Statistical inference for calibration points in nonlinear mixed effects models

Many disciplines conduct studies in which the primary objectives depend on inference based on a nonlinear relationship between the treatment and response. In particular, interest often focuses on calibration—that is, estimating the best treatment level to achieve a particular result. Often, data for such calibration come from experiments with split-plots or other features that result in multiple error terms or other nontrivial error structures. One such example is the time-of-weed-removal study in weed science, designed to estimate the critical period of weed control. Calibration, or inverse prediction, is not a trivial problem with simple linear regression, and the complexities of experiments such as the time-of-weed-removal study further complicate the procedure. In this article, we extend existing calibration techniques to nonlinear mixed effects models, and illustrate the procedure using data from a time-of-weed-removal study.     

THE CONSTRUCTION OF CALIBRATION CURVES FOR DETERMINING WATER CONTENT FROM RADIATION COUNTS

The application of regression theory to the construction of calibration curves for the estimation of water content from an observed radiation count is possible only when the relationship between count and water content is linear, a homogeneous error applies to the dependent variate, count, whatever its value, and the independent variate, water content, is determined free of error. Determination of the errors of estimation is further complicated by the necessity to fit the regression of count, as the dependent variate, on water content and then to invert the equation in order to estimate moisture content from count. It is shown that these requirements can be fulfilled by an initial transformation of the data and by repeated sub-sampling for the determination of water content. A method is given for calculating errors of estimation. Experimentally, it was found that a transformation (logarithmic) was necessary when calibrating a beta-gauge for leaf moisture measurement. When calibrating a neutron probe for soil-moisture measurement no transformation was required, but it was necessary to take repeated sub-samples for water content determinations.     

Potential Use of Nitrogen Reflectance Index to estimate Plant Parameters and Yield of Maize

Estimating the spatial variability of various plant parameters during the growing season can assist in timely correction of stress conditions within a field. This research illustrates that the nitrogen reflectance index (NRI) developed to estimate plant nitrogen status can be used to estimate plant parameters and yield potential. The study was conducted on two experimental maize sites. Selected maize hybrids were ‘Pioneer 3790’, which was a planophile canopy architecture and ‘NC+ 1598’ with an erectophile canopy architecture. The first site consisted of six non-replicated fertiliser plots. Data from these plots were used to develop the relationships between reflectance data and the plant parameters. The second site contained four plots with various nitrogen (N) and water treatments on which the developed relationships were verified. Leaf area, biomass, and plant reflectance data were collected almost weekly from both sites during the 1996 growing season. Measured and estimated yield, leaf area index (LAI) and dry matter were mapped in ArcVIEW geographical information system. Results showed that the NRI was a comparable estimator of potential yield to the normalised difference vegetation index or to the modified soil adjusted vegetation index. For the LAI and biomass, all vegetation indices produced similar coefficients of determination. Results showed that the NRI could be used to estimate the within-field variation of yield potential and plant parameters.     

The potential for Scottish cultivated topsoils to lose or gain soil organic carbon

Scotland's cultivated topsoils are rich in carbon with a median soil organic carbon (SOC) content of ca. 3.65%. The storage of carbon in soil is a means to offset GHG emissions, but equally carbon losses from soils can add to these emissions. We estimate the amount of carbon stored in Scottish cultivated mineral topsoils (246 ± 9 Mt), the potential carbon loss (112 ± 12 Mt) and the carbon storage potential of between 150 and 215 Mt based on national‐scale legacy data with uncertainty around the estimate due to error terms in predicting bulk densities for stock calculations. We calculate that Scotland's mineral cultivated topsoils hold the carbon equivalent of around 18 years of GHG emissions (based on 2009 emissions from all sources). We also derive a theoretical carbon saturation potential using a published, linear relationship with the <20‐μm mineral fraction (116 ± 14 Mt). Although the calculated uncertainties are quite small, care needs to be taken when using the results of such analyses as a policy instrument, and while the potential storage capacity seems large, it is unlikely to be achieved while still maintaining current land use patterns in Scotland. The methodology relies on legacy data (which may not reflect the current status of Scottish cultivated topsoils) and on summary statistics calculated from national‐scale data; however, those land management strategies that may mitigate GHG emissions are likely to be implemented at the field scale.     

