得率达到6.05%。     

通径分析理论与实践中的几个问题

本文讨论了通径分析理论与应用中常见的几个问题．分析了剩余效应对结果的决定系数的理论组成,和剩余效应与观测的自变量间存在相关时对通径分析结果的影响．     

关于数量化I方法的自变量之间交互作用计算

自变量之间存在交互作用时,在应用数量化方法Ｉ时如何计算自变量间的交互作用建立数量化方程．     

关于数量化Ⅰ方法的自变量之间交互作用计算

自变量之间存在交互作用时,在应用数量化方法Ⅰ时如何计算自变量间的交互作用建立数量化方程。     

用岭回归预测水稻螟害的白穗率

<正> 预测是回归方程的一项重要的应用,评价一个经验回归方程的好坏,一个常用的重要标准就是看由它所作的预测的精度如何。因为在线性回归前提下,经验回归方程的形状,取决于选择的自变量,以及回归系数的估计方法。Hoerl和Kennard提出的岭回归(Ride Regression)与最小二乘法相比,其变量的选择,回归系数的估计及回归效果均令人满意。本文利用岭回归分析法从多元共线性的变量中,选择最佳的因子来建立水稻三化螟第二代螟害白穗率的预测方程,其结果要比多元回归的效果好。     

千烟洲人工林主要树种地上生物量的估算

利用不同参数和函数,模拟了千烟洲人工林主要树种马尾松、湿地松和杉木的枝条、叶生物量和总生物量及单株各器官生物量,选择最佳函数计算生物量在各树种不同器官中的分配,估算不同林型的地上生物量.结果表明,不同树种的枝条基径(d)和枝条生物量(BW)、叶生物量(LW)之间,当d³为自变量时,相关系数最高,湿地松利用线性函数、马尾松和杉木利用幂函数模拟效果最佳;单木总生物量以利用D²H(胸径²×树高)为自变量的幂函数模拟相关系数最高;3个树种叶和枝生物量各有不同的最佳自变量和函数类型,但同一树种的叶、枝生物量最佳拟合方程的自变量和函数类型一致.马尾松林、湿地松林和杉木林的地上生物量分别为83.6、72.1和59 t·hm^-2,其中树干生物量所占比重最大,叶生物量最小.根据前人的研究结果推算3种林分地下生物量分别为10.44、9.42和11.48 t·hm^-2,其固碳量分别为47.94、45.14和37.52 t·hm^-2.     

响应面分析法优化超声提取蓖麻碱工艺

以蓖麻叶为原料,对蓖麻碱的超声提取工艺优化进行研究,在单因素试验的基础上,选择超声时间、超声功率、料液比为自变量,以蓖麻碱提取率为影响值,采用响应面试验设计方法,研究各自变量及其交互作用对蓖麻碱提取率的影响。利用Design Expert8软件得到回归方程得模型并进行响应面分析,确定超声提取蓖麻碱的最佳工艺条件为料水比为1∶25 g/mL,超声时间为103.03 min,超声功率为621.05 W,此条件下蓖麻碱的提取率为2.63‰。     

基于机载激光雷达的小兴安岭温带森林组分生物量反演

使用小兴安岭温带森林机载遥感-地面观测同步试验获取的机载激光雷达(light detection and ranging, Lidar)点云数据和地面实测样地数据, 估测了典型森林类型的树叶、树枝、树干、地上、树根和总生物量等组分的生物量。从激光雷达数据中提取了两组变量(树冠高度变量组和植被密度变量组)作为自变量, 并采用逐步回归方法进行自变量选择。结果表明: 激光雷达数据得到的变量与森林各组分生物量有很强的相关性; 对于针叶林、阔叶林和针阔叶混交林三种不同森林类型生物量的估测结果是: 针叶林优于阔叶林, 阔叶林优于针阔叶混交林; 不区分森林类型的各组分生物量估测与地面实测值显著相关, 模型决定系数在0.6以上; 区分森林类型进行建模可以进一步提高生物量的估测精度。     

西安市4种城市绿化灌木单株生物量估算模型

以西安市常见的4种绿化灌木(小叶女贞、雀舌黄杨、紫叶小檗、大叶黄杨)为研究对象,利用不同函数和自变量构建单一物种的器官及个体生物量估算模型,筛选出相关性最高、拟合度最好的模型作为生物量最佳估算模型.结果表明： 4种灌木各器官及个体生物量最优估算模型除大叶黄杨叶生物量模型为对数函数(VAR)模型外,其余无论是器官生物量模型还是个体生物量模型均为幂函数(CAR)模型.模型包含的自变量有基径、植株冠幅直径、植株冠幅直径与株高乘积、植冠面积和植冠体积.大叶黄杨和其他3种灌木在自变量选取上有着明显不同.大叶黄杨生物量模型主要以基径为自变量,其他3种灌木生物量模型主要以与冠幅相关的因子为自变量.
     

