D-optimal designs for mixed discrete and continuous outcomes analyzed using nonlinear models

Many dose-response experiments in toxicology and other biological sciences are designed to measure multiple outcomes. Unfortunately, most of these studies are powered or designed for a single response, and the inference on the under-powered endpoints is limited. As additional design challenges, the outcomes may have different regions and shapes of activity or have different response types. As a new application to the traditional D-optimality criterion, we have developed optimal designs for mixed discrete and continuous outcomes that are analyzed with nonlinear models. These designs use a numerical algorithm to choose the location of the dose groups and proportion of total sample size allocated to each group that minimize the generalized variance of a model-based covariance matrix that incorporates the correlation between outcomes. Using this methodology, we designed a dose-response experiment with binary, count, and continuous outcomes to evaluate neurotoxicity. In this example, the optimal designs placed dose groups at the predicted dose thresholds and throughout the active range. The designs were generally robust to different correlation structures. In addition, when the expected correlation was moderate or large, we observed a substantial gain in efficiency compared to optimal designs created for each outcome separately.     

Two latent variable risk assessment approaches for mixed continuous and discrete outcomes from developmental toxicity data

Measurements of both continuous and discrete outcomes are encountered in many statistical problems. Here we consider the particular context of teratology studies, where quantitative risk asessment is aimed at determining the effect of dose on the probability that an individual fetus is malformed or of low birth weight, both being important measures of teratogenicity. We will introduce two different joint marginal mean models for outcomes of a mixed nature. First, we propose the Plackett-Dale approach, where for each binary outcome it is assumed that there exists an underlying glatent variable. The latent malformation outcomes are then assumed to follow a Plackett distribution. The second approach we consider is a probit approach. Here it is assumed that there exists an underlying continuous variable for each binary outcome, so the joint distribution for weight and malformation can be assumed to follow a multivariate normal distribution. In both cases, specification of the full distribution will be avoided using pseudolikelihood and generalized estimating equations methodology, respectively. Quantitative risk assessment is illustrated using data from two developmental toxicology experiments.     

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.     

Transformations in mixed models: Application to risk analysis for a multienvironment trial

An important trait in crop cultivar evaluation is stability of performance across environments. There are many different measures of stability, most of which are related to variance components of a mixed model. We believe that stability measures assessing yield risk are of particular relevance, because they integrate location and scale parameters in a meaningful way. A prerequisite for obtaining valid risk estimates is an appropriate model for the distribution of yield across environments. Multienvironment trials (MET) are often analyzed by mixed linear models, assuming that environments are a random sample from a target population, and that random terms in the model are normally distributed. The normality assumption may not always be tenable, and consequently, risk estimates may be biased. In this article, we suggest a transformation approach based on the Johnson system to cope with nonnormality in mixed models. The methods are exemplified using an international wheat yield trial. The importance of accounting for nonnormality in risk analyses based on MET is emphasized. We suggest that transformations should be routinely considered in analyses to assess risk.     

Modeling combined continuous and ordinal outcomes in a clustered setting

Measurements of both continuous and categorical outcomes appear in many statistical problems. One such example is the study of teratology and developmental toxicity, where both the probability that a live fetus is malformed (ordinal) or of low birth weight (continuous) are important measures in the context of teratogenicity. Although multivariate methods of the analysis of continuous outcomes are well understood, methods for jointly continuous and discrete outcomes are less familiar. We propose a likelihood-based method that is an extension of the Plackett-Dale approach. Specification of the full likelihood will be avoided using pseudo-likelihood methodology. The estimation of safe dose levels as part of quantitative risk assessment will be illustrated based on a developmental toxicity experiment of diethylene glycol dimethyl ether in mice.     

估算区域蒸发蒸腾量的遥感模型对比分析

蒸发蒸腾量是地球表面水量和能量平衡中的重要分量。蒸发蒸腾通过水文循环影响着区域乃至全球的气候、生态及农业生产。与传统的地面点观测手段相比,利用遥感监测区域蒸发蒸腾具有快捷、宏观、经济等优势和特点。该文在阐述利用遥感研究蒸发蒸腾的基本原理和方法的基础上,综述了国内外常用的遥感蒸发蒸腾模型,并着重对SEBAL、VITT等模型进行了评述和对比分析,指出了利用遥感研究区域蒸发蒸腾中存在的问题。     

Power analysis based on spatial effects mixed models: A tool for comparing design and analysis strategies in the presence of spatial variability

Spatial variability among experimental units is known to exist in many designed experiments. Agronomic field trials are a particularly well-known example, but there are others. Historically, spatial variability has been dealt with in one of two ways: either though design, by blocking to account for spatial effects, or though analysis, by nearest neighbor adjustment. More recently, mixed models with spatial covariance structures such as those used in geostatistics have been proposed. These mixed model procedures have tempted some to conclude—to the dismay of many consulting statisticians—that design principles may be bypassed, since spatial covariance models can recover any lost information. Although design principles clearly should not be ignored, spatial procedures do raise questions. Are traditional notions of appropriate design affected? If so, how? How do spatial effects mixed models compare to conventional analysis of variance used in conjunction with blocked designs? This article presents mixed model methods to assess power and precision of proposed designs in the presence of spatial variability and to compare competing design and analysis strategies. The main conclusion is that, if anything, spatial models reinforce the need for sound design principles, particularly the use of incomplete block designs.     