Validation of the ANOCOVA model for regional‐scale ECa to ECe calibration

Two approaches have emerged as the preferred means for assessing salinity at regional scale: (i) vegetative indices from satellite imagery (e.g., MODIS enhanced vegetative index, NDVI) and (ii) analysis of covariance (ANOCOVA) calibration of apparent soil electrical conductivity (EC_a) to salinity. The later approach is most recent and least extensively validated. It is the objective of this study to provide extensive validation of the ANOCOVA approach. The validation comprised 77 fields in California's Coachella Valley, ranging from 1.25 to 30.0 ha in size with an average size of 12.8 ha. Mobile electromagnetic induction (EMI) equipment surveyed the fields obtaining geospatial measurements of EC_a. Soil sample sites selected following EC_a‐directed soil sampling protocols characterized the range and spatial variation in EC_a across the field. From the data, a regional ANOCOVA model was developed. The regional ANOCOVA model successfully reduced cross‐validated, average log salinity prediction error (variance) estimate by more than 30% across the 77 fields and improved the depth‐averaged prediction accuracy in 58 of the 77 fields. The results show that the ANOCOVA modelling approach improves soil salinity predictions from EMI signal data in most of the surveys conducted, particularly fields where only a limited number of calibration sampling locations were available. The establishment of ANOCOVA models at each depth increment for a representative set of fields within a regional‐scale study area provides slope coefficients applicable to all future fields within the region, significantly reducing ground‐truth soil samples at future fields.     

A comprehensive study on irrigation management in Asia and Oceania

The aim of this paper was to study the land use index (equipped area for irrigation per cultivated area, AI) and irrigation management in Asia and Oceania during past decades. For this purpose, all necessary information was collected from Food and Agriculture Organization of the United Nations (FAO). Among all presented data in the FAO database, 10 indices were selected. These indices were analysed for all 64 countries in Asia and Oceania, and the extent of AI was estimated by two different methods and other 9 indices. The results show that using all the 9 indices, the value of relative error will be less than 20%. Prioritization of the indices has shown that national rainfall index (NRI) and the difference between NRI and irrigation water requirement had a highlighted effect on the estimation of AI.     

A Measurement Error Model for Heterogeneous Capture Probabilities in Mark-Recapture Experiments: An Estimating Equation Approach

Logistic models for capture probabilities that depend on covariates are effective if the covariates can be measured exactly. If there is measurement error so that a surrogate for the covariate is observed rather than the covariate itself, simple adjustments may be made if the parameters of joint distribution of the covariate and the surrogate are known. Here we consider the case when a surrogate is observed whenever an individual is captured and the parameters must also be estimated from the data. An estimating equation regression calibration approach is developed and it is illustrated on a real dataset where the surrogate is an individual bird’s wing-length, which varies from occasion to occasion.     

Improved Calibration for Estimating Soil Properties with a Multifunctional Heat Pulse Probe

A multifunctional heat pulse probe (MFHPP) can measure soil thermal and hydraulic properties. Though its successful implementation has been documented, previous studies have reported some limitations. One specific cause of the limitations is the absorption of the generated heat pulse within the probe itself, which creates error in the measurements. The objective of this study was to develop and evaluate a new calibration method to account for measurement error due to heat loss to the probe. A MFHPP was constructed and tested in six soil types using both a traditional method and the newly developed calibration method. The new calibration utilizes heat pulse response curves from real soils with thermal conductivities similar to that of the MFHPP rather than the traditional agar-stabilized water solution. This new approach significantly reduced average measurement errors from 9.1% to 2.4% for heat capacity and 13.5% to 4.5% for volumetric water content.     

The devil is in the detail: Discrepancy between soil organic carbon stocks estimated from regional and local data sources in Flanders,Belgium

Storage of soil organic carbon (SOC) is an essential function of ecosystems underpinning the delivery of multiple services to society. Regional SOC stock estimates often rely on data collected during land‐use‐specific inventory schemes with varying sampling depth and density. Using such data requires techniques that can deal with the associated heterogeneity. As the resulting SOC assessments are not calibrated for the local scale, they could suffer from oversimplification of landscape processes and heterogeneity. This might especially be the case for sandy regions where typical historical land use practices and soil development processes determine SOC storage. The aims of this study were (a) to combine four land‐use‐specific SOC stock assessments to estimate the total stock in Flanders, Belgium, and (b) to evaluate the applicability of this regional‐scale estimate at the local scale. We estimated the SOC stock in the upper 100 cm of the unsealed area in Flanders (887,745 ha) to be 111.67 Mt OC, or 12.6 ± 5.65 kg OC m^?2 on average. In general, soils under (semi‐) natural land‐use types, for example forests, store on average more organic carbon than under agriculture. However, overall agricultural soils store the largest amounts of SOC due to their vast spatial extent. Zooming in on a sandy location study (13.55 km²) revealed the poor performance of the regional estimates, especially where Histosols occurred. Our findings show that a greater spatial sampling density is required when SOC stock estimates are needed to inform carbon‐aware land management rather than to provide for regional reporting.     