Independent contrasts and PGLS regression estimators are equivalent

We prove that the slope parameter of the ordinary least squares regression of phylogenetically independent contrasts (PICs) conducted through the origin is identical to the slope parameter of the method of generalized least squares (GLSs) regression under a Brownian motion model of evolution. This equivalence has several implications: 1. Understanding the structure of the linear model for GLS regression provides insight into when and why phylogeny is important in comparative studies. 2. The limitations of the PIC regression analysis are the same as the limitations of the GLS model. In particular, phylogenetic covariance applies only to the response variable in the regression and the explanatory variable should be regarded as fixed. Calculation of PICs for explanatory variables should be treated as a mathematical idiosyncrasy of the PIC regression algorithm. 3. Since the GLS estimator is the best linear unbiased estimator (BLUE), the slope parameter estimated using PICs is also BLUE. 4. If the slope is estimated using different branch lengths for the explanatory and response variables in the PIC algorithm, the estimator is no longer the BLUE, so this is not recommended. Finally, we discuss whether or not and how to accommodate phylogenetic covariance in regression analyses, particularly in relation to the problem of phylogenetic uncertainty. This discussion is from both frequentist and Bayesian perspectives.     

A Technique for the Analysis of Unbalanced Data

The regression methods with dummy variables have been shown to be effective in preventing confusion in the analysis of linear models. In particular, this model simplifies interpretation of parameters and clarifies hypothesis statements. All existing methods have been shown as special cases of the general linear hypothesis in regression setting. Three regression on dummy variables methods are examined critically to bring out the salient features of each method. The choice of a method should be based on the way definitions of the parameters are desired. The linear models are considered in a regression model setting. This has been done by defining appropriate dummy variables in a regression model which often is desirable, if not mandatory, when dealing with unbalanced data involving two or more factors.     

An adaptive test for a subset of coefficients in a multivariate regression model

An adaptive multivariate test is proposed for a subset of regression coefficients in a linear model. This adaptive method uses the studentized deleted residuals to calculate an appropriate weight for each observation. The weights are then used to compute Wilk's lambda for the weighted model. The adaptive test is performed by permuting the independent variables corresponding to those parameters that are assumed to equal zero in the null hypothesis. The permuted variables are then weighted to obtain a permutation test statistic that is used to estimate the p-value. An example is presented of a multivariate regression that uses systolic and diastolic blood pressure as dependent variables with age and body mass index as independent variables. The simulation results show that the adaptive test maintains its size for the three multivariate error distributions that were used in the study. For normal error models the power of the adaptive test nearly equaled that of the non-adaptive test. For models that used non-normal errors the adaptive test was considerably more powerful than the traditional non-adaptive test.     

Three algorithms and SAS macros for estimating power and sample size for logistic models with one or more independent variables of interest in the presence of covariates

Background

Commonly when designing studies, researchers propose to measure several independent variables in a regression model, a subset of which are identified as the main variables of interest while the rest are retained in a model as covariates or confounders. Power for linear regression in this setting can be calculated using SAS PROC POWER. There exists a void in estimating power for the logistic regression models in the same setting.

Methods

Currently, an approach that calculates power for only one variable of interest in the presence of other covariates for logistic regression is in common use and works well for this special case. In this paper we propose three related algorithms along with corresponding SAS macros that extend power estimation for one or more primary variables of interest in the presence of some confounders.

Results

The three proposed empirical algorithms employ likelihood ratio test to provide a user with either a power estimate for a given sample size, a quick sample size estimate for a given power, and an approximate power curve for a range of sample sizes. A user can specify odds ratios for a combination of binary, uniform and standard normal independent variables of interest, and or remaining covariates/confounders in the model, along with a correlation between variables.

Conclusions

These user friendly algorithms and macro tools are a promising solution that can fill the void for estimation of power for logistic regression when multiple independent variables are of interest, in the presence of additional covariates in the model.