基于离散元非线性弹塑性接触模型的免耕土壤参数标定

为了进一步提升基于离散元法对免耕作业机具与土壤互作关系研究的准确性,以华北麦玉两熟区免耕壤土为研究对象,基于离散元软件(Discrete Element Modeling,DEM)扩展的The Edinburgh Elasto-Plastic Adhesion非线性弹塑性接触模型开展常年免耕农田土壤离散元仿真模型参数标...     

连作植烟土壤酚酸类物质变化特征及其与主要环境因子的Mantel Test分析

为明确酚酸类物质在连作植烟土壤中的变化特征,探讨土壤主要环境因子对酚酸类物质的影响,以不同连作年限（4 a,6 a,8 a,14 a和16 a）植烟土壤为对象,研究了不同连作年限植烟土壤酚酸类物质、理化性状、酶活性和细菌多样性的变化特征,并利用Mantel Test分析了酚酸类物质与土壤主要环境因子的相关性。结果表明,随连作年限增加,土壤酚酸类物质和速效钾含量升高,pH、有机质含量、细菌菌群丰度和多样性降低,水解性氮和有效磷含量呈先降低后升高趋势,酶活性呈先升高后降低趋势。Mantel Test分析表明,土壤酚酸类物质含量与理化性状、酶活性和细菌丰度显著相关,且与理化性状相关性最高;不同酚酸类物质含量与土壤主要环境因子相关性存在差异,其中,对羟基苯甲酸和阔马酸与植烟土壤理化性状、酶活性以及细菌丰度的相关性最高。因此,在本试验条件下,连作植烟土壤酚酸类物质具有明显积累特征,植烟土壤环境恶化;酚酸类物质积累受理化性状、酶活性和细菌多样性影响,且理化性状影响最大;不同酚酸类物质受主要土壤环境因子的影响存在差异,其中对羟基苯甲酸和阔马酸积累所受影响最大。     

基于TOPSIS-RSR法的三七连作障碍消减效应综合评价

为筛选能有效消减三七连作障碍的技术措施,本研究选择出苗率(反映出苗状况)、存苗率(反映存苗状况)、地上和地下鲜重、干重及总干重(反映生长状况)等8项指标,引入TOPSIS法和RSR法,综合评价了添加土壤改良剂、有机肥、有益微生物等措施及其组合,共67个处理对三七连作障碍的消减效应。评价结果表明:土壤消毒剂+有益微生物+有机肥(WY)及土壤消毒剂+土壤改良剂+有益微生物(WX)等措施均可在一定程度上增加连作三七的出苗率和存苗率,促进三七植株生长,提高干物质积累,较好地消减障碍效应;尤以WY7(4 500 kg·hm-2石灰+22 500 kg·hm-2猪粪)、WY8(4 500 kg·hm-2石灰+450 kg·hm-2金宝贝微生物菌肥)、WX7(4 500 kg·hm-2石灰+4 500 kg·hm-2膨润土)、WX9(4 500 kg·hm-2石灰+675 kg·hm-2肥士特生物菌肥+4 500 kg·hm-2活性炭粉)处理的效果更为理想;TOPSIS法和RSR法均适用于三七连作障碍消减效应评价,且表现出很好的一致性。可以看出,TOPSIS法结合RSR法准确地筛选出了WY7、WX9等能够有效消减三七连作障碍的处理;其他处理排序结果也与盆栽试验结果相吻合,表明TOPSIS法结合RSR法可增加对各处理评价的准确性,适用于三七连作障碍有效消减技术措施的筛选。     

Identification of model components for a class of continuous spatiotemporal models

Environmental data routinely are collected at irregularly spaced monitoring stations and at intermittent times, times which may differ by location. This article introduces a class of continuous-time, continuous-space statistical models that can accommodate many of these more complex environmental processes. This class of models in corporates temporal and spatial variability in a cohesive manner and is broad enough to include temporal processes that are assumed to be generated by stochastic differential equations with possibly temporally and spatially correlated errors. A wide range of ARIMA temporal models and geostatistical spatial models are included in the class of models investigated. Techniques for identifying the structure of the temporal and spatial components of this class of models are detailed. Point estimates of model parameters, asymptotic distributions, and Kalman-filter prediction methods are discussed.     

