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1.
QUADRATIC PLS REGRESSION 总被引：2，自引：0，他引：2
AGNAR HSKULDSSON 《地理学报(英文版)》1992,(6)
We treat here an extension of linear PLS regression to include regression on quadratic PLS components.The quadratic regression can be viewed as a natural extension of linear PLS regression to quadratic PLSaccording to the H-principle of mathematical modelling.The numerical implementation is treated indetail.It is shown that this approach can be used for models with large numbers of variables.Somemodelling strategies are discussed depending on the purpose of the modelling.Applications of thisapproach are treated. 相似文献
2.
The use of continuum regression(CR)for the identification of finite impulse response(FIR)dynamicmodels is investigated.CR encompasses the methods of principal component regression(PCR),partialleast squares(PLS)and multiple linear regression(MLR).PCR and MLR are at the two extremes of thecontinuum.In PCR and PLS,cross-validation is used to determine the optimum number of factors or‘latent variables’to retain in the regression model.CR allows one to vary the method in addition.Cross-validation then determines both the optimum method and the number of latent variables.The CR‘prediction error surface’—a function of the method and number of latent variables—is elucidated.Theoptimal model is defined as the minimum of this surface.Among the cases studied,the optimal modelusually comes from the region of the continuum between PCR and PLS.Few derive from the regionbetween PLS and MLR.It is also demonstrated that FIR models identified by CR have frequency domainproperties similar to those identified by PCR. 相似文献
3.
Brent Yarnal 《The Professional geographer》1985,37(2):197-203
Multiple regression is often complicated by collinearity of the predictor variables. This study demonstrates the use of ridge regression as a method for determining those correlated variables which must be eliminated from an analysis and for maximizing the amount of information gained from a set of correlated predictors. The model is reviewed and a case study, based on an objective synoptic climatology of the Pacific Northwest coast, is presented in which the technique is applied to a correlated set of climatological predictors. One highly collinear variable is identified and discarded while the effect of moderate collinearity in the remaining predictors is lessened and explained variance is optimized by ridge regression. 相似文献
4.
In geographical research the data of interest are often in the form of counts. Standard regression analysis is inappropriate for such data, but if certain assumptions are met, a form of regression based on the Poisson distribution can be used. This paper illustrates the use of Poisson regression in the computer package GLIM with an example from historical geography. Apprentice migration to Edinburgh is regressed on a combination of categorical, count, and continuous explanatory variables. 相似文献
5.
This study proposes a method of using ecological1 variables in regression analysis to identify the weak or secondary effects of independent variables without introducing spurious correlation due to aggregation. 相似文献
6.
《The Professional geographer》2013,65(4):424-431
This study proposes a method of using ecological1 variables in regression analysis to identify the weak or secondary effects of independent variables without introducing spurious correlation due to aggregation. 相似文献
7.
Principal components(PCs)for principal component regression(PCR)have historically been selectedfrom the top down for a reliable predictive model.That is,the PCs are arranged in a list starting withthe most informative(PC associated with the largest singular value)and proceeding to the leastinformative(PC associated with the smallest singular value).PCs are then chosen starting at the top ofthis list.This paper discusses an alternative procedure of treating PC selection as an optimization prob-lem.Specifically,without any regard to the ordering,the optimal subset of PCs for an acceptablepredictive model is desired.Five data sets are analyzed using the conventional and alternative approaches.Two data sets are spectroscopic in nature,two data sets deal with quantitative structure-activityrelationships(QSARs)and one data set is concerned with modeling.All five data sets confirm thatselection of a subset without consideration to order secures the best results with PCR.One data set isalso compared using partial least squares 1. 相似文献
8.
A validation protocol for multicomponent spectroscopic assays based on principal componentsregression is described. Factorial design and hypothesis tests are used to establish the linearity andabsence of interaction between components in the regression model. Testing considers multiple responsevariables simultaneously so that correlation between residuals is properly treated. Assay reproducibilityand sensitivity to related substances are evaluated. 相似文献
9.