MODIS水稻面积提取中独立成分端元丰度校正方法

为了解决独立成分分析中端元丰度校正结果同实际丰度相差较大的问题,该文提出了一种基于回归分析的独立成分端元丰度校正方法。具体是:首先应用ICA对遥感时序数据进行分解,获取目标地物的ICA分解结果;再抽选一定量的样本,将样本目标地物的真实丰度与ICA分解结果进行回归;最后根据回归关系推算每个像元的目标地物丰度。基于MODIS时序数据,将该文方法和线性拉伸方法应用于江苏兴化地区的水稻面积提取,并将2种方法的提取结果同水稻准真值图像进行对比。分析结果表明,该文方法得到的水稻丰度图像的均方根误差、偏差在不同的空间尺度下均小于线性拉伸方法,而不同空间尺度下的决定系数(R2)均高于线性拉伸方法。与线性拉伸方法相比,该文方法能获得更接近实际情况的端元丰度校正结果,增强了ICA在农作物面积提取中的应用能力,为大尺度农作物识别和面积提取提供了依据。     

Analyzing highly variable potency data using a linear mixed-effects measurement error model

A house standard lot is tested along with experimental samples in a variable TCID₅₀ assay in order to monitor and control assay performance. Instead of being simply a control, it is proposed to use this lot as a calibration standard to reduce the systematic variability in the assay caused by acknowledged sources of variability such as the age of the cells used in the assay and interlaboratory differences. Because of this new proposal, the consistency of the relationship between the test sample and the house standard is assessed within the acceptance range of the house standard. A linear mixed-effects measurement error model is proposed for the data. The slope curve is then used to assess the dynamic relationship between the sample and the house standard within the house standard range. It is shown with these analyses that the sample and the house standard have uniformly good agreement within the house standard range.     

平板闸门自由-淹没孔流统一流量率定模型

中国灌区的常用量水方法中,利用水工建筑物尤其是闸门量水是目前应用最为广泛的,但传统的闸门过流公式林林总总,实际应用中需区分自由、淹没流态选择对应的公式,理论值与实测值偏差较大,该研究拟提出一种基于实测数据率定的形式简单、可应用于多种流态的流量计算模型。主要采用三维数值模拟的方法,通过建立实际水闸的三维流体力学模型,研究不同流态下的闸门水力特性,并结合室内模型试验和野外原型观测提出基于实测数据率定的流量计算模型。研究步骤为：1）验证基于实测数据的率定模型的有效性及精确性;2）分析该模型应用于闸门不同流态的率定效果,判断其是否可用于自由及淹没孔流建立统一的流量关系;3）对所提出的模型方法进行野外实测数据验证,并进行误差来源分析。结果表明：1）该模型能够进行区分流态的率定且精度较高,90.63%的数据误差在5%以内;2）该模型能够统一自由-淹没孔流率定,使用仿真数据进行统一率定时数据误差在5%以内的占比为86.67%,使用南水北调中线某闸门8、10、11月份验证模型精度可达到77.64%的数据误差在5%以内,95%以上数据误差在10%以内的效果。该模型具有简单、光滑连续的特点,在实际工程应用中建议通过大量实测提高模型精度。     

基于高光谱成像的肉品检测去条带噪声方法

推扫式高光谱成像系统通常因电荷耦合器件（Charge Coupled Device,CCD）各像元响应不一致而产生条带噪声,该研究以猪肉为研究对象,设计一种基于多块标准反射率板进行逐波段逐像素相对辐射定标的去除条带噪声方法。该方法基于最小二乘法,利用不同反射率标准板的反射率值与CCD输出值,采用多项式拟合出接近于各个波段逐像元真实响应函数的拟合响应函数;选取每一波段图像中的任一像元作为参考,将其余像元与参考像元的拟合响应函数做差,作为其余像元的补偿函数,再采用样本的输出值加补偿值以校正样本。分别采用逐波段逐像素相对辐射定标法和传统矩匹配法对猪肉高光谱图像进行处理,并以四阶标准反射率板各反射区均值与参考值的绝对误差评估反射率校正结果。结果表明,逐波段逐像素相对辐射定法在有效去除条带噪声的同时,不会产生新的噪声,同时能够保持原始图像的灰度分布,校正后图像条带系数最大值比原始图像减少63.5%;相比矩匹配法,反射率误差大幅下降,其中条带系数最大波段（200波段）4个反射区的绝对误差为0.003～0.089,随机抽取波段（300波段）4个反射区的绝对误差为0.009～0.083。该研究为消除条带噪声提供了一种可靠方法,同时为提高后续基于推扫式光谱成像的指标空间可视化精度奠定了良好的基础。     

