Qualitative interpretation of physico-chemical and isotopic parameters in the Krka River (Croatia) assessed by multivariate statistical analysis

Multivariate statistical analyses were applied on the measured physico-chemical (Cd, Pb, Cu, Zn, Mg, Ca, O₂, alkalinity, temperature, pH, SAS, DOC and DIC) and isotopic parameters (δ¹³C and δ¹⁸O) to estimate and distinguish anthropogenic from natural influences to the water system of the Krka River. Analyses were conducted on the data collected during six years from twelve sampling sites. On the basis of orientation, positioning and grouping of parameters arranged by biplots, four main hypotheses were defined and finally statistically confirmed. Thereof, two main and distinct processes occurring in the Krka River could be highlighted: (i) upstream pollution, caused by the inflow of untreated waste-waters of city of Knin and (ii) downstream self-purification, caused by the sedimentation and/or co-precipitation of pollutants coupled by the inflow of clean subterranean water (groundwater recharge). Grouping of (i) hydrological and carbon cycle connected parameters, and (ii) anthropogenically influenced correlated parameters were proposed as a result of statistical analysis. Regarding the pH, it is shown that a stream section influenced by the subterranean inflow of Zrmanja River is statistically significantly different for all sampling campaigns during six years, being lower for about 0.5 pH unit.     

因子双重信息图在识别城市重金属污染中的应用

对国外流行的Beozecri对应分析法,这里用变量型数据阵指出该方法很大程度改变了数据阵的特征,不能达到对应分析目的,以致不能解决问题.为此,这里用因子双重信息图解决问题,通过比较,因子双重信息图优良地图示了数据阵中:变量之间、样品之间、样品与变量之间的关系,达到了对应分析目的,方法直接且简便,因子双重信息图较适应变量型数据阵这类问题的对应分析.     

Evaluation of the predictive power of biplot axes to automate the construction and layout of biplots based on the accuracy of direct readings from common outputs of multivariate analyses: 1. application to principal component analysis

Predictive biplots, as developed by J.C. Gower and coworkers, can be a very useful tool to aid the interpretation of the outcomes of multivariate analyses. This paper covers a statistical methodology that enables the automation of the construction of predictive biplots, as well as an R function, AutoBiplots.PCA( ), which applies the methodology to principal components analysis. A case study based on the sensory analysis of coffees is used to illustrate the methodology as well as the outputs of the R function. The method relies on the definition of a variable's mean standard predictive error, mspe, as the degree of accuracy in the process of predicting the original values from the biplots, which is compared with a predefined tolerance value (T_axis) to decide if the correspondent biplot axis is drawn in the biplot. Standard predictive errors, spe, are calculated for each unit in relation to each biplot axis in each two‐dimensional plot and are compared with a predefined tolerance value (T_units) to decide which units shall be faced as outliers. The R function automates the process, enabling the user to decide on the degree of precision of the actual analysis. Besides providing a solution for the automatic production of predictive biplots, the methodology offers new insights for the interpretation of multivariate analyses outputs on the basis of a sound principle, the degree of precision of the analysis. This provides an automatic way for the selection of variables that explain latent dimensions and also helps in deciding on the number of important latent dimensions for model developments. Copyright © 2012 John Wiley & Sons, Ltd.     

Mining performance data through nonlinear PCA with optimal scaling

Performance data are usually collected in order to build well‐defined performance indicators. Since such data may conceal additional information, which can be revealed by secondary analysis, we believe that mining of performance data may be fruitful. We also note that performance databases usually contain both qualitative and quantitative variables for which it may be inappropriate to assume some specific (multivariate) underlying distribution. Thus, a suitable technique to deal with these issues should be adopted. In this work, we consider nonlinear principal component analysis (PCA) with optimal scaling, a method developed to incorporate all types of variables, and to discover and handle nonlinear relationships. The reader is offered a case study in which a student opinion database is mined. Though generally gathered to provide evidence of teaching ability, they are exploited here to provide a more general performance evaluation tool for those in charge of managing universities. We show how nonlinear PCA with optimal scaling applied to student opinion data enables users to point out some strengths and weaknesses of educational programs and services within a university. Copyright © 2009 John Wiley & Sons, Ltd.