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.     

Generalized linear models in soil science

Classical linear models are easy to understand and fit. However, when assumptions are not met, violence should not be used on the data to force them into the linear mould. Transformation of variables may allow successful linear modelling, but it affects several aspects of the model simultaneously. In particular, it can interfere with the scientific interpretation of the model. Generalized linear models are a wider class, and they retain the concept of additive explanatory effects. They provide generalizations of the distributional assumptions of the response variable, while at the same time allowing a transformed scale on which the explanatory effects combine. These models can be fitted reliably with standard software, and the analysis is readily interpreted in an analogous way to that of linear models. Many further generalizations to the generalized linear model have been proposed, extending them to deal with smooth effects, non-linear parameters, and extra components of variation. Though the extra complexity of generalized linear models gives rise to some additional difficulties in analysis, these difficulties are outweighed by the flexibility of the models and ease of interpretation. The generalizations allow the intuitively more appealing approach to analysis of adjusting the model rather than adjusting the data.     

Bootstrap model selection in generalized linear models

Model selection is a central component of data analysis. Though there are a variety of methods for likelihood-based estimation methods, there are relatively few for non-likelihood-based generalized linear models (GLMs), such as in the quasi-likelihood and generalized estimating equation (GEE) approaches. In this paper, we develop basic and bias-corrected bootstrap approaches to estimate the predictive mean squared error (PMSE) of a model and use the PMSE for model selection. Simulation studies show that the bias-corrected bootstrap estimate works well when quasi-likelihood or GEE is used to fit either overdispersed or correlated response GLMs. For correlated response data, when the marginal distribution assumption is (almost) correct, Akaike’s information criterion (AIC) and Bayesian information criterion (BIC) calculated under the working independence model also perform well. For illustration, the methods are applied to data sets from evolutionary biology and teratology.     

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.     

How to make biological surveys go further with generalised linear models

The cost of surveys, both in terms of dollars and manpower, will prevent total inventories of complete regions being completed, if in fact ever undertaken, before decisions have to be made to change current land use practices. There exists a need to be able to extrapolate existing location-specific information over complete regions with increased confidence in the subsequent spatial predictions. Recent developments in statistical modelling provide methods appropriate to many types of biological data and taken together with the application of regression-diagnostic techniques offer the biologist or land manager improved, in terms of reliability and spatial completeness, species distribution data bases on which to base conservation decisions.

This paper describes one component of such development and the application of three regression-diagnostic techniques: the use of residuals to test the statistical assumptions implicit in the fitted regression model; the use of estimates of potential influence each observation has on the fitted model; and the use of the coefficient of sensitivity of the model to individual observations. Guidelines are given to assist with the construction of a predictive model from a group of potential explanatory or predictor variables.

The use of generalised linear regression models and regression diagnostics is discussed in terms of their impact on survey design.     

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.     

An application of the mixed linear model and the dirichlet process prior in veterinary medicine research

This article applies Bayesian nonparametric techniques of analysis to the mixed linear model. The distribution of the random effects is specific as a nonparametric prior. A Dirichlet process prior is specified on the space of prior distributions. A modified Dirichlet process is described and applied using a Gibbs sampler. The approach is demonstrated in an investigation of the changes over time of packed cell volume in two breeds of cattle.     

降香黄檀不同混交模式土壤肥力的比较研究

以海南澄迈林场的4种降香黄檀混交模式为研究对象,即降香黄檀×檀香、降香黄檀×母生、降香黄檀×沉香和降香黄檀×奥氏黄檀,分析比较不同混交模式下的土壤物理、化学和生物学性质,并运用主成分分析法对其土壤肥力进行比较评价。结果表明:不同混交模式土壤的理化性质和生物学性质均体现出垂直分布规律;土壤含水量、容重、pH值、养分含量、微生物数量和酶活性在不同混交模式间以及同一模式的不同土层间均存在差异性;4种混交模式中,降香黄檀×檀香模式的含水量、有机质、碱解N、有效P含量、细菌数量均最多,pH值最高,容重最小。通过主成分分析法计算4种混交模式土壤肥力大小顺序为降香黄檀×檀香降香黄檀×母生降香黄檀×奥式黄檀降香黄檀×沉香,综合可知,檀香是降香黄檀最适宜的造林树种,能有效提高土壤肥力。     

The simultaneous analysis of mixed discrete and continuous outcomes using nonlinear threshold models

Mixed discrete and continuous outcomes are commonly measured on each experimental unit in dose-response studies in toxicology. The dose-response relationships for these outcomes often have dose thresholds and nonlinear patterns. In addition, the endpoints are typically correlated, and a statistical analysis that incorporates the association may result in improved precision. We propose an extension of the generalized estimating equation (GEE) methodology to simultaneously analyze binary, count, and continuous outcomes with nonlinear threshold models that incorporates the intra-subject correlation. The methodology uses a quasi-likelihood framework and a working correlation matrix, and is appropriate when the marginal expectation of each outcome is of primary interest and the correlation between endpoints is a nuisance parameter. Because the derivatives of threshold models are not continuous at each point of the parameter space, we describe the necessary modifications that result in asymptotically normal and consistent estimators. Using dose-response data from a neurotoxicity experiment, the methodology is illustrated by analyzing five outcomes of mixed type with nonlinear threshold models. In this example, the incorporation of the intra-subject correlation resulted in decreased standard errors for the threshold parameters.     

