On a generalization of a result of W. G. Cochran

A relationship due to W.G. Cochran showing the effect on leastsquares regression coefficients of marginalizing over or conditioningon an explanatory variable is generalized to quantile regressioncoefficients. The condition under which conditioning does notinduce interaction or effect reversal is shown. Examples aregiven. The discussion is simplest when all variables are continuous;the extension to discrete variables is outlined.     

度量误差模型及其应用

本文介绍度量误差模型的基本概念和参数估计的基本结果以及与通常回归之间的关系．并讨论了这个模型在生物学中应用的可能性．     

A Primer on Interpreting Regression Models

Abstract: We perceive a need for more complete interpretation of regression models published in the wildlife literature to minimize the appearance of poor models and to maximize the extraction of information from good models. Accordingly, we offer this primer on interpretation of parameters in single- and multi-variable regression models. Using examples from the wildlife literature, we illustrate how to interpret linear zero-intercept, simple linear, semi-log, log-log, and polynomial models based on intercepts, coefficients, and shapes of relationships. We show how intercepts and coefficients have biological and management interpretations. We examine multiple linear regression models and show how to use the signs (+, -) of coefficients to assess the merit and meaning of a derived model. We discuss 3 methods of viewing the output of 3-dimensional models (y, x₁, x₂) in 2-dimensional space (sheet of paper) and illustrate graphical model interpretation with a 4-dimensional logistic regression model. Statistical significance or Akaike best-ness does not prevent the appearance of implausible regression models. We recommend that members of the peer review process be sensitive to full interpretation of regression models to forestall bad models and maximize information retrieval from good models     

The Analysis of Life Table and Follow-up Data with Covariates Using Poisson Regression Model

The Poisson regression model for the analysis of life table and follow-up data with covariates is presented. An example is presented to show how this technique can be used to construct a parsimonious model which describes a set of survival data. All parameters in the model, the hazard and survival functions are estimated by maximum likelihood.     

A goodness-of-fit test for multinomial logistic regression

This article presents a score test to check the fit of a logistic regression model with two or more outcome categories. The null hypothesis that the model fits well is tested against the alternative that residuals of samples close to each other in covariate space tend to deviate from the model in the same direction. We propose a test statistic that is a sum of squared smoothed residuals, and show that it can be interpreted as a score test in a random effects model. By specifying the distance metric in covariate space, users can choose the alternative against which the test is directed, making it either an omnibus goodness-of-fit test or a test for lack of fit of specific model variables or outcome categories.     

DenNit – Experimental analysis and modelling of soil N2O efflux in response on changes of soil water content, soil temperature, soil pH, nutrient availability and the time after rain event

To quantify the effects of soil temperature (T_soil), and relative soil water content (RSWC) on soil N₂O emission we measured N₂O soil efflux with a closed dynamic chamber in situ in the field and from soil cores in a controlled climate chamber experiment. Additionally we analysed the effect of soil acidity, ammonium, and nitrate concentration in the field. The analysis was performed on three meadows, two bare soils and in one forest. We identified soil water content, soil temperature, soil nitrogen content, and pH as the main parameters influencing soil N₂O emission. The response of N₂O emission to soil temperature and relative soil water content was analysed for the field and climate chamber measurements. A non-linear regression model (DenNit) was developed for the field data to describe soil N₂O efflux as a function of soil temperature, soil moisture, pH value, and ammonium and nitrate concentration. The model could explain 81% of the variability in soil N₂O emission of all individual field measurements, except for data with short-term soil water changes, namely during and up to 2 h after rain stopped. We validated the model with an independent dataset. For this additional meadow site 73% of the flux variation could be explained with the model.     

Additive risk models for survival data with high-dimensional covariates

As a useful alternative to Cox's proportional hazard model, the additive risk model assumes that the hazard function is the sum of the baseline hazard function and the regression function of covariates. This article is concerned with estimation and prediction for the additive risk models with right censored survival data, especially when the dimension of the covariates is comparable to or larger than the sample size. Principal component regression is proposed to give unique and numerically stable estimators. Asymptotic properties of the proposed estimators, component selection based on the weighted bootstrap, and model evaluation techniques are discussed. This approach is illustrated with analysis of the primary biliary cirrhosis clinical data and the diffuse large B-cell lymphoma genomic data. It is shown that this methodology is numerically stable and effective in dimension reduction, while still being able to provide satisfactory prediction and classification results.     

A dynamic analysis of air pollution emissions in China: Evidence from nonparametric additive regression models

PM_2.5 emissions not only have serious adverse health effects, but also impede transportation activities, especially in air and highway transport. As a result, PM_2.5 emissions have become a public policy concern in China in recent years. Currently, the vast majority of existing researches on PM_2.5 are based on natural science perspective. Very few economic studies on the subject have been conducted with linear models. This paper adopts provincial panel data from 2001 to 2012, and uses the STIRPAT model and nonparametric additive regression models to examine the key driving forces of PM_2.5 emissions in China. The results show that the nonlinear effect of economic growth on PM_2.5 emissions is consistent with the Environmental Kuznets Curve (EKC) hypothesis. The nonlinear impact of urbanization exhibits an inverted “U-shaped” pattern due to the rapid development of urban real estate in the early stages and the strengthening of environmental protection measures in the latter stage. Coal consumption follows an inverted “U-shaped” relationship with PM_2.5 emissions owing to massive coal consumption at the beginning and efforts to optimize the energy structure as well as technological progress in clean energy in the latter stages. The nonlinear inverted “U-shaped” impact of private vehicles may be due to the different roles of scale, structural and technical effects at different stages. However, energy efficiency improvement follows a positive “U-shaped” pattern in relation to PM_2.5 emissions because of differences in the scale of the economy and the speed of technological progress at different times. As a result, the differential dynamic effects of the driving forces of PM_2.5 emissions at different times should be taken into consideration when initiating policies to reduce PM_2.5 emissions in China.     