A membrane-discriminated gas phase analyzer is proposed for multicomponent determinations. Nitrogengas flows countercurrent through outer and inner channels in a tube-in-tube arrangement. The onlycommunication between the two channels occurs through a 500μm aperture covered by a porous PTFEmembrane. A mixture of organic compounds (up to four components) is injected into the inner channelby a heated backflushed injector and the sample components diffusing into the outer channel aremonitored by a flame ionization detector (FID). A calibration set, consisting of pure components, binary,ternary and quaternary mixtures (a total of 64 samples), provides the known data base: temporal profilesof the FID output as a function of sample composition, Although the overall response behavior is nota linearly additive function of individual analyte concentrations, the use of successive inverse multiplelinear regression (while continually altering the choice of the calibration samples considered for theforward regression, on the basis of the most recent values of the predicted unknown sample composition)is shown to yield analytical results for unknown samples that are in good agreement with their true values. 相似文献
10.
目前,被称为"无烟工业"的旅游业正在迅速发展,山东省地处中国的东部沿海,交通便利,旅游资源丰富,这就为山东省旅游业的发展提供了良好的基础。根据山东省2006～2010年的国内旅游收入数据,运用线性回归分析和灰色关联分析相结合的方法,选取旅游经济支持、生态环境质量、旅游交通、旅游服务、社会文明程度和居民生活水平6个方面14个指标,对影响山东省国内旅游收入的相关因素及各因素的重要程度进行了分析。结果表明,国内旅游收入与居民生活水平联系最为密切,与交通因素关联性最弱。 相似文献
11.
Robert Haining 《The Professional geographer》1990,42(3):336-344
A simple graphical method for developing regression models for spatially referenced data is presented. The method supplements formal testing procedures and provides the analyst with useful information helpful in developing an understanding of data properties without the need for complex data manipulations. The paper includes a worked example and suggests directions for further work in this area. 相似文献
12.
Kalman滤波方法在黑河出山径流年平均流量预报中的应用 总被引：21，自引：10，他引：11
应用Kalman滤波方法,以流域平均降水量、气温、太阳黑子相对数及莺落峡站6年显著周期序列等为控制参数,对黑河出山径流年平均流量的预测问题进行了初步研究和探讨。 相似文献
13.
Kjeld Rasmussen cand.silv. Henrik Hagen Olesen 《Geografisk tidskrift / udgivet af Bestyrelsen for Det Kongelige danske geografiske selskab》2013,113(1):100-107
Rasmussen, Kjeld & Olesen, Henrik Hagen: Applications of multivariate statistical analysis in remote sensing of agriculture. Geografisk Tidsskrift 88:100–107. Copenhagen 1988. Applications of satellite remote sensing to agriculture involve two main objectives, the identification and mapping of crops, including estimation of acreages, and monitoring of plant growth or production factors, aiming at estimation/prediction of yields. Deterministic models of the interaction of electromagnetic radiation and plant canopies are used to relate the measured reflected or emitted radiation to crop type and agronomically relevant parameters. The great natural variation of reflectance properties of crops does, however, call for use of a statistical approach. The high dimensionality of the data-sets involved, very often more than ten, requires the use of multivariate techniques. This paper will deal with the use of multivariate statistical techniques for both crop identification and crop monitoring based on high-resolution satellite remote sensing data, such as those produced by Landsat MSS and -TM and SPOT. Emphasis will be placed upon use of statistical methods in classification and on removal of redundancy in multi-dimensional data-sets. The relative merits of deterministic and statistical methods will be discussed as will the possibilities of incorporating spatial information into statistical methods. 相似文献
14.
THE PERFORMANCE OF LEAST SQUARES AND ROBUST REGRESSION IN THE CALIBRATION OF ANALYTICAL METHODS UNDER NON-NORMAL NOISE DISTRIBUTIONS 总被引：1，自引：0，他引：1
By means of Monte Carlo simulations a comparison has been made between ordinary least squaresregression and robust regression. The robust regression procedure is based on the Huber estimate and iscomputed by means of the iteratively reweighted least squares algorithm. The performance of bothprocedures has been evaluated for estimation of the parameters of a calibration function and fordetermination of the concentration of unknown samples. The influence of the distributionalcharacteristics skewness and kurtosis has been studied, and the number of measurements used forconstructing the calibration curve has also been taken into account, Under certain conditions robustregression offers an advantage over least squares regression. 相似文献
15.