Using distribution models to test alternative hypotheses about a species’ environmental limits and recovery prospects

Distribution models are commonly used to generalise across species distributions, to project future potential range changes, and to identify potential areas for species reintroductions and recovery plans. Building several models that incorporate different potential causal factors is a useful way of formalising alternative hypotheses. We developed a series of models to test hypotheses about the factors influencing the distribution of a species of conservation importance - the hen harrier Circus cyaneus.A climate-based model using continental distribution data was consistent with the continental distribution and observational studies in Britain. According to the climate-model the parts of Britain occupied by the hen harrier are the least climatically suitable.Habitat-based models using detailed distribution data from seven Scottish areas explained the recent British distribution well, with birds largely confined to heather dominated areas. These patterns were inconsistent with historical data on the species’ distribution, its habitat use in other parts of its range and with the climate-based model.Our burn intensity index of gamekeeper activity was highly correlated with climatic suitability within the best 25% of 10 km squares by modelled habitat suitability, negatively associated with the productivity data and associated with a decrease in abundances between 1998 and 2004. Gamekeeper activity may be keeping hen harriers out of the most climatically suitable areas with habitat similar to that which they currently occupy within Britain and or keeping the population numbers too low and isolated for the natural re-expansion of the species into parts of the range where it was historically extirpated.     

低温下复合发酵剂对牛粪与鸡粪混合堆肥有机氮变化的影响

从低温条件下牛粪、鸡粪混合堆肥过程中有机氮组分变化入手,研究接种不同的复合发酵剂对堆肥有机氮素形态转化的影响.结果表明,各处理全氮、酸水解有机氮、氨基酸态氮含量均呈先降低后升高的趋势;堆肥结束时接种复合发酵剂的处理全氮量较不接种的对照提高30.81%;接种含纤维素分解菌发酵剂的处理全氮量较接种复合发酵剂的处理提高6.54%.表明接种含纤维素分解菌的复合发酵剂能有效减少堆肥氮损失,提高产品肥效.     

Adequacy of transport parameters obtained in soil column experiments for selected chemicals

The transport parameters were determined for the ¹⁸O isotope (in the form of H₂ ¹⁸O), the Br^? ion, and atrazine in intact columns of allophanic Andosol (Mexico State, Mexico). A one-dimensional model for the convective-dispersive transport of chemicals with account for the decomposition and equilibrium adsorption (HYDRUS-1D), which is widely applied for assessing the risk of the chemical and bacterial contamination of natural waters, was used. The model parameters were obtained by solving the inverse problem on the basis of laboratory experiments on the transport of the ¹⁸O isotope, the Br^? ion, and atrazine in intact soil columns at a fixed filtration velocity. The hydrodynamic dispersion parameters determined for the ¹⁸O and Br^? ions in one column were of the same order of magnitude, and those for atrazine were higher by 3?C4 times. The obtained parameters were used to calculate the transport of these substances in another column with different values of the water content and filtration velocity. The transport process was adequately described only for the ¹⁸O isotope. In the case of the Br^? ion, the model significantly underestimated the transport velocity; for atrazine, its peak concentration in the column was overestimated. The column study of the transport of the three chemical compounds showed that transport parameters could not be reliably predicted from the results of a single experiment, even when several compounds were used in this experiment.     

Hierarchical models for estimating herd prevalence and test accuracy in the absence of a gold standard

A common assumption made in studies involving two or more binary diagnostic tests in the absence of a gold standard is one of conditional independence among tests given disease status. Although reasonable in some cases, often this assumption is untenable or untested and may lead to biased results. We proposed a class of hierarchical models for the purpose of estimating the herd-level prevalence distribution and the accuracies of two tests in the absence of a gold standard when several exchangeable populations with differing disease prevalence are available for sampling, relaxing the assumption of conditional independence between tests. The models are used to estimate the prevalence of bovine brucellosis in Mexican cow herds and to estimate the error rates of two tests for the detection of swine pneumonia.     