Use of time series analysis and mixed models in studying the long-term dynamics of soil temperature and moisture in a catena on loess deposits

Data on the dynamics of the temperature and moisture of four soils in a catena (Luvisol, calcaric Regosol, gleyic-calcaric Regosol, and Anthrosol) in the western Kraichgau region (Germany) were analyzed. The statistical processing of the data involved methods of time series analysis, including Census I decomposition, as well as analysis of variance (ANOVA) for repeated measurements using SAS PROC MIXED. From the ANOVA results, a reliable difference in the average values of the soil temperature and moisture was revealed, as well as the amplitudes of their annual variations. The highest dynamics of the parameters studied were typical for the calcaric Regosol.     

Changes in variance and correlation of soil properties with scale and location: analysis using an adapted maximal overlap discrete wavelet transform

The magnitude of variation in soil properties can change from place to place, and this lack of stationarity can preclude conventional geostatistical and spectral analysis. In contrast, wavelets and their scaling functions, which take non‐zero values only over short intervals and are therefore local, enable us to handle such variation. Wavelets can be used to analyse scale‐dependence and spatial changes in the correlation of two variables where the linear model of coregionalization is inadmissible. We have adapted wavelet methods to analyse soil properties with non‐stationary variation and covariation in fairly small sets of data, such as we can expect in soil survey, and we have applied them to measurements of pH and the contents of clay and calcium carbonate on a 3‐km transect in Central England. Places on the transect where significant changes in the variance of the soil properties occur were identified. The scale‐dependence of the correlations of soil properties was investigated by calculating wavelet correlations for each spatial scale. We identified where the covariance of the properties appeared to change and then computed the wavelet correlations on each side of the change point and compared them. The correlation of topsoil and subsoil clay content was found to be uniform along the transect at one important scale, although there were significant changes in the variance. In contrast, carbonate content and pH of the topsoil were correlated only in parts of the transect.     

基于离散单元分析与物场分析的盆花移栽手爪优化

该文针对盆花移栽作业过程中出现的移栽手爪提取基质不完整的现象,基于离散单元分析方法,利用EDEM(enhanced discrete element method)软件建立起机构(移栽手爪)、作用对象(带有根系的盆花基质)、作用条件(花盆)间的离散元仿真模型,对手爪钢针的插入和提离过程进行离散元仿真分析,确定基质断层为提取基质不完整的原因,并通过对基质提离过程进行受力分析发现,导致基质发生断层现象的根本原因是基质提离总阻力大于基质内部所能提供的最大凝聚力。鉴于如上分析,利用物场分析方法提出在原有系统中添加揉盆机构的解决方案,通过对揉盆机构工作过程进行离散元仿真分析发现,在揉盆机构的作用下基质与花盆之间产生了缝隙,使花盆对基质由于粘附作用产生的摩擦阻力降低,减小了基质提离总阻力,证明在工作过程中揉盆机构可以通过减小基质提离总阻力来解决基质断层问题。分别对添加揉盆机构前后的样机进行3组100盆的花苗移栽试验,移栽手爪完整提取基质成功率从84.67%提升到97.67%。该研究将EDEM离散单元分析与物场分析方法结合应用在机构优化设计过程,可以为盆间自动化移栽领域的设备研制与开发提供参考。     

应用同步热分析仪确定小麦秸秆热解需热量

为了解决生物质热解过程需热量的定量问题,该文应用热重—差示扫描（TG/DSC）同步热分析仪对小麦秸秆进行了热解实验研究。将约5 mg的小麦秸秆粉样品装入带盖的铂铑坩锅中,放在热解炉中的DSC-cp高精度样品支架上,在流量为25 mL/min的高纯氮气吹扫下,以10 K/min的升温速率从常温升至973 K,记录生物质的热重(TG)曲线和差示扫描(DSC)曲线。通过对实验所得微分热重(DTG)曲线和DSC曲线对比分析,对小麦秸秆热解过程进行了详细的探讨。在DSC曲线上扣除水分的影响后对其积分得出热解过程需热量的规律。结果表明,要使1 kg干小麦秸秆完成从常温303 K到673 K,773 K,873 K的升温和热解,所需的总热量分别为523 kJ,558 kJ,592 kJ。     

System for quasi‐continuous simultaneous measurement of oxygen diffusion rate and redox potential in soil

