A comparison of simultaneous autoregressive and generalized least squares models for dealing with spatial autocorrelation

Aim  In their recent paper, Kissling & Carl (2008 ) recommended the spatial error simultaneous autoregressive model (SAR_err) over ordinary least squares (OLS) for modelling species distribution. We compared these models with the generalized least squares model (GLS) and a variant of SAR (SAR_vario). GLS and SAR_vario are superior to standard implementations of SAR because the spatial covariance structure is described by a semivariogram model.
Innovation  We used the complete datasets employed by Kissling & Carl (2008 ), with strong spatial autocorrelation, and two datasets in which the spatial structure was degraded by sample reduction and grid coarsening. GLS performed consistently better than OLS, SAR_err and SAR_vario in all datasets, especially in terms of goodness of fit. SAR_vario was marginally better than SAR_err in the degraded datasets.
Main conclusions  GLS was more reliable than SAR-based models, so its use is recommended when dealing with spatially autocorrelated data.     

Statistical error in isothermal titration calorimetry: variance function estimation from generalized least squares

The method of generalized least squares (GLS) is used to assess the variance function for isothermal titration calorimetry (ITC) data collected for the 1:1 complexation of Ba(2+) with 18-crown-6 ether. In the GLS method, the least squares (LS) residuals from the data fit are themselves fitted to a variance function, with iterative adjustment of the weighting function in the data analysis to produce consistency. The data are treated in a pooled fashion, providing 321 fitted residuals from 35 data sets in the final analysis. Heteroscedasticity (nonconstant variance) is clearly indicated. Data error terms proportional to q(i) and q(i)/v are well defined statistically, where q(i) is the heat from the ith injection of titrant and v is the injected volume. The statistical significance of the variance function parameters is confirmed through Monte Carlo calculations that mimic the actual data set. For the data in question, which fall mostly in the range of q(i)=100-2000 microcal, the contributions to the data variance from the terms in q(i)(2) typically exceed the background constant term for q(i)>300 microcal and v<10 microl. Conversely, this means that in reactions with q(i) much less than this, heteroscedasticity is not a significant problem. Accordingly, in such cases the standard unweighted fitting procedures provide reliable results for the key parameters, K and DeltaH(degrees) and their statistical errors. These results also support an important earlier finding: in most ITC work on 1:1 binding processes, the optimal number of injections is 7-10, which is a factor of 3 smaller than the current norm. For high-q reactions, where weighting is needed for optimal LS analysis, tips are given for using the weighting option in the commercial software commonly employed to process ITC data.     

Least median of squares and iteratively re‐weighted least squares as robust linear regression methods for fluorimetric determination of α‐lipoic acid in capsules in ideal and non‐ideal cases of linearity

This study outlines two robust regression approaches, namely least median of squares (LMS) and iteratively re‐weighted least squares (IRLS) to investigate their application in instrument analysis of nutraceuticals (that is, fluorescence quenching of merbromin reagent upon lipoic acid addition). These robust regression methods were used to calculate calibration data from the fluorescence quenching reaction (?F and F‐ratio) under ideal or non‐ideal linearity conditions. For each condition, data were treated using three regression fittings: Ordinary Least Squares (OLS), LMS and IRLS. Assessment of linearity, limits of detection (LOD) and quantitation (LOQ), accuracy and precision were carefully studied for each condition. LMS and IRLS regression line fittings showed significant improvement in correlation coefficients and all regression parameters for both methods and both conditions. In the ideal linearity condition, the intercept and slope changed insignificantly, but a dramatic change was observed for the non‐ideal condition and linearity intercept. Under both linearity conditions, LOD and LOQ values after the robust regression line fitting of data were lower than those obtained before data treatment. The results obtained after statistical treatment indicated that the linearity ranges for drug determination could be expanded to lower limits of quantitation by enhancing the regression equation parameters after data treatment. Analysis results for lipoic acid in capsules, using both fluorimetric methods, treated by parametric OLS and after treatment by robust LMS and IRLS were compared for both linearity conditions.     

别拉洪河流域湿地鸟类丰富度的空间自相关分析

人类的开垦和开发活动使湿地生物多样性遭到严重的干扰和破坏,随着人们对湿地功能和价值的正确认识,湿地生物多样性保护越来越被广泛关注,湿地生物多样性空间分布格局及其影响因素是湿地生物多样性保护要解决的关键问题。利用空间自相关与空间滞后模型,对三江平原别拉洪河流域湿地鸟类丰富度的空间自相关性及其驱动因子进行了研究,结果表明:别拉洪河流域湿地鸟类丰富度及其驱动因子都具有明显的空间自相关性;影响别拉洪河流域湿地鸟类丰富度空间分布的主要因子是干扰度、生境类型数、到道路的距离、到沟渠的距离、到湖泊的距离、到居民点的距离、海拔高度、坡度和人口密度;由于受空间自相关的影响,空间自回归模型优于传统的回归模型。研究有助于人们更好地理解湿地生物多样性保护的热点地区及其形成机制,对人们更好地保护和利用湿地生物多样性具有重要价值,同时也为研究湿地鸟类分布与环境因子的关系,建立预测物种分布模型提供科学依据。     