The state of statistics in agricultural science

The history of statistics in agricultural research is a history of designed experiments in the basic sciences combined with applications on production agriculture and commodity processing. In agriculture, we deal with the variabilities between and within plantand animal species growing and reproducing in variable environments. Early statistical procedures were primarily concerned with partitioning of variances and hypothesis testing. We continue to use these basic procedures, with many modern updates. The basic statistical toolbox of the agricultural scientist was changed by the computer revolution and is continuing to be changed by advances in experimental designs, computer graphics, and measurement systems. Agricultural scientists are using statistical procedures adapted from engineers, ecologists, and economists in order to deal with the growing problems of analysis and interpretation of more and more data. Problems associated with sampling will continue to grow, especially when dealing with rare or highly variable events, such as insect counts, microorganisms, mycotoxins, or specific metabolites. The statisticians will be asked to provide usable, efficient, understandable, user-friendly procedures to analyze and interpret more and more complex data.     

Contributions of cloud processes to precipitation chemistry in mixed phase clouds

The role clouds play as processors of atmospheric aerosols and trace gases was studied along the slope of Mt. Rigi in central Switzerland. Upon cloud formation many aerosols and trace gases are efficiently scavenged by cloud drops. The cloud drops can enhance removal of pollutants from the atmosphere by transferring them to snow or rain which falls rapidly to the ground. This often occurs through a process known as riming, where falling ice crystals capture cloud drops. When ice crystals are grown primarily via water vapor deposition, without significant capture of cloud drops, however, the cloud drops isolate atmospheric pollutants from the precipitation process, thereby inhibiting their deposition. Increased riming results in increased precipitation ion concentrations. The extent of ice crystal riming at times exhibits spatial inhomogeneities with greater riming apparent near the mountain summit. Variations in cloud chemistry with drop size indicate that bulk cloudwater composition is not an accurate predictor for the composition of cloud drops captured by the ice crystals.     

气吸式玉米高速精量排种器直线投种过程分析与试验

为解决气吸式玉米精量排种器在高速作业条件下投种过程种子与导种管碰撞异位造成排种粒距合格率下降和排种粒距变异系数增大的问题,该文提出了一种利用推种装置配合种盘吸孔实现直线投种的方法,并对直线投种原理进行分析,阐明直线投种过程中种子与排种器的运动和力学关系,明确种盘吸孔曲线方程,确定了推种装置结构曲线参数方程。选取投种位置和作业速度为主要因素进行全因素试验,对试验结果进行显著性分析,确定了因素与指标的回归方程,以排种粒距合格率、漏播率以及排种粒距变异系数为寻优条件,确定较优的投种位置为直线推种区角度=15°,直线落种角度=21°,并进行验证试验。试验结果表明,作业速度12 km/h时,排种粒距合格率为98.68%,漏播率为0.69%,排种粒距变异系数为15.03%,与理论优化结果基本一致。进行了直线投种方式与原有阻气投种方式的对比试验,结果表明,各个作业速度下排种器性能指标均有所提升,且提升幅度随着作业速度的提高而增大,在作业速度14 km/h时,直线投种较原有阻气投种排种粒距合格率提高4.22个百分点,漏播率降低4.20个百分点,排种粒距变异系数降低4.55个百分点,采用直线投种方式可大...     

Evaluation of different procedures to interpolate particle-size distributions to achieve compatibility within soil databases

Many environmental and agricultural problems are not restricted to national boundaries and therefore require international cooperation if solutions are to be found. Often, these solutions require the ability to use soil data as input in simulation models, however, despite a number of recognised international standards, soil data are rarely compatible across national frontiers. This problem was encountered when creating the draulic operties of uropean oils (HYPRES) database. The data, which includes particle-size distributions, were collected from 20 institutions in 12 countries. Only a few of these institutions adhered strictly to a recognised international system. Therefore, interpolation of the cumulative particle-size distribution was required to achieve compatibility of particle-size distributions within the HYPRES database. In this study, four different interpolation procedures were evaluated. The accuracy of the different procedures was found to vary with size intervals between measured points of the particle-size distribution. The loglinear interpolation of the cumulative particle-size distribution has previously been used in various studies but was found to give the least accurate estimation of the four procedures. Fitting the Gompertz curve, which is a special asymmetric type of curve described by a closed-form equation, showed less sensitivity to size intervals between measured points. However, interpolation within some of the particle-size distributions was not sufficiently accurate and this procedure could not be applied to particle-size distributions where the number of measured size fractions was less than the number of model parameters. Fitting a nonparametric spline function to the particle-size distributions showed a considerable increase in accuracy of the interpolation with decreasing size intervals between measured points. As a novel approach, the similarity procedure was introduced which does not use any mathematical interpolation functions. It uses an external source of soil information from which soils are selected with particle-size distributions that match the distribution of the soil under investigation. This similarity procedure was capable of giving the most accurate interpolations. Once an extensive external reference data set with well-quantified particle-size distributions is available, the similarity procedure becomes a very powerful tool for interpolations. Based on the number and distribution of measured points on the particle-size distributions, a general rule was formulated to decide whether to fit a spline function or use the novel similarity procedure to estimate missing values. Results of this study were used to classify all soils in the HYPRES database into the same soil texture classes used in the 1:1.000.000 scale Soil Geographical Database of Europe.