Some Cautionary Notes on the Use of Principal Components Regression

Hadi, Ali S.; Ling, Robert F.

doi:10.2307/2685559

Cited by 65 publications

(67 citation statements)

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“…So, the contribution of each PC to the regression sum of squares is also important for selection of PCs (Hadi and Ling, 1998). The findings of Jolliffe (1982) and Hadi and Ling (1998) provide a justification for using non-primary PCs, (e.g., of second and higher order) in our regression, given that correlations with temperature may be overpowered by affects from precipitation in our study area (E. R. Cook, personal communication, 2011).…”

Section: March-april Temperature Reconstructionmentioning

confidence: 99%

“…The last two PCs contain a too-small part of the total variance to be used in the regressions. However, even if Jolliffe (1982) and Hadi and Ling (1998) claimed that certain PCs with small eigenvalues (even the last one), which are commonly ignored by principal components regression methodology, may be related to the independent variable, we must be cautious with that because they may be much more dominated by noise than the first ones. So, the contribution of each PC to the regression sum of squares is also important for selection of PCs (Hadi and Ling, 1998).…”

Section: March-april Temperature Reconstructionmentioning

confidence: 99%

“…However, even if Jolliffe (1982) and Hadi and Ling (1998) claimed that certain PCs with small eigenvalues (even the last one), which are commonly ignored by principal components regression methodology, may be related to the independent variable, we must be cautious with that because they may be much more dominated by noise than the first ones. So, the contribution of each PC to the regression sum of squares is also important for selection of PCs (Hadi and Ling, 1998). The findings of Jolliffe (1982) and Hadi and Ling (1998) provide a justification for using non-primary PCs, (e.g., of second and higher order) in our regression, given that correlations with temperature may be overpowered by affects from precipitation in our study area (E. R. Cook, personal communication, 2011).…”

Section: March-april Temperature Reconstructionmentioning

confidence: 99%

See 2 more Smart Citations

Spring temperature variability over Turkey since 1800 CE reconstructed from a broad network of tree-ring data

et al. 2017

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Abstract. The meteorological observational period in Turkey, which starts ca. 1930 CE, is too short for understanding long-term climatic variability. Tree rings have been used intensively as proxy records to understand summer precipitation history of the region, primarily because they have a dominant precipitation signal. Yet, the historical context of temperature variability is unclear. Here, we used higher-order principle components of a network of 23 tree-ring chronologies to provide a high-resolution spring (March-April) temperature reconstruction over Turkey during the period 1800-2002. The reconstruction model accounted for 67 % (Adj. R 2 = 0.64, p < 0.0001) of the instrumental temperature variance over the full calibration period . The reconstruction is punctuated by a temperature increase during the 20th century; yet extreme cold and warm events during the 19th century seem to eclipse conditions during the 20th century. We found significant correlations between our March-April spring temperature reconstruction and existing gridded spring temperature reconstructions for Europe over Turkey and southeastern Europe. Moreover, the precipitation signal obtained from the tree-ring network (first principle component) showed highly significant correlations with gridded summer drought index reconstruction over Turkey and Mediterranean countries. Our results showed that, beside the dominant precipitation signal, a temperature signal can be extracted from tree-ring series and they can be useful proxies in reconstructing past temperature variability.

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Section: March-april Temperature Reconstructionmentioning

confidence: 99%

Section: March-april Temperature Reconstructionmentioning

confidence: 99%

Section: March-april Temperature Reconstructionmentioning

confidence: 99%

See 1 more Smart Citation

Spring temperature variability over Turkey since 1800 CE reconstructed from a broad network of tree-ring data

et al. 2017

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“…10,20 Another commonly recommended method by statistical textbooks, though relatively unknown to most dental researchers, is ridge regression. 21 By adding small values to the explanatory variables, this approach provides biased but more stable estimates of regression coefficients.…”

Section: Principal Component Analysis and Ridge Regressionmentioning

confidence: 99%

Problems of correlations between explanatory variables in multiple regression analyses in the dental literature

et al. 2005

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Multivariable analysis is a widely used statistical methodology for investigating associations amongst clinical variables. However, the problems of collinearity and multicollinearity, which can give rise to spurious results, have in the past frequently been disregarded in dental research. This article illustrates and explains the problems which may be encountered, in the hope of increasing awareness and understanding of these issues, thereby improving the quality of the statistical analyses undertaken in dental research. Three examples from different clinical dental specialities are used to demonstrate how to diagnose the problem of collinearity/multicollinearity in multiple regression analyses and to illustrate how collinearity/multicollinearity can seriously distort the model development process. Lack of awareness of these problems can give rise to misleading results and erroneous interpretations. Multivariable analysis is a useful tool for dental research, though only if its users thoroughly understand the assumptions and limitations of these methods. It would benefit evidencebased dentistry enormously if researchers were more aware of both the complexities involved in multiple regression when using these methods and of the need for expert statistical consultation in developing study design and selecting appropriate statistical methodologies.

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“…This version of DBR amounts to performing a Principal Components Regression (PCR) (see, e.g., Jolliffe 2002). One of the pitfalls of PCR (Cuadras 1993, 1998, Hadi & Ling 1998is the fact that the first few Principal Axes, with a greater variance, are not necesarily highly correlated with the response y . Furthermore, diagonalization of large n × n matrices presents substantial computational problems.…”

Section: Distance Based Regressionmentioning

confidence: 99%

Implementing PLS for distance-based regression: computational issues

Val

Grané

Fortiana

et al. 2007

Computational Statistics

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Distance-based regression allows for a neat implementation of the Partial Least Squares recurrence. In this paper we address practical issues arising when dealing with moderately large datasets (n ~ 10 4 ) such as those typical of automobile insurance premium calculations.Keywords: Distance-based prediction; PLS regression; Large datasets; Automobile insurance data.(1) Dept. SummaryDistance-based regression allows for a neat implementation of the Partial Least Squares recurrence. In this paper we address practical issues arising when dealing with moderately large datasets (n ∼ 10 4 ) such as those typical of automobile insurance premium calculations.

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Some Cautionary Notes on the Use of Principal Components Regression

Cited by 65 publications

References 0 publications

Spring temperature variability over Turkey since 1800 CE reconstructed from a broad network of tree-ring data

Spring temperature variability over Turkey since 1800 CE reconstructed from a broad network of tree-ring data

Problems of correlations between explanatory variables in multiple regression analyses in the dental literature

Implementing PLS for distance-based regression: computational issues

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Some Cautionary Notes on the Use of Principal Components Regression

Cited by 65 publications

References 0 publications

Spring temperature variability over Turkey since 1800 CE reconstructed from a broad network of tree-ring data

Spring temperature variability over Turkey since 1800 CE reconstructed from a broad network of tree-ring data

Problems of correlations between explanatory variables in multiple regression analyses in the dental literature

Implementing PLS for distance-based regression: computational issues

Contact Info

Product

Resources

About

Spring temperature variability over Turkey since 1800 CE reconstructed from a broad network of tree-ring data

Spring temperature variability over Turkey since 1800 CE reconstructed from a broad network of tree-ring data