Analysis of multitemperature isothermal titration calorimetry data at very low c: Global beats van't Hoff

Isothermal titration calorimetry data for very low c (≡K[M]₀) must normally be analyzed with the stoichiometry parameter n fixed — at its known value or at any reasonable value if the system is not well characterized. In the latter case, ΔH° (and hence n) can be estimated from the T-dependence of the binding constant K, using the van't Hoff (vH) relation. An alternative is global or simultaneous fitting of data at multiple temperatures. In this Note, global analysis of low-c data at two temperatures is shown to estimate ΔH° and n with double the precision of the vH method.     

Effects of incorporating spatial autocorrelation into the analysis of species distribution data

Aim  Spatial autocorrelation (SAC) in data, i.e. the higher similarity of closer samples, is a common phenomenon in ecology. SAC is starting to be considered in the analysis of species distribution data, and over the last 10 years several studies have incorporated SAC into statistical models (here termed 'spatial models'). Here, I address the question of whether incorporating SAC affects estimates of model coefficients and inference from statistical models.
Methods  I review ecological studies that compare spatial and non-spatial models.
Results  In all cases coefficient estimates for environmental correlates of species distributions were affected by SAC, leading to a mis-estimation of on average c . 25%. Model fit was also improved by incorporating SAC.
Main conclusions  These biased estimates and incorrect model specifications have implications for predicting species occurrences under changing environmental conditions. Spatial models are therefore required to estimate correctly the effects of environmental drivers on species present distributions, for a statistically unbiased identification of the drivers of distribution, and hence for more accurate forecasts of future distributions.     

Using the EM algorithm to weight data sets of unknown precision when modelling fish stocks

Stocks of commercial fish are often modelled using sampling data of various types, of unknown precision, and from various sources assumed independent. We want each set to contribute to estimates of the parameters in relation to its precision and goodness of fit with the model. Iterative re-weighting of the sets is proposed for linear models until the weight of each set is found to be proportional to (relative weighting) or equal to (absolute weighting) the set-specific residual invariances resulting from a generalised least squares fit. Formulae for the residual variances are put forward involving fractional allocation of degrees of freedom depending on the numbers of independent observations in each set, the numbers of sets contributing to the estimate of each parameter, and the number of weights estimated. To illustrate the procedure, numbers of the 1984 year-class of North Sea cod (a) landed commercially each year, and (b) caught per unit of trawling time by an annual groundfish survey are modelled as a function of age to estimate total mortality, Z, relative catching power of the two fishing methods, and relative precision of the two sets of observations as indices of stock abundance. It was found that the survey abundance indices displayed residual variance about 29 times higher than that of the annual landings.     

A Modified Chi-squared Approach for Fitting WEIBULL Models to Synthetic Life Tables1

WEIBULL models are fitted to synthetic life table data by applying weighted least squares analysis to log log functions which are constructed from appropriate underlying contingency tables. As such, the resulting estimates and test statistics are based on the linearized minimum modified X²₁-criterion and thus have satisfactory properties in moderately large samples. The basic methodology is illustrated in terms of an example which is bivariate in the sense of involving two simultaneous, but non-competing, vital events. For this situation, the estimation of WEIBULL model parameters is described for both marginal as well as certain conditional distributions either individually or jointly.     

Are neighbour methods preferable to analysis of variance for completely systematic designs? 'Silly designs are silly!'

It is shown that the usual analysis of a complete-block designis weakly valid under a range of assumptions but that more sophisticatedanalyses of systematic block designs may not be.     

An assessment of seed quality and its influence on productivity estimation in an industrial antibiotic fermentation

This study investigates the benefits of including seed quality information into data-based models for final productivity estimation in an industrial antibiotic fermentation process. Multiway principal component analysis is applied to assess the seed quality using routinely gathered plant data. Multiway partial least-squares regression is then used to estimate the final productivity using data from the main fermentation only. The issue of selecting appropriate process variables as inputs is investigated. Subsequently, seed characteristics are included into the estimation models to assess the benefits of including information from this stage for productivity estimation. It is shown that it is possible to extract seed fermentation features related to the final productivity both at pilot and production scales. It is postulated that significant influential variations are mirrored in monitored variables during the main fermentation, and therefore seed quality is implicitly accounted for.     