THE KERNEL ALGORITHM FOR PLS 总被引：3，自引：0，他引：3
A fast and memory-saving PLS regression algorithm for matrices with large numbers of objects ispresented.It is called the kernel algorithm for PLS.Long(meaning having many objects,N)matricesX (N×K)and Y(N×M)are condensed into a small(K×K)square‘kernel’matrix X~TYY~TX of sizeequal to the number of X-variables.Using this kernel matrix X~TYY~TX together with the small covariancematrices X~TX(K×K),X~TY(K×M)and Y~TY(M×M),it is possible to estimate all necessaryparameters for a complete PLS regression solution with some statistical diagnostics.The newdevelopments are presented in equation form.A comparison of consumed floating point operations isgiven for the kernel and the classical PLS algorithm.As appendices,a condensed matrix algebra versionof the kernel algorithm is given together with the MATLAB code. 相似文献
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17.
RECENT DEVELOPMENTS IN MULTIVARIATE CALIBRATION 总被引：1，自引：0，他引：1
B.R.KOWALSKI M.B.SEASHOLTZ Laboratory for Chemometrics BG- University of Washington Seattle WA U.S.A. 《地理学报(英文版)》1991,(3)
With the goal of understanding global chemical processes,environmental chemists have some of the mostcomplex sample analysis problems.Multivariate calibration is a tool that can be applied successfully inmany situations where traditional univariate analyses cannot.The purpose of this paper is to reviewmultivariate calibration,with an emphasis being placed on the developments in recent years.The inverseand classical models are discussed briefly,with the main emphasis on the biased calibration methods.Principal component regression(PCR)and partial least squares(PLS)are discussed,along with methodsfor quantitative and qualitative validation of the calibration models.Non-linear PCR,non-linear PLSand locally weighted regression are presented as calibration methods for non-linear data.Finally,calibration techniques using a matrix of data per sample(second-order calibration)are discussed briefly. 相似文献
18.
Calibrations to predict crude protein (CP) and in vitro dry matter digestibility (IVDMD) in dried grasssilage from reflectance data collected at 19 wavelengths on an InfraAlyzer 400R have been developedusing stepwise multiple linear (SML) and principal component (PC) regression techniques. A directcomparison of the efficacy of each multivariate technique in this application has been possible by usingidentical calibration development and evaluation sample sets. The effect of two data transformation stepsprior to PC regression was also investigated. PC regression of raw reflectance data yielded no significantimprovement in the standard errors of prediction (SEP) for CP and IVDMD over those obtained bySMLR, viz. 0.61 vs 0.63 and 2.9 vs 3.0 respectively. Computation time for development and evaluation ofthe PC regression equation was less than for selection of the best SMLR equation, and PCR equationsmay be more robust. Data transformation to reduce granularity effects prior to PCR did not produce anyimprovement in predictive accuracy for either IVDMD or CP. 相似文献
19.
Images can contain chemical information and many chemical methods can generate image data. For anefficient extraction of chemical data from images, data analysis techniques are necessary, It is a greatadvantage to be able to work on multivariate images. Many imaging techniques allow the extraction ofchemical information. Inorganic analytical chemistry seems to have the longest tradition here, butorganic chemistry and biochemistry may soon be catching up. Also large data arrays from non-imagingtechniques can be combined with image analysis in a useful way, provided certain conditions are fulfilled. 相似文献
20.
FOREST C.GARNER MARTIN A.STAPANIAN KIRK E.FITZGERALD Lockheed Engineering Sciences Co. E.Flamingo R Las Vegas NV U.S.A. 《地理学报(英文版)》1991,(3)
Multivariate outliers in environmental data sets are often caused by atypical measurement error in a singlevariable.From a quality assurance perspective it is important to identify these variables efficiently so thatcorrective actions may be performed.We demonstrate a procedure for using two multivariate tests toidentify which variable‘caused’each outlier.The procedure is tested with simulated data sets that havethe same correlation structure as selected water chemistry variables from a survey of lakes in the WesternUnited States.The success rates are evaluated for three of the variables for sample sizes of 50 and 100,significance levels of 0.01 and 0.05 and various amounts of mean shift.The procedure works best forhighly correlated variables. 相似文献