| A TEST OF SIGNIFICANCE FOR PARTIAL LEAST SQUARES REGRESSION |
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| 作者姓名： | IAN N. WAKELING JEFF J. MORRIS AFRC Institute of Food Research Earley Gate Whiteknights Ro Reading RG EF U.K.Zeneca Pharmaceuticals Mereside Alderley Park Macclesfiel Cheshire SK TG U.K. |
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| 作者单位： | IAN N. WAKELING;JEFF J. MORRIS*，AFRC Institute of Food Research，Earley Gate，Whiteknights Road，Reading RG6 2EF，U.K.Zeneca Pharmaceuticals，Mereside，Alderley Park，Macclesfield，Cheshire SK10 4TG，U.K. |
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| 摘 要： | Partial least squares (PLS) regression is a commonly used statistical technique for performingmultivariate calibration, especially in situations where there are more variables than samples. Choosingthe number of factors to include in a model is a decision that all users of PLS must make, but iscomplicated by the large number of empirical tests available. In most instances predictive ability is themost desired property of a PLS model and so interest has centred on making this choice based on aninternal validation process. A popular approach is the calculation of a cross-validated r~2 to gauge howmuch variance in the dependent variable can be explained from leave-one-out predictions. Using MonteCarlo simulations for different sizes of data set, the influence of chance effects on the cross-validationprocess is investigated. The results are presented as tables of critical values which are compared againstthe values of cross-validated r~2 obtained from the user's own data set. This gives a formal test forpredictive ability of a PLS model with a given number of dimensions.
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A TEST OF SIGNIFICANCE FOR PARTIAL LEAST SQUARES REGRESSION |
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| IAN N. WAKELING,JEFF J. MORRIS,AFRC Institute of Food Research,Earley Gate,Whiteknights Ro,Reading RG EF,U.K.Zeneca Pharmaceuticals,Mereside,Alderley Park,Macclesfiel,Cheshire SK TG,U.K..A TEST OF SIGNIFICANCE FOR PARTIAL LEAST SQUARES REGRESSION[J].Journal of Geographical Sciences,1993(4). |
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| Authors: | IAN N WAKELING JEFF J MORRIS AFRC Institute of Food Research Earley Gate Whiteknights Roa Reading RG EF UKZeneca Pharmaceuticals Mereside Alderley Park Macclesfiel Cheshire SK TG UK |
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| Abstract: | Partial least squares (PLS) regression is a commonly used statistical technique for performing multivariate calibration, especially in situations where there are more variables than samples. Choosing the number of factors to include in a model is a decision that all users of PLS must make, but is complicated by the large number of empirical tests available. In most instances predictive ability is the most desired property of a PLS model and so interest has centred on making this choice based on an internal validation process. A popular approach is the calculation of a cross-validated r~2 to gauge how much variance in the dependent variable can be explained from leave-one-out predictions. Using Monte Carlo simulations for different sizes of data set, the influence of chance effects on the cross-validation process is investigated. The results are presented as tables of critical values which are compared against the values of cross-validated r~2 obtained from the user's own data set. This gives a formal test for predictive ability of a PLS model with a given number of dimensions. |
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| Keywords: | Partial least squares Monte Carlo methods Cross validation |
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