Oxygen diffusion rate (ODR) and redox potential (E_H) are quantitative indices representing oxygen availability and redox status in soils, which is valuable information for better understanding causes and effects of soil aeration. Because these indices are spatially and temporally highly variable, continuous measurements and adequate numbers of repetitions are essential for accurate in situ monitoring. Here, we present a new, fully automated recording system for in situ measurements where ODR and E_H are measured at the same platinum electrode. The conflict between electrode polarization for ODR and the resulting biased E_H readings is solved by reducing the polarization time and introducing a recovery interval between two consecutive measurement cycles. The shorter polarization time ensures accurate E_H readings. It also results in moderately overestimated ODR readings, but this can be corrected before data analysis. The recovery interval restricts temporal resolution of the E_H‐ODR data pairs to 8 h. We illustrate the use of the system with measurements in a field experiment in Zürich, Switzerland. ODR curves at different depths ran roughly parallel to the corresponding curves of O₂ concentration in soil air but ODR was much more sensitive to precipitation. Low ODR was a necessary but not a sufficient condition for declining E_H. E_H ran parallel to O₂ concentration in soil air rather than to ODR. The fully automated system allows for time series of replicate measurements in multifactorial field studies with reasonable labor requirements. It may be particularly suitable for studies examining the effects of soil tillage, compaction, and irrigation, where structure‐related soil properties such as porosity, gas permeability, and soil aeration play a dominant role.     

Adequacy of approximations to distributions of test statistics in complex mixed linear models

A recent study of lady beetle antennae was a small sample repeated measures design involving a complex covariance structure. Distributions of test statistics based on mixed models fitted to such data are unknown, but two recently developed methods for approximating the distributions of test statistics in mixed linear models have been included as options in the latest release of the MIXED procedure of SAS®. One method (FC, from Fai and Cornelius) computes degrees of freedom of an approximating F distribution for the test statistic using spectral decomposition of the hypothesis matrix together with repeated application of a method for single-degree-of-freedom tests. The other method (KR, from Kenward and Roger) adjusts the estimated covariance matrix of the parameter estimates, computes a scale adjustment to the test statistic, and computes the degrees of freedom of an approximating F distribution. Using the two methods, p values for a hypothesis of interest in the lady beetle study were quite different. Simulation studies on the Proc MIXED implementation of these methods showed that Type I error rates of both methods are affected by covariance structure complexity, sample size, and imbalance. Nonetheless, the KR method performs well in situations with fairly complicated covariance structures when sample sizes are moderate to small and the design is reasonably balanced. The KR method should be used in preference to the FC method, although it had inflated Type I error rates for complex covariance structures combined with small sample sizes.     

Local linear mixed effect models—Model specification and interpretation in a biological context

Clustered data, either as an explicit part of the study design or due to the natural distribution of habitats, populations, and so on, are frequently encountered by biologists. Mixed effect models provide a framework that can handle clustered data by estimating cluster-specific random effects and introducing correlated residual structures. General parametric models have been shown not to suit all biological problems, resulting in an increased popularity for local regression procedures, such as LOESS and splines. To evaluate similar biological problems for clustered data with cluster-specific random effects and potential dependencies between within-cluster residuals, we suggest a local linear mixed model (LLMM). The LLMM approach is a local version of a linear mixed-effect model (LME), and the LLMM approach produces: (1) local shared predictions, (2) local cluster-specific predictions, and (3) estimates of cluster-specific random effects conditioned on the covariates. Thus, in addition to the local estimates of the expected response, we obtain information about how the cluster-specific random variability depends on the values of the covariate. Ovary data are used to illustrate the flexibility and potential of this procedure in biological contexts.     

Bayesian analysis of semiparametric linear-circular models

In many environmental and agricultural studies, data are collected on both linear and circular random variables, with possible dependence between the variables. Classically, the analysis of such data has been carried out in a classical regression framework. We propose a Bayesian hierarchical framework to handle all forms of uncertainty arising in a linear-circular data set. One novelty of our multivariate linear-circular model is that, marginally, the circular component is assumed to be a mixture model with an unknown number of von Mises (or circular normal) distributions. We use the Dirichlet process to introduce variability in the model dimensionality, and develop a simple Gibbs sampling algorithm for simulating the mixture components. Although we illustrate our methodology on von Mises mixtures, it is widely applicable. We thus avoid complicated reversible-jump Markov chain Monte Carlo methods, which are considered ideal for analyzing mixtures of unknown number of distributions. We illustrate our methodologies with simulated and real data sets. Using pseudo-Bayes factors, we also compare different models associated with both fixed and variable numbers of von Mises distributions. Our findings suggest that models associated with varying numbers of mixture components perform at least as well as those with known numbers of mixture components. We tentatively argue that model averaging associated with variable number of mixture components improves the model’s predictive power, which compensates for the lack of knowledge of the actual number of mixture components.