一种多元非线性度量误差模型的参数估计及算法

本文讨论多元函数关系度量误差模型中参数的一种估计方法及算法的实现．     

线性度量误差模型的参数估计法与最小二乘法的关系

线性度量误差模型的参数分为度量误差向量的参数和非度量误差向量的参数,本文的研究表明,不论是非度量误差向量的参数估计还是度量误差向量的参数估计都可以由最小二乘估计法推广得到.     

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．     

NEE观测误差分布类型对陆地生态系统机理模型参数估计的影响——以长白山温带阔叶红松林为例

基于观测数据的陆地生态系统模型参数估计有助于提高模型的模拟和预测能力,降低模拟不确定性.在已有参数估计研究中,涡度相关技术测定的净生态系统碳交换量(NEE)数据的随机误差通常被假设为服从零均值的正态分布.然而近年来已有研究表明NEE数据的随机误差更服从双指数分布.为探讨NEE观测误差分布类型的不同选择对陆地生态系统机理模型参数估计以及碳通量模拟结果造成的差异,以长白山温带阔叶红松林为研究区域,采用马尔可夫链-蒙特卡罗方法,利用2003～2005年测定的NEE数据对陆地生态系统机理模型CEVSA2的敏感参数进行估计,对比分析了两种误差分布类型(正态分布和双指数分布)的参数估计结果以及碳通量模拟的差异.结果表明,基于正态观测误差模拟的总初级生产力和生态系统呼吸的年总量分别比基于双指数观测误差的模拟结果高61～86 g C m-2 a-1和107～116 g C m-2 a-1,导致前者模拟的NEE年总量较后者低29～47 g C m-2 a-1,特别在生长旺季期间有明显低估.在参数估计研究中,不能忽略观测误差的分布类型以及相应的目标函数的选择,它们的不合理设置可能对参数估计以及模拟结果产生较大影响.     

线性规划法在植物生态学数学模型参数估计中的应用初探

本文提出了一种植物生态学数学模型参数估计的新方法——线性规划法,并结合最小二乘法对模型参数的估计进行了实例分析。认为某种程度上前者更优于后者。是一种值得进一步研究的方法。     

Bayesian model predicts the aboveground biomass of Caragana microphylla in sandy lands better than OLS regression models

回归模型可用于预测森林生态系统地上生物量,其中最为常用的是最小二乘回归模型。在预测灌木,尤其是多茎灌木的地上生物量 时,最小二乘法与贝叶斯方法的比较很少被研究。我们开发了小叶锦鸡儿(Caragana microphylla Lam.)生物量预测模型。小叶锦鸡儿是科尔 沁沙地广泛分布的多茎灌木,对减少风蚀、固定沙丘具有重要作用。本研究建立6种表征生物量的异速增长模型,并基于统计标准选择 在预测生物量方面表现最佳的1种,然后分别用最小二乘法与贝叶斯方法对模型中的参数进行估计。参数估计过程中用自助法考察样本量大 小的影响,同时区分测试集与训练集。最后,我们比较了最小二乘法与贝叶斯方法在小叶锦鸡儿地上生物量预测中的表现。异速增长的6个 模型均达到显著水平,其中幂指数为1的模型表现最佳。研究结果表明,采用无先验信息与有先验信息的贝叶斯方法进行估计,得到的均 方误差在测试集上低于最小二乘法。另外,基径作为预测变量在最小二乘法与贝叶斯方法中均不显著,表明在生物量预测模型中应谨慎选 择合适变量。本研究强调贝叶斯方法、自助法和异速增长模型相结合能够提升沙地灌木生物量预测模型的准确度。     

用度量误差模型方法编制相容的生长过程表和材积表

指出了按照常规方法建立的生长模型和材积模型不相容的原因、利用两阶段度量误差模型方法估计生长模型和材积模型的参数,进而编制相容的生长过程表和材积表．     

单木生物量模型估计区域尺度生物量的不确定性

采用系统抽样体系江西省固定样地杉木连续观测数据和生物量数据,通过Monte Carlo法反复模拟由单木生物量模型推算区域尺度地上生物量的过程,估计了江西省杉木地上总生物量。基于不同水平建模样本量n及不同决定系数R~2的设计,分别研究了单木生物量模型参数变异性及模型残差变异性对区域尺度生物量估计不确定性的影响。研究结果表明:2009年江西省杉木地上生物量估计值为(19.84±1.27)t/hm~2,不确定性占生物量估计值约6.41%。生物量估计值和不确定性值达到平稳状态所需的运算时间随建模样本量及决定系数R~2的增大而减小;相对于模型参数变异性,残差变异性对不确定性的影响更小。     