Evaluating the applicability of the water erosion prediction project (WEPP) model to runoff and soil loss of sandstone reliefs in the Loess Plateau,China

Soil erosion is one of the most serious environmental issues, especially in vulnerable areas such as the Pisha sandstone regions located in the Loess Plateau (China). In these types of reliefs, long-term studies monitoring runoff and soil loss are scarce, and even more considering the efficiency of different soil management techniques applied to reduce land degradation. In this study, seven years (2014–2020) of in-situ measurements of surface runoff and soil loss for different land uses (forestland, shrubland, grassland, farmland, and bare land) in a Pisha Sandstone environment at the Loess Plateau were conducted. We applied the Water Erosion Prediction Project (WEPP) model combining the large database with the precipitation regimes. Our results showed that runoff volume coming from observed and simulated data exhibited significant differences among them depending on the different vegetation types. Runoff and soil loss were different among diverse land use types as follows: farmland > grassland > shrubland > forestland. After conducting a calibration, we found satisfactorily simulated surface runoff and sediment yield based on precipitation regimes and land uses at sandstone reliefs. Simulation performance of surface runoff was better than sediment yield. The range of standard error of the model simulation for event and annual values of runoff were 4.71 mm and 12.19 mm, respectively. The standard error for event and annual values of soil loss were 4.19 t/hm² and 21.86 t/hm². In the calibration group, R² of runoff and soil loss were 0.92 and 0.86 respectively, while Nash-Sutcliffe coefficient (E) reached 0.90 and 0.85, respectively. In the validation group, the R² for both runoff and soil loss were 0.82 and 0.56, respectively. Nash-Sutcliffe coefficient (E) were 0.77 and 0.54 for the runoff and sediment yield. We concluded that using a detailed monitoring dataset, the WEPP model could accurately simulate and predict water erosion in the hillslopes of Pisha sandstone area.     

Potential to predict depth‐specific soil–water content beneath an olive tree using electromagnetic conductivity imaging

Efficient monitoring of soil moisture is becoming increasingly important. To understand soil–plant–water dynamics, we evaluate the potential of using a multiple‐coil‐array electromagnetic induction instrument and inversion software to map soil moisture beneath an olive tree. On twelve different days, we collected apparent electrical conductivity (EC _a) data using a DUALEM ‐21S and the volumetric soil moisture (θ ) using a bank of soil moisture sensors on opposite sides of the tree. Using EM 4Soil, we inverted the EC _a data on five of the days and established a site‐specific calibration between estimates of true electrical conductivity (σ ) and θ . The strongest calibration relationship between σ and θ (R ² = 0.65) was obtained for a full‐solution, S2 algorithm and damping factor of 1.2. A leave one out cross‐validation (LOOCV ) showed the calibration was robust, with a root mean square error (RMSE ) of 0.046 m³/m³, a mean error (ME ) of 0.001 m³/m³ and a Lin's concordance of 0.72. We subsequently evaluated the calibration relationship on the seven remaining days and over a drying period of 120 days. This approach provides information about the temporal evolution of θ by a LOOCV of validation with a RMSE of 0.037, ME of −0.003 and a Lin's concordance of 0.54. Improvement could be achieved by aligning the DUALEM ‐21S in the same orientation as the sensors, with time‐lapse inversion also being advantageous.     

可见/近红外光谱技术无损检测果实坚实度的研究

该研究的目的是建立可见/近红外光谱与梨果实坚实度之间的数学模型,评价可见/近红外光谱技术无损测量梨果实坚实度的应用价值.在可见/近红外光谱区域(350～1800nm),试验对比分析了不同测量部位、不同光谱预处理方法和不同校正建模算法的梨果实坚实度校正模型.结果表明:赤道部位吸光度一阶微分光谱的偏最小二乘回归所建梨果实坚实度校正模型的预测性能较优,其校正和预测相关系数分别为0.8779和0.8087,校正和预测均方误差分别为1.0804N和1.4455N.研究表明:可见/近红外光谱技术无损检测梨果实坚实度是可行的.     