Supervised two-dimensional functional principal component analysis with time-to-event outcomes and mammogram imaging data

Screening mammography aims to identify breast cancer early and secondarily measures breast density to classify women at higher or lower than average risk for future breast cancer in the general population. Despite the strong association of individual mammography features to breast cancer risk, the statistical literature on mammogram imaging data is limited. While functional principal component analysis (FPCA) has been studied in the literature for extracting image-based features, it is conducted independently of the time-to-event response variable. With the consideration of building a prognostic model for precision prevention, we present a set of flexible methods, supervised FPCA (sFPCA) and functional partial least squares (FPLS), to extract image-based features associated with the failure time while accommodating the added complication from right censoring. Throughout the article, we hope to demonstrate that one method is favored over the other under different clinical setups. The proposed methods are applied to the motivating data set from the Joanne Knight Breast Health cohort at Siteman Cancer Center. Our approaches not only obtain the best prediction performance compared to the benchmark model, but also reveal different risk patterns within the mammograms.     

A study of statistical error in isothermal titration calorimetry

In isothermal titration calorimetry (ITC), the two main sources of random (statistical) error are associated with the extraction of the heat q from the measured temperature changes and with the delivery of metered volumes of titrant. The former leads to uncertainty that is approximately constant and the latter to uncertainty that is proportional to q. The role of these errors in the analysis of ITC data by nonlinear least squares is examined for the case of 1:1 binding, M+X right arrow over left arrow MX. The standard errors in the key parameters-the equilibrium constant Ko and the enthalpy DeltaHo-are assessed from the variance-covariance matrix computed for exactly fitting data. Monte Carlo calculations confirm that these "exact" estimates will normally suffice and show further that neglect of weights in the nonlinear fitting can result in significant loss of efficiency. The effects of the titrant volume error are strongly dependent on assumptions about the nature of this error: If it is random in the integral volume instead of the differential volume, correlated least-squares is required for proper analysis, and the parameter standard errors decrease with increasing number of titration steps rather than increase.     

PCA 和PLS 应用于胃癌亚型分类研究

文章研究了基于微阵列基因表达数据的胃癌亚型分类。微阵列基因表达数据样本少、纬度高、噪声大的特点,使得数据降维成为分类成功的关键。作者将主成分分析(PCA) 和偏最小二乘（PLS）两种降维方法应用于胃癌亚型分类研究,以支持向量机（SVM）、K- 近邻法（KNN）为分类器对两套胃癌数据进行亚型分类。分类效果相比传统的医理诊断略高,最高准确率可达100%。研究结果表明,主成分分析和偏最小二乘方法能够有效地提取分类特征信息,并能在保持较高的分类准确率的前提下大幅度地降低基因表达数据的维数。     

Statistical uncertainty and its propagation in the analysis of quantitative polymerase chain reaction data: Comparison of methods

Most methods for analyzing real-time quantitative polymerase chain reaction (qPCR) data for single experiments estimate the hypothetical cycle 0 signal y₀ by first estimating the quantification cycle (C_q) and amplification efficiency (E) from least-squares fits of fluorescence intensity data for cycles near the onset of the growth phase. The resulting y₀ values are statistically equivalent to the corresponding C_q if and only if E is taken to be error free. But uncertainty in E usually dominates the total uncertainty in y₀, making the latter much degraded in precision compared with C_q. Bias in E can be an even greater source of error in y₀. So-called mechanistic models achieve higher precision in estimating y₀ by tacitly assuming E = 2 in the baseline region and so are subject to this bias error. When used in calibration, the mechanistic y₀ is statistically comparable to C_q from the other methods. When a signal threshold y_q is used to define C_q, best estimation precision is obtained by setting y_q near the maximum signal in the range of fitted cycles, in conflict with common practice in the y₀ estimation algorithms.     

Using nonlinear least squares to assess relative expression and its uncertainty in real-time qPCR studies

Relative expression ratios are commonly estimated in real-time qPCR studies by comparing the quantification cycle for the target gene with that for a reference gene in the treatment samples, normalized to the same quantities determined for a control sample. For the “standard curve” design, where data are obtained for all four of these at several dilutions, nonlinear least squares can be used to assess the amplification efficiencies (AE) and the adjusted ΔΔC_q and its uncertainty, with automatic inclusion of the effect of uncertainty in the AEs. An algorithm is illustrated for the KaleidaGraph program.     

Monitoring the biochemical changes occurring to human keratinocytes exposed to solar radiation by Raman spectroscopy

Solar radiation exposure is recognised to be a significant contributor to the development of skin cancer. Monitoring the simultaneous and consecutive mechanisms of interaction could provide a greater understanding of the process of photocarcinogenesis. This work presents an analysis of the biochemical and morphological changes occurring to immortalised human epithelial keratinocyte (HaCaT) cell cultures exposed to simulated solar radiation (SSR). Cell viability was monitored with the aid of the Alamar Blue assay, morphological examination was done with haematoxylin and eosin staining (H&E) and changes to the biochemical constituents (nucleic acids and proteins) as a result of the radiation insult were demonstrated through a combination of Raman microspectroscopy and multivariate analysis of spectral patterns. The spectral results suggest that SSR induces changes to the conformational structure of DNA as an immediate result of the radiation, whereas alteration in the protein signature is mostly seen as a later response.