三种线性模型在杉木与马尾松地位指数相关关系研究中的比较

地位指数法是当前立地质量评价中广泛采用的一种评定方法。在同一立地上,实现不同树种地位指数之间的转换,建立地位指数互导模型有助于立地质量的评定.譬如,在某一立地上现时生长着马尾松,欲知在马尾松被采伐后营造杉木林的生长潜力,这时就可利用上层木树种间地位指数的关系进行立地质量评定。以雪峰山杉木与马尾松地位指数配对样地数据为基础,建立了杉木与马尾松地位指数的常规线性模型、对偶回归模型和度量误差线性模型,从建模精度和模型适用性检验两方面,对3种模型进行了比较分析。结果表明3种模型的精度均比较高,模型效果差异不明显,其中,常规线性模型、度量误差模型和对偶回归模型的相对误差分别为5.39%、5.39%和5.54%。由于杉木地位指数和马尾松地位指数均存在度量误差,因此,线性度量误差模型和对偶回归模型比常规线性模型更适宜,这是因为,前两种模型的自变量和因变量是可以存在度量误差的,而后者的因变量是没有度量误差的。此外,线性度量误差模型的相对误差比对偶回归模型的要小,所以,3种线性模型中,线性度量误差模型最优。研究结果实现了相同立地条件下杉木地位指数和马尾松地位指数的互导,为不同树种间的立地质量评价提供了可行的方法。     

作物模型区域应用两种参数校准方法的比较

区域模拟的目的是利用有限的空间数据模拟出产量等作物性状的时空变异规律.然而站点作物模型应用到区域范围时涉及到数据归一化、参数简化、模型的校准和验证等问题.利用CERES-Rice模型对作物模型在我国的区域应用进行了尝试并对部分参数进行了校准.首先利用田间观测数据在各实验点上对模型进行了详细的站点校准,以验证模型在我国的模拟能力;其次,以我国水稻种植区(精确到亚区)为单位,运用平均值和标准差(RMSE)两种方法进行了区域校准和验证,即找出能反映出品种空间差异的代表性品种参数集;然后分别运用两种方法的校准结果,模拟水稻产量和成熟期,并将模拟结果与实测值进行了比较.结果表明:区域校准能反映出水稻生育期和产量的时空变化规律,其中RMSE法较平均值法效果好.目前作物模型区域应用过程中还存在大量的误差来源,有待进一步研究.     

A zero‐augmented generalized gamma regression calibration to adjust for covariate measurement error: A case of an episodically consumed dietary intake

Measurement error in exposure variables is a serious impediment in epidemiological studies that relate exposures to health outcomes. In nutritional studies, interest could be in the association between long‐term dietary intake and disease occurrence. Long‐term intake is usually assessed with food frequency questionnaire (FFQ), which is prone to recall bias. Measurement error in FFQ‐reported intakes leads to bias in parameter estimate that quantifies the association. To adjust for bias in the association, a calibration study is required to obtain unbiased intake measurements using a short‐term instrument such as 24‐hour recall (24HR). The 24HR intakes are used as response in regression calibration to adjust for bias in the association. For foods not consumed daily, 24HR‐reported intakes are usually characterized by excess zeroes, right skewness, and heteroscedasticity posing serious challenge in regression calibration modeling. We proposed a zero‐augmented calibration model to adjust for measurement error in reported intake, while handling excess zeroes, skewness, and heteroscedasticity simultaneously without transforming 24HR intake values. We compared the proposed calibration method with the standard method and with methods that ignore measurement error by estimating long‐term intake with 24HR and FFQ‐reported intakes. The comparison was done in real and simulated datasets. With the 24HR, the mean increase in mercury level per ounce fish intake was about 0.4; with the FFQ intake, the increase was about 1.2. With both calibration methods, the mean increase was about 2.0. Similar trend was observed in the simulation study. In conclusion, the proposed calibration method performs at least as good as the standard method.     

Seemingly unrelated measurement error models, with application to nutritional epidemiology

Motivated by an important biomarker study in nutritional epidemiology, we consider the combination of the linear mixed measurement error model and the linear seemingly unrelated regression model, hence Seemingly Unrelated Measurement Error Models. In our context, we have data on protein intake and energy (caloric) intake from both a food frequency questionnaire (FFQ) and a biomarker, and wish to understand the measurement error properties of the FFQ for each nutrient. Our idea is to develop separate marginal mixed measurement error models for each nutrient, and then combine them into a larger multivariate measurement error model: the two measurement error models are seemingly unrelated because they concern different nutrients, but aspects of each model are highly correlated. As in any seemingly unrelated regression context, the hope is to achieve gains in statistical efficiency compared to fitting each model separately. We show that if we employ a "full" model (fully parameterized), the combination of the two measurement error models leads to no gain over considering each model separately. However, there is also a scientifically motivated "reduced" model that sets certain parameters in the "full" model equal to zero, and for which the combination of the two measurement error models leads to considerable gain over considering each model separately, e.g., 40% decrease in standard errors. We use the Akaike information criterion to distinguish between the two possibilities, and show that the resulting estimates achieve major gains in efficiency. We also describe theoretical and serious practical problems with the Bayes information criterion in this context.     