基于近红外法的棉花回潮率测量系统研制与试验

该研究针对棉花回潮率的测量问题,进行了烘箱法、电阻法、红外法3种棉花回潮率检测方法的试验,基于理论及实际测试试验证明了基于红外法非接触测量棉花回潮率的可行性,并在现有红外水分仪的基础上开发了棉花回潮率非接触测量系统上位机软件。首先进行了6%、8%、10%、12%、14%、16%这6个不同回潮率水平棉花样本的制备。然后分别用现有基于电阻的测试方法和基于红外的水分测量仪以及烘箱法3种测试方法进行对照试验,研究了测量距离和样本密度对红外法测量棉花回潮率的影响。最后进行了红外法可行性验证,通过分析测试结果的相关性,提出了基于烘箱回潮率数据回归方法以实现较精准的红外法棉花回潮率测量,对基于红外的棉花回潮率在线检测方法的可行性进行了验证。试验结果表明,测量距离和样本密度的变化对测量结果的影响较小,不同测量距离下测量数据的极差在0.6%以内,标准差在0.134%之内。不同密度下测量结果的极差在0.5%以内,标准差在0.15%之内,可满足在线加工对回潮率的测量精度要求。基于标准烘箱回潮值拟合校准后的红外测量方法可以较准确地实现棉花回潮率的在线测量,和实际的烘箱数据对比,标准偏差在0.5%左右。因此,基于红外的棉花回潮率非接触测量系统可行,可解决现有电阻法测量效率低,实时性不够好的问题。     

Chemometric Localization Approach to NIR Measurement of Apparent Amylose Content of Ground Wheat

The development of new wheat cultivars that target specific end‐uses, such as low or zero amylose contents of partially waxy and waxy wheats, has become a modern focus of wheat breeding. But for efficient and cost‐effective breeding, inexpensive and high‐throughput quality testing procedures, such as near infrared (NIR) spectroscopy, are required. The genetic nature of a set of wheat lines, which included waxy to nonwaxy cultivars, results in a bimodal distribution of amylose contents that presents some special challenges for the formulation of stable NIR calibrations for this property. The obvious and intuitive solution lies in the use of some form of localization procedure and we explored three localization algorithms in comparison with the default partial least squares. Localization with respect to the waxy (zero amylose) cultivars resulted in a modified partial least squares calibration with a standard error of prediction of 0.16%. The results establish unambiguously that there are advantages in performing a suitable localization to achieve a reliable NIR calibration and prediction. The accuracy of the method can also be enhanced by application of an appropriate resampling strategy. In addition, there are advantages in performing a suitable localization to achieve a reliable NIR calibration‐prediction. It resolves the issue of how to utilize the bimodal distribution of apparent amylose values. The best results are obtained when the localization is performed simultaneously with respect to the sample property under investigation and the NIR spectra. The key problem with the measurement of amylose is the laboratory reference method which, in reality, only measures the apparent amylose content of the wheat. As a direct consequence, the measurements of amylose have such a large error that traditional calibration‐prediction procedures generate unacceptable results. To resolve this difficulty, a statistically based resampling strategy is proposed as a method of identifying samples where there is a large error in the reference measurement.     

Laboratory and Field Assessment of the Decagon 5TE and GS3 Sensors for Estimating Soil Water Content in Saline-Alkali Reclaimed Soils

The objective of this study was to assess, under laboratory and field conditions, the performance of the Decagon 5TE and GS3 soil water sensors in estimating the soil water content of saline-alkali reclaimed land in South Korea. The error due to increased bulk soil EC was greater for the 5TE sensor than for the GS3 sensor and was greater in soil with higher bulk soil EC. Therefore, it is recommended that the soil electrical conductivity be considered in the calibration process for the 5TE. The calibration equations developed for the 5TE and GS3 sensors during laboratory experiments were highly accurate. Testing of the 5TE and GS3 sensors showed very good agreement between actual VWC and VWC calculations resulting from the field-derived calibration. These results suggest that either sensor can be used to acquire accurate soil water content data in the field.     

Testing for trends when there are changes in methods

Data from monitoring projects often include sampling or analytical changes that preclude trend analysis on the entire period of record. A modification of the nonparametric Kendall's test for monotonic trends, which accounts for such changes in the period of record, is described here. This approach blocks the data so that only data collected or analyzed under similar circumstances are compared. Alternatively, when appropriate data exist, data collected using the old method may be calibrated to values expected from the new method. Traditional trend tests may then be applied to resulting data sets. Results from simulations assessing both the power of the blocked test and the standard test performed on calibrated data are presented. The power of the blocked test exceeded the power of the calibration approach only when the calibration error was extremely large. Both the blocking and calibration approaches were applied to and compared for chemical data from Vermont lakes.