     

Analysis and estimative of schistosomiasis prevalence for the state of Minas Gerais, Brazil, using multiple regression with social and environmental spatial data

The aim of this work is to establish a relationship between schistosomiasis prevalence and social-environmental variables, in the state of Minas Gerais, Brazil, through multiple linear regression. The final regression model was established, after a variables selection phase, with a set of spatial variables which contains the summer minimum temperature, human development index, and vegetation type variables. Based on this model, a schistosomiasis risk map was built for Minas Gerais.     

Evaluation of regression models in metabolic physiology: predicting fluxes from isotopic data without knowledge of the pathway

This study explores the ability of regression models, with no knowledge of the underlying physiology, to estimate physiological parameters relevant for metabolism and endocrinology. Four regression models were compared: multiple linear regression (MLR), principal component regression (PCR), partial least-squares regression (PLS) and regression using artificial neural networks (ANN). The pathway of mammalian gluconeogenesis was analyzed using [U−¹³C]glucose as tracer. A set of data was simulated by randomly selecting physiologically appropriate metabolic fluxes for the 9 steps of this pathway as independent variables. The isotope labeling patterns of key intermediates in the pathway were then calculated for each set of fluxes, yielding 29 dependent variables. Two thousand sets were created, allowing independent training and test data. Regression models were asked to predict the nine fluxes, given only the 29 isotopomers. For large training sets (>50) the artificial neural network model was superior, capturing 95% of the variability in the gluconeogenic flux, whereas the three linear models captured only 75%. This reflects the ability of neural networks to capture the inherent non-linearities of the metabolic system. The effect of error in the variables and the addition of random variables to the data set was considered. Model sensitivities were used to find the isotopomers that most influenced the predicted flux values. These studies provide the first test of multivariate regression models for the analysis of isotopomer flux data. They provide insight for metabolomics and the future of isotopic tracers in metabolic research where the underlying physiology is complex or unknown.We acknowledge the support of NIH Grant DK58533 and the DuPont-MIT Alliance.     

A note on the use of multiple linear regression in molecular ecology

Multiple linear regression analyses (also often referred to as generalized linear models – GLMs, or generalized linear mixed models – GLMMs) are widely used in the analysis of data in molecular ecology, often to assess the relative effects of genetic characteristics on individual fitness or traits, or how environmental characteristics influence patterns of genetic differentiation. However, the coefficients resulting from multiple regression analyses are sometimes misinterpreted, which can lead to incorrect interpretations and conclusions within individual studies, and can propagate to wider‐spread errors in the general understanding of a topic. The primary issue revolves around the interpretation of coefficients for independent variables when interaction terms are also included in the analyses. In this scenario, the coefficients associated with each independent variable are often interpreted as the independent effect of each predictor variable on the predicted variable. However, this interpretation is incorrect. The correct interpretation is that these coefficients represent the effect of each predictor variable on the predicted variable when all other predictor variables are zero. This difference may sound subtle, but the ramifications cannot be overstated. Here, my goals are to raise awareness of this issue, to demonstrate and emphasize the problems that can result and to provide alternative approaches for obtaining the desired information.     

降水量和温度对植被覆盖指数影响的空间非平稳性特征——以新疆伊犁河谷地区为例

多变量空间相关分析多基于时间序列数据,对数据时长与统计要求严格,空间非平稳性特征分析可以利用单期数据分析多变量之间的相关性。通过空间变系数回归模型分析了2006年和2011年的新疆伊犁地区降水量和温度对植被覆盖度指数影响的空间变化特征,利用局部线性地理加权回归(GWR)方法估计得到了回归系数曲面,揭示出变量间相互影响的空间异质性,同时利用线性回归最小二乘估计进行了对比。结果表明:(1)空间变系数回归模型可以用于变量间的空间相关分析;(2)局部线性GWR估计方法明显优于线性回归最小二乘估计;(3)拟合结果表明,伊犁地区降水量和温度对植被覆盖指数的影响具有显著的空间非平稳性特征;(4)模型估计误差是降水、气温之外的地形、地貌及人类活动等多种因素造成的,需进一步研究。方法可为具有空间非平稳性特征变量间空间相关性分析以及植被覆盖指数的空间模拟分布提供思路和方法。     

The Treatment of Missing Values in Logistic Regression

The efficiencies of the estimators in the linear logistic regression model are examined using simulations under six missing value treatments. These treatments use either the maximum likelihood or the discriminant function approach in the estimation of the regression coefficients. Missing values are assumed to occur at random. The cases of multivariate normal and dichotomous independent variables are both considered. We found that in general, there is no uniformly best method. However, mean substitution and discriminant function estimation using existing pairs of values for correlations turn out to be favourable for the cases considered.