Measurement error: Inter-and Intraobserver Variability. An Empiric Study

The intra- and inter-observer measurement error variability was studied using univariate and multivariate statistical tests. Eleven skeletal variables of four individuals each in four Primate species were measured ten times by three different researchers, using six different tools. An average measurement error of 0.52 mm. was obtained. Univariate statistics showed significant differences among reseachers. A multivariate discriminant analysis could also discriminate them. The measurement error may be either systematic or random, and depends not only on the researcher, but also on the tool used, the variable measured, and on the magnitude of the variable. The technique of Measurement Replication is proposed in order to reduce the measurement error, specially when compairing small samples or when trying to find small average differences between populations. The replication technique also reduces the standard deviation of the population sample.     

A simulation study of measurement error correction methods in logistic regression

Measurement error models in logistic regression have received considerable theoretical interest over the past 10-15 years. In this paper, we present the results of a simulation study that compares four estimation methods: the so-called regression calibration method, probit maximum likelihood as an approximation to the logistic maximum likelihood, the exact maximum likelihood method based on a logistic model, and the naive estimator, which is the result of simply ignoring the fact that some of the explanatory variables are measured with error. We have compared the behavior of these methods in a simple, additive measurement error model. We show that, in this situation, the regression calibration method is a very good alternative to more mathematically sophisticated methods.     

Measurement error and confidence intervals for ROC curves

Measurement error in a continuous test variable may bias estimates of the summary properties of receiver operating characteristics (ROC) curves. Typically, unbiased measurement error will reduce the diagnostic potential of a continuous test variable. This paper explores the effects of possibly heterogenous measurement error on estimated ROC curves for binormal test variables. Corrected estimators for specific points on the curve are derived under the assumption of known or estimated measurement variances for individual test results. These estimators and associated confidence intervals do not depend on normal assumptions for the distribution of the measurement error and are shown to be approximately unbiased for moderate size samples in a simulation study. An application from a study of emerging imaging modalities in breast cancer is used to demonstrate the new techniques.     

A longitudinal measurement error model with a semicontinuous covariate

Covariate measurement error in regression is typically assumed to act in an additive or multiplicative manner on the true covariate value. However, such an assumption does not hold for the measurement error of sleep-disordered breathing (SDB) in the Wisconsin Sleep Cohort Study (WSCS). The true covariate is the severity of SDB, and the observed surrogate is the number of breathing pauses per unit time of sleep, which has a nonnegative semicontinuous distribution with a point mass at zero. We propose a latent variable measurement error model for the error structure in this situation and implement it in a linear mixed model. The estimation procedure is similar to regression calibration but involves a distributional assumption for the latent variable. Modeling and model-fitting strategies are explored and illustrated through an example from the WSCS.     

Control for confounding in the presence of measurement error in hierarchical models

Hierarchical modeling is becoming increasingly popular in epidemiology, particularly in air pollution studies. When potential confounding exists, a multilevel model yields better power to assess the independent effects of each predictor by gathering evidence across many sub-studies. If the predictors are measured with unknown error, bias can be expected in the individual substudies, and in the combined estimates of the second-stage model. We consider two alternative methods for estimating the independent effects of two predictors in a hierarchical model. We show both analytically and via simulation that one of these gives essentially unbiased estimates even in the presence of measurement error, at the price of a moderate reduction in power. The second avoids the potential for upward bias, at the price of a smaller reduction in power. Since measurement error is endemic in epidemiology, these approaches hold considerable potential. We illustrate the two methods by applying them to two air pollution studies. In the first, we re-analyze published data to show that the estimated effect of fine particles on daily deaths, independent of coarse particles, was downwardly biased by measurement error in the original analysis. The estimated effect of coarse particles becomes more protective using the new estimates. In the second example, we use published data on the association between airborne particles and daily deaths in 10 US cities to estimate the effect of gaseous air pollutants on daily deaths. The resulting effect size estimates were very small and the confidence intervals included zero.     

实验室质量与实验室条件建设的关系概论

对测量误差的处理、控制和评定方法是决定测量数据质量即实验室质量水平的基础。实验室条件建设是降低和控制测量误差的保障,实验室质量控制的有效手段是建立适合的实验室条件。     

Statistical modelling and forecasting annual sugarcane production in India: Using various time series models

This paper proposes a comparison of various time series forecasting models to forecast annual data on sugarcane production over 63 years from 1960 to 2022. In this research, the Mean Forecast Model, the Naive Model, the Simple Exponential Smoothing Model, Holt's model, and the Autoregressive Integrated Moving Average time series models have all been used to make effective and accurate predictions for sugarcane. Different scale-dependent error forecasting techniques and residual analysis have been used to examine the forecasting accuracy of these time series models. SE of Residuals, Root Mean Squared Error (RMSE), Mean Absolute Error (MAE) and Akaike's Information Criterion (AIC) are used to analyse the forecast's accuracy. The best model has been selected based on the predictions with the lowest value, according to the three-performance metrics of RMSE, MAE, and AIC. The estimated sugarcane production shows an increasing trend for the next 10 years and is projected to be 37,763.38 million tonnes in the year 2032. Further, empirical results support the plan and execution of viable strategies to advance sugarcane production in India to fulfil the utilisation need of the increasing population and further improve food security.