Estimating severity of sideways fall using a generic multi linear regression model based on kinematic input variables

Many research groups have studied fall impact mechanics to understand how fall severity can be reduced to prevent hip fractures. Yet, direct impact force measurements with force plates are restricted to a very limited repertoire of experimental falls. The purpose of this study was to develop a generic model for estimating hip impact forces (i.e. fall severity) in in vivo sideways falls without the use of force plates.Twelve experienced judokas performed sideways Martial Arts (MA) and Block (‘natural’) falls on a force plate, both with and without a mat on top. Data were analyzed to determine the hip impact force and to derive 11 selected (subject-specific and kinematic) variables. Falls from kneeling height were used to perform a stepwise regression procedure to assess the effects of these input variables and build the model.The final model includes four input variables, involving one subject-specific measure and three kinematic variables: maximum upper body deceleration, body mass, shoulder angle at the instant of ‘maximum impact’ and maximum hip deceleration. The results showed that estimated and measured hip impact forces were linearly related (explained variances ranging from 46 to 63%). Hip impact forces of MA falls onto the mat from a standing position (3650 ± 916 N) estimated by the final model were comparable with measured values (3698 ± 689 N), even though these data were not used for training the model. In conclusion, a generic linear regression model was developed that enables the assessment of fall severity through kinematic measures of sideways falls, without using force plates.     

黑龙江省红松人工林枝条分布数量模拟

基于黑龙江省佳木斯市孟家岗林场的12块样地65株人工红松解析木的955个枝解析数据,以Poisson回归模型和负二项回归模型作为备选模型,构建了人工红松二级枝条数量分布模型,并采用AIC、Pseudo-R²、均方根误差(RMSE)和Vuong检验对模型的拟合优度进行比较.结果表明: 每轮一级枝条分布数量集中在3~5个,均值为4个,一级枝条分布数量与人工红松自身的枝条属性相关.一级标准枝上二级枝条分布的离散程度较大,利用全部子回归技术构建二级枝条分布数量模型,最终选择以负二项回归模型为基础的E(Y)=exp(β₀+β₁lnRDINC+β₂RDINC²+β₃HT/DBH+β₄CL+β₅DBH)作为二级枝条分布数量最优预测模型(β为参数;RDINC为相对着枝深度;HT为树高;DBH为胸径;CL为冠长).最优模型的Pseudo-R²为0.79,平均偏差接近于0,平均绝对偏差<7.对于所建立的模型,lnRDINC、CL和DBH的参数为正值,RDINC²和HT/DBH的为负值,随着RDINC增大,在树冠内二级枝条分布数量存在最大值.总的来说,所建立的人工红松二级枝条分布数量模型的预测精度为96.4%,可以很好地预估该研究区域人工红松二级枝条分布数量,为以后枝条的光合作用和生物量的研究提供了理论基础.     

豫西日本落叶松引种区环境因子对林木生长制约的数学模型研究

本研究以豫西日本落叶松引种区143块标准地及配套的5l株解析木资料,以及与此对应的土壤样品和气象等资料为研究材料,采用计算机程序模拟了优势水平均高对立地因子的数量化回归模型、年轮指数对气象因子及优势木高对土壤理化性状的最优回归模型．通过对三种数学模型的模拟,筛选出该引种区影响日本落叶松生长的主要环境因子为海拔高、冬春季气温及6～7月份降雨、土壤全氮及速效磷,并以此指导生产,避免盲目推广所造成的损失．     

数量化理论应用于现代林业的研究

本文对山地人工用材林关键技术组合优化模型及其应用进行了研究．     

Association of twenty-three plasma elements with fasting serum glucose among Chinese population from four areas with different pollution level

BackgroundAssociation between fasting serum glucose (FSG) and certain mineral elements has been extensively reported. Investigation regarding multi-element exposure among subjects with different exposure level is warranted to confirm the association and further explore dose-dependent relationship.MethodsA total of 3488 participants were recruited from four counties of Hunan province, South China. Basic characteristics were collected by face to face interview and 23 elements in plasma were determined by inductively coupled plasma mass spectrometry. We applied fully adjusted generalized linear regression model and multivariable restricted cubic spline function to test the association and dose-response relationship of FSG with 23 elements.ResultsThe results indicated that FSG was positively associated with plasma⁷⁸selenium level [regression coefficient (β), 0.001; 95 % confidence interval (CI), 0.001, 0.001] in a dose-dependent manner, robust to the adjustment for suspected covariates and stratification by age, gender, BMI and smoking status. A negative association was found between FSG and plasma ²⁰⁸lead (β, -0.004; 95 % CI, -0.016, -0.002), ⁵²chromium (β, -0.002; 95 % CI, -0.004, -0.001) and ⁴⁷titanium (β, -0.001; 95 % CI, -0.002, -0.001).Conclusion⁷⁸selenium was positively while ²⁰⁸lead, ⁵²chromium and ⁴⁷titanium were negatively associated with FSG in the present study. However, prospective studies are needed to confirm the results.