11,211
Views
22
CrossRef citations to date
0
Altmetric
Research article

The principal problem with principal components regression

& | (Reviewing editor)
Article: 1622190 | Received 07 Apr 2018, Published online: 31 May 2019

References

  • Alibuhtto, M. C., & Peiris, T. S. G. (2015). Principal component regression for solving multicollinearity problem. 5th International Symposium. Southeastern University of Sri Lanka, Sri Lanka.
  • Athey, S. (2018). The impact of machine learning on economics. In A. Agrawal, J. Gans, & A. Goldfarb (Eds.), The economics of artificial intelligence: An agenda (pp. 507-547). University of Chicago Press.
  • Bitetto, A., Mangone, A., Mininni, R. M., & Giannossa, L. C. (2016). A nonlinear principal component analysis to study archeometric data. Journal of Chemometrics, 30(7), 405–11. doi:10.1002/cem.2807
  • Chen, K., Zhang, X., Petersen, A., & Müller., H.-G. (2017). Quantifying infinite-dimensional data: Functional data analysis in action. Statistics in Biosciences, 9(2), 582–604. doi:10.1007/s12561-015-9137-5
  • Cowe, I. A., & McNicol, J. W. (1985). The use of principal components in the analysis of near-infrared spectra. Applied Spectroscopy, 39(2), 257–266. doi:10.1366/0003702854248944
  • Deng, X., Tian, X., & Chen, S. (2013). Modified Kernel principal component analysis based on local structure analysis and its application to nonlinear process fault diagnosis. Chemometrics and Intelligent Laboratory Systems, 127, 195–209. doi:10.1016/j.chemolab.2013.07.001
  • Dray, S. (2008). On the number of principal components: A test of dimensionality based on measurements of similarity between matrices. Computational Statistics and Data Analysis, 52, 2228–2237. doi:10.1016/j.csda.2007.07.015
  • Garcia, C. B., Garcia, J., & Soto, J. (2011). The raise method: An alternative procedure to estimate the parameters in presence of collinearity. Quality and Quantity, 45, 403–423. doi:10.1007/s11135-009-9305-0
  • George, G., Osinga, E. C., Lavie, D., & Scott, B. A. (2016). Big data and data science methods for management research: From the editors. Academy of Management Journal, 59(5), 1493–1507. doi:10.5465/amj.2016.4005
  • Gimenez, Y., & Giussani, G. (2018). Searching for the core variables in principal components analysis. Brazilian Journal of Probability and Statistics, 32(4), 730–754. doi:10.1214/17-BJPS361
  • Hadi, A. S., & Ling, R. F. (1998). Some cautionary notes on the use of principal components regression. The American Statistician, 52(1), 15–19.
  • Hocking, R. R. (1976). The analysis and selection of variables in linear regression. Biometrics, 32, 1–49. doi:10.2307/2529336
  • Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology, 24, 417–441 and 498–520. doi:10.1037/h0071325
  • Hotelling, H. (1936). Relations between two sets of variates. Biometrika, 28, 321–377. doi:10.1093/biomet/28.3-4.321
  • Hotelling, H. (1957). The relations of the newer multivariate statistical methods to factor analysis. British Journal of Statistical Psychology, 10, (2), 69–79. doi:10.1111/j.2044-8317.1957.tb00179.x
  • Jensen, D. R., & Ramirez, D. E. (2010). Surrogate models in ill-conditioned systems. Journal of Statistical Planning and Inference, 140, 2069–2077. doi:10.1016/j.jspi.2010.02.001
  • Jolliffe, I. T., & Cadima, J. (2016). Principal component analysis: A review and recent developments. Philosophical Transactions of the Royal Society A, Mathematical, Physical, and Engineering Sciences, 374(2065), 20150202. doi:10.1098/rsta.2015.0202
  • Kendall, M. G. (1957). A course in multivariate analysis. Griffin: London.
  • Kudyba, S. (2014). Big Data, mining, and analytics: Components of strategic decision making. New York: Auerbach.
  • Liu, X., Li, K., McAfee, M., & Deng, J. (2012). Application of nonlinear PCA for fault detection in polymer extrusion processes. Neural Computing and Applications, 21(6), 1141–1148. doi:10.1007/s00521-011-0581-y
  • Mansfield, E. R., Webster, J. T., & Gunst, R. F. (1977). An analytic variable selection technique for principal component regression. Applied Statistics, 26(1), 34–40. doi:10.2307/2346865
  • Mosteller, F., & Tukey, J. W. (1977). Data analysis and regression: A second course in statistics. Reading, Mass.: Addison-Wesley.
  • Pearson, K. (1901). On lines and planes of closest fit to systems of points in space. Philosophical Magazine, 2(11), 559–572. doi:10.1080/14786440109462720
  • Price, A. L., Patterson, N. J., Plenge, R. M., Weinblatt, M. E., Shadick, N. A., & Reich, D. (2006). Principal components analysis corrects for stratification in genome-wide association studies. Nature Genetics, 38, 904–909. doi:10.1038/ng1847
  • Qi, D., & Roe, B. E. (2015). Household food waste: Multivariate regression and principal components analyses of awareness and attitudes among U.S. consumers. PLoS One, 11(7), e0159250. doi:10.1371/journal.pone.0159250
  • Sabharwal, C. L., & Anjum, B. (2016). Data reduction and regression using principal component analysis in qualitative spatial reasoning and health informatics. Polibits, 53, 31–42. doi:10.17562/PB-53-3
  • Sainani, K. L. (2014). Introduction to principal components analysis. PM&R, 6(3), 275–278. doi:10.1016/j.pmrj.2014.02.001
  • Sakr, S., & Gaber, M. M. (Eds.). (2014). Large scale and Big Data: Processing and management. London: CRC Press.
  • Sanguansat, P. (Ed.). (2012). Principal component analysis – Engineering applications. Rijeka, Croatia: InTech.
  • Stock, J. H., & Watson, M. W. (2002). Forecasting using principal components from a large number of predictors. Journal of the American Statistical Association, 97(460), 1167–1179. doi:10.1198/016214502388618960
  • Taylor, J., & Tibshirani, R. J. (2015). Statistical learning and selective inference. Proceedings of the National Academy of Sciences, 112, 7629–7634. doi:10.1073/pnas.1507583112
  • Verhoef, P. C., Kooge, E., & Walk, N. (2016). Creating value with Big Data analytics: Making smarter marketing decisions. Abingdon, UK: Routledge.
  • Yu, H., & Khan, F. (2017). Improved latent variable models for nonlinear and dynamic process monitoring. Chemical Engineering Science, 168, 325–338. doi:10.1016/j.ces.2017.04.048
  • Yuan, X., Ye, L., Bao, L., Ge, Z., & Song, Z. (2015). Nonlinear feature extraction for soft sensor modeling based on weighted probabilistic PCA. Chemometrics & Intelligent Laboratory Systems, 147, 167–175. doi:10.1016/j.chemolab.